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Time-Dependent Confounding in Antihypertensive Drug Studies


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TIME-DEPENDENT CONFOUNDING IN ANTIHYPERTENSIVE DRUG STUDIES By TOBIAS GERHARD A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2007 1

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Copyright 2007 by Tobias Gerhard 2

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To my parents, Gertrud and Albrecht Gerhard 3

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ACKNOWLEDGMENTS I want to thank my adviser, Almut Winterstein, for her contin uous support. She has been a terrific mentor and has never stopped challenging me to do my best. I would also like to thank my supervisory committee members Julie John son, Abraham Hartzema, Carl Pepine, and Jonathan Shuster for their expe rtise, advice, and encouragemen t. I thank Yan Gong and Rhonda Cooper-DeHoff for their help with the INVEST dataset. Finally, I thank my fellow graduate students for their support and friendship. 4

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TABLE OF CONTENTS page ACKNOWLEDGMENTS...............................................................................................................4 LIST OF TABLES................................................................................................................. ..........7 LIST OF FIGURES.........................................................................................................................8 ABSTRACT...................................................................................................................................10 1 INTRODUCTION................................................................................................................. .12 Background.............................................................................................................................12 Need for Study........................................................................................................................13 Association of a Surrogate with Clinical Outcome: Surrogates are Time-Dependent Variables......................................................................................................................13 Association of a Surrogate with Clin ical Outcome: Confounding by Treatment...........14 Estimation of Drug Effectiveness in Observational Research........................................15 Purpose of the Study........................................................................................................... ....16 Research Questions and Hypotheses......................................................................................18 2 LITERATURE REVIEW.......................................................................................................21 Surrogates...............................................................................................................................21 The Epidemiology of Blood Pressure C ontrol and Cardiovascular Outcomes......................23 Time-Dependent Confounding in Pharmacoepidemiology....................................................26 Marginal Structural Models.............................................................................................27 3 METHODS...................................................................................................................... .......31 The INVEST and the INVEST Dataset..................................................................................31 Descriptive Statistics......................................................................................................... .....33 Blood Pressure and CV Outcomes.........................................................................................33 Incidence Rates by Categories of Systolic Blood Pressure.............................................33 Cox Proportional Hazards Models..................................................................................34 Marginal Structural Cox Model.......................................................................................37 Antihypertensive Treatment and CV Outcomes.....................................................................40 Marginal Structural Cox Models.....................................................................................40 Cox Proportional Hazards Models..................................................................................41 4 RESULTS...................................................................................................................... .........44 Descriptives................................................................................................................... .........44 Blood Pressure.................................................................................................................45 Antihypertensive Drugs...................................................................................................46 Primary Outcome Events.................................................................................................48 5

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Hazard Ratios..........................................................................................................................48 Baseline SBP Model........................................................................................................49 Average SBP Model........................................................................................................49 Average SBP Weighted by Follow-up Time Model.......................................................50 Time-Dependent SBP Models.........................................................................................50 Updated Mean SBP Model..............................................................................................51 Incidence.................................................................................................................................52 Comparisons.................................................................................................................... .......53 Average SBP and Bias............................................................................................................53 Marginal Structural Models....................................................................................................59 Effect of Systolic Bl ood Pressure Control..............................................................................60 Effects of Antihypertensive Drugs.........................................................................................60 5 DISCUSSION................................................................................................................... ......78 Descriptive Analyses: Antihypertensive Treatment and SBP in the INVEST.......................78 Operationalization of SBP......................................................................................................80 Modeling Assumptions....................................................................................................81 Baseline SBP Model........................................................................................................83 Average SBP Models......................................................................................................84 Short Term SBP Models (Time-Dependent)...................................................................85 Model Selection...............................................................................................................86 Time-dependent Confounding................................................................................................89 Limitations.................................................................................................................... ..........93 Future Research......................................................................................................................96 Summary and Conclusions.....................................................................................................97 LIST OF REFERENCES...............................................................................................................99 BIOGRAPHICAL SKETCH.......................................................................................................103 6

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LIST OF TABLES Table page 4-1 Composition of the INVEST Cohort at Baseline...............................................................62 4-2 Comparison of models....................................................................................................... 63 4-3 Simulation of six scenarios using average over follow-up................................................64 4-4 Simulation of six scenarios using updated mean...............................................................65 4-5 Inverse probability of treatment weighted es timates for the causal effect of controlled SBP on primary INVEST primary outcome event............................................................66 4-6 Inverse probability of treatment weighted estimates for the effect of receiving more than two total antihypertensive drugs on primary INVEST primary outcome event........66 4-7 Inverse probability of treatment weighted estimates for the causal effect of receiving various numbers of total an tihypertensive drugs on INVE ST primary outcome event.....66 7

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LIST OF FIGURES Figure page 2-1 Prentice criteria satisfied................................................................................................ ....28 2-2 The surrogate is correlated with the clinical outcome but captures no treatment effect....28 2-3 Net effect of treatment is only partially captured by the surrogate....................................29 2-4 Mortality from stroke (A) and ischemic heart disease (B) in each decade of age versus usual systolic blood pressu re at the start of that decade.........................................29 2-5 Algorithm for the treatment of hypertension.....................................................................30 2-6 Directed acyclic graph for time-dependent confounding...................................................30 3-1 Treatment strategies in the INVEST..................................................................................42 3-2 Operationalization of SBP: Examples for a sample patient...............................................43 4-1 Patients remaining in the study at each visit......................................................................67 4-2 Mean systolic blood pressure over follow-up (observed vs. imputed data)......................67 4-3 Percentage of patients within each SBP category over follow-up.....................................68 4-4 Percentage of patients within each SBP category who were not within the same SBP category at the prior visit...................................................................................................6 8 4-5 Number of total antihypertensive dr ugs and antihypertensive study drugs over follow-up............................................................................................................................69 4-6 Percentage of patients on each individual study drug over follow-up...............................69 4-7 Number of INVEST st udy drugs over follow-up..............................................................70 4-8 Number of total antihyper tensive drugs over follow-up....................................................70 4-9 Percentage of patients on a specific number of antihypertensive study drugs who were not on the same number of antihype rtensive drugs at the prior visit........................71 4-10 Percentage of patients on a specific number of antihype rtensive drugs who were not on the same number of antihyperten sive drugs at the prior visit.......................................71 4-11 Cumulative incidence of the pr imary outcome event over follow-up...............................72 4-12 Hazard ratios for an INVEST primary outcome event by categories of baseline systolic blood pressure.......................................................................................................72 8

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4-13 Hazard ratios for an INVEST primary outcome event by categories of average systolic blood pressure over follow-up..............................................................................73 4-14 Hazard ratios for an INVEST primary outcome event by categories of average systolic blood pressure over follow-up, weighted by time of follow-up...........................73 4-15 Hazard ratios for an INVEST primary out come event by categories of systolic blood pressure (updated; carried forw ard from last observed visit)............................................74 4-16 Hazard ratios for an INVEST primary out come event by categories of systolic blood pressure (updated; from next observed visit).....................................................................74 4-17 Hazard ratios for an INVEST primary out come event by categories of updated mean systolic blood pressure (time-dependent; updated at each visit).......................................75 4-18 Crude incidence of primary outcome events by SBP category..........................................75 4-19 Adjusted incidence of primary outcome events for White, female, US patients between the ages of 60 to 70 years by SBP category........................................................76 4-20 Bias of outcome event hazard ratios obtained average SBP compared to updated mean SBP...........................................................................................................................76 4-21 Proportion of events within category of average SBP by number of observed visits at the occurrence of the event................................................................................................77 4-22 Bias and timing of events by category of SBP..................................................................77 9

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Abstract of Dissertation Pres ented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy TIME-DEPENDENT CONFOUNDING IN ANTIHYPERTENSIVE DRUG STUDIES By Tobias Gerhard May 2007 Chair: Almut Winterstein Major Department: Pharmacy Health Care Administration Accurate estimation of blood pressure (BP) e ffects on the risk for cardiovascular outcomes has important implications for the treatm ent of hypertension. The extent to which operationalization of BP affects these risk estimates is unclear. Furthermore, the presence of a time-dependent confounder may lead to biased estimates for the risk of BP on cardiovascular outcomes and can not be adjusted for by standard statistical methods. The same bias may occur in the estimation of drug effects in the presence of time-dependent confounding by BP. To examine the impact of systolic blood pressure (SBP) opera tionalization on risk estimates for myocardial infarction, stroke, or all cause death (primary outcome) we estimated the hazard ratios of 7 SBP categories for six different Cox proportional hazards models in patients of the International Verapamil-Trandolapril Study (INVEST), a randomized study of 22,576 hypertensive coronary artery disease patients. To test for the presence of time-dependent confounding by antihypertensive treatment (or, al ternatively, SBP control), we estimated both standard Cox models and marginal structural Cox models (causal models) for the effect of SBP control (or, respectively, aggres sive antihypertensive treatment), adjusting for the number of concurrently used antihypertensi ve drugs (or, respectively, SPB). 10

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Estimates of the effect of SBP on primary outcome vary significantly depending on the method of SBP operationalization. Some of the operationalization approaches, most notably the use of average SBP, may lead to systematically biased estimates. Causal analyses suggest that time-dependent confounding by SBP may bias estimates of treatment effect s (Hazard ratio [HR] standard model: 0.96; 95% confid ence interval [CI] 0.87-1.07; HR marginal structural model: 0.81; 95% CI 0.71-0.92), but provides no evidence of time-dependent confounding by treatment in the estimation of risk associated with SBP control (HR standard model: 0.54; 95% CI 0.480.60; HR marginal structural model: 0.55; 95% CI 0.50-0.61). Our results suggest that time-dependent c onfounding by SBP, leads to an underestimation of the effectiveness of antihypertensive treatment. No evidence for time-dependent confounding of the effect of SBP control by antihyper tensive treatment was found, implying, that antihypertensive treatment as modeled in our anal ysis does not affect cardiovascular outcomes in pathways other than through SBP. 11

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CHAPTER 1 INTRODUCTION Background In 2005, chronic diseases, such as cardiovasc ular disease, diabet es, or cancer were estimated to be responsible for 60% of the total global mortality (35 million deaths).1 In the United States alone, chronic diseases affect the lives of over 90 million Americans and account for 70% of all deaths.2 Treatment of patients suffering from chronic diseases occurs over extended periods of time, frequently involves multi -drug regimens, and often relies on surrogates (i.e., intermediate markers of hea lth) to evaluate the effectiveness of treatment in the individual patient. Clinically relevant outcomes of chronic diseases such as my ocardial infarction, stroke, or death often occur only in a proporti on of affected patients and often after years or even decades of the disease. As a consequence, immediatel y observable surrogate measures such as blood pressure, low density lipoprotein (LDL) level, or CD4 cell count (a marker of circulating T helper cells) play an important role in the treat ment of patients suffering from chronic disease as they predict the risk for manifestation of a dverse outcomes. In addition, surrogate measures typically facilitate shorter clinical trials with smaller sample sizes. Accurate estimation of the association between the surrogate measure and the risk of clinical ly relevant outcomes over time is a prerequisite for the informed use of a surrogate measure in treatment and research. Furthermore, to avoid confounding, the influence of the surrogate has to be carefully considered in the planning and analysis of observational stud ies of drug effects, because surrogate measures play an important role in the determination and management of drug therapy. 12

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Need for Study Association of a Surrogate with Clinical Outcome: Surrogates are Time-Dependent Variables Surrogate measures are rarely constant over time. Disease progression, life-style modification, pharmacologic and nonpharmacologic tr eatments may all contribute to changes in a surrogate measure over time. Thus, any analysis that aims to quantif y an association of a surrogate with a relevant clini cal outcome (i.e., morbidity or mo rtality) over a prolonged period of time and uses a single, fixed value to represen t the true surrogate valu es over the course of time will lead to misclassification. Inclusion of multiple values of the surrogate over time (i.e., its inclusion as a time-depende nt variable) can significantl y reduce misclassification bias. However, it is often unclear to what extend bias introduced by such misclassification will alter estimates of the effect of a su rrogate on a clinical outcome in practice. Since, time-dependent modeling of surrogates involves more complex statistical methods and requires regularly measured data-points for the surrogate over time, study results are frequently based on single, fixed surrogate values (such as baseline, or average over follow-up). Another problem closely related to the time-dependent nature of surrogate measures is the potential lag time of a surrogates effect on the clinical outcome. Depending on the pathophysiological mechanism through which the surrogate affects the clinical outcome, associations between the surrogate and the clinical outcome may be immediate or delayed. This has profound consequences for analysis because it determines whether current or historical values (or a combination of the tw o) of the surrogate should be used to model the risk for the clinical outcome (e.g., it would affect to what extend BP history, as opposed to current BP values, should be included in risk models for cardiovascular disease). 13

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Association of a Surrogate with Clinical Outcome: Confounding by Treatment Surrogate measures are routinely used to gui de clinical practice. Physicians will for example, increase the dose of an antihypertensive medication or add an additional agent, if a patients blood pressure is considered uncontrolle d, and patients with elevated cholesterol may be treated with increasing doses of statins until recommended LDL leve ls are achieved. The validity of this approach relies on unbiased estimation of the causa l effect of the surrogate on the clinical outcome. Severa l factors make this estimation diffi cult. As mentioned above, surrogate measures are not constant over time, and thus, es timation of the causal eff ect of the surrogate on clinical outcome needs to account for these tim e-dependent changes. In addition, surrogate measures are rarely observable in untreated patients, because changes in a surrogate are expected to result in changes in clinical outcomes, and thus once identified, patients with elevated values of a surrogate are routinely rece iving treatment. This treatment may confound the estimation of a causal effect between surrogate a nd clinical outcome in a treated cohort. Specifically, only if the effect of a given drug is entirely mediated by th e surrogate, which rarely is the case in practice, will an estimate of the causal effect of the surrogate on a clinical outcome in the presence of the drug be unconfounded. If a drug affects clinical outcome in parts through pathways different from the surrogate measure of interest, the dr ug acts as a confounder and needs to be controlled for in any analysis that aims to estimate the causa l effect of the surrogate on the clinical outcome. However, since drug use is commonly affected by a prior value of the surrogate, and thus is simultaneously a direct cause for subsequent values and a direct result of prior values of the surrogate, assumptions for standa rd methods of confounder adjustme nts, such as inclusion in regression models are violated, and such methods fail to produ ce unbiased, causally interpretable estimates.3 14

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In summary, the evaluation of the causal eff ect of surrogate measures must incorporate changes of the surrogate observed over time and account for time-dependent confounding by treatment. To the best of our knowledge, tim e-dependent confounding by treatment has never been accounted for in the anal ysis of surrogate measures. Estimation of Drug Effectiven ess in Observational Research Pharmacoepidemiological research, particular ly when it relates to drugs used in the treatment of chronic diseases, commonly deals with the risks a nd benefits of drugs used over prolonged periods of time. More often than not, treat ment will not be stable over time but rather will doses be adjusted and drugs added or removed from the treatment regimen. Such adjustments of therapy over time do not occur at random and thus, control of factors that influence both treatment changes and treatmen t outcome (i.e., confounders) is necessary to obtain unbiased estimates of risks and benefits for the various tr eatment choices. However, as detailed in the previous section, when factors that predict changes in treatment are also affected by the change in the treatment regimen, as is common for surrogate measures of chronic disease states (e.g., BP, HDL/LDL, HbA1C), assumptions for standard methods of confounder adjustments are violated and these methods fa il to produce unbiased es timates. Conventional evaluation of drug effects in the presence of a time-dependent confounder therefore may produce biased estimates. For a number of reasons evidence from random ized clinical trials alone is often insufficient to provide the evidence needed for optimal selection of individual treatment strategies. First, randomized clinical trials ar e typically conducted over short periods of time and take place in narrow study populations defined by explicit inclusion and exclusion criteria. In contrast, drug use in clinical practice will occur over extended periods of time in less homogeneous populations. Second, and more importantly in the context of this study, the 15

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comparisons made in clinical trials are lim ited, frequently involving comparisons of single therapeutic agents with each ot her or placebo. In practice however, many chronic disease patients will require a combination of two or more drugs to be ad equately treated. While clinical trials comparing specific combination therapies or flexible treatment strategies are possible, and have been conducted, the number of possible drug (and dose) combinations will likely exceed what can be feasibly tested in a clinical trial setting. Thus, observational pharmacoepidemiological re search, which is able to explore the broad spectrum of treatments occurring in practi ce over extended periods of time, could play an important role in evaluating the long-term e ffectiveness of complex multi-drug strategies. However, careful control of treatment decisions that determine the exposure of individual patients to specific drug regimens over the course of a study and th at may lead to time-dependent confounding is necessary to avoid biased estimates of regimen effectiveness. Purpose of the Study Our study used a dataset from a large international antihypert ensive trial to estimate the association of systolic blood pressure (sur rogate measure) over time on the risk for cardiovascular morbidity and mort ality (clinical outcome) and to assess whether timedependent changes in treatment confound this association. In addition, this study will evaluate the effects of treatment on clinical outcome, when initiation of treatment is partly conditional on inadequate response to prior treatment and thus, conf ounded by a surrogate measure. Our study will illustrate problems arising from the presence of time-dependent conf ounding in such a setting and use newly developed statistical methods to obtain estimates of unbiased effects for both the surrogate and treatment on clin ical outcome in the presence of time-dependent confounding. Specifically, this study will describe blood pre ssure and antihypertensive drug use patterns for patients participating in the Interna tional Verapamil SR/Tra ndolapril Study (INVEST)4, 5 over 16

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the time of follow-up. It will then evaluate how syst olic blood pressure over time associates with the incidence of primary outcome events (nonfatal myocardial infarction, nonfatal stroke, or all cause death) and compare this time-dependent appr oach to analytic approaches that use single, fixed SBP estimates (e.g., baseline SBP, averag e SBP over treatment period). Using marginal structural Cox models, the present study will then assess whether time-dependent treatment with antihypertensive drugs confounds the association of blood pressu re control (SBP <140 mm Hg versus 140 mm Hg) with clinical outcome and to what extend failure to consider this in traditional methods biases these estimates. Last ly, adjusting for SBP control over time using marginal structural Cox models, this study will derive an unbiased estimate for the effect of antihypertensive therapy (aggressive versus standard antihypertensive therapy) on the clinical outcome. Of note, the necessity to dichotomize the independent variables of interest (SBP control, aggressive antihyperten sive therapy) is a limitation i nherent in the use of current marginal structural models and will likely produ ce estimates of association that are of limited clinical utility. More complex and specific comparisons between individual drug combinations or use of multiple BP categories may be possible and should be addressed in future research. The present study will use hypertension to il lustrate the aforementioned problems arising from timedependent confounding when treatm ent initiation and choice are a ffected by the prior surrogate and the surrogate lies on the hypothesized pathwa y through which the treatment affects the risk for the clinical outcome. Blood pressure is an im portant and widely used surrogate measure that plays an essential role in the selection and management of antihypertensive treatment and is likely to be the major pathway through which anti hypertensive drugs affect the risk of clinical outcome. Causal methods such as marginal structural models may indirectly contribute to better 17

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answer the question to which extent the eff ects of specific antihypertensive drugs and drug classes are mediated by blood pressure and may ultimately contribute to the identification of optimized combination therapies. The INVEST cohort provides the opportunity to investigate the independent effects of antihypertensive drug use and a surrogate meas ure (blood pressure) on a clinical outcome (INVEST primary outcome) in a rich and valid ated clinical dataset with independently adjudicated outcomes. Although INVEST is a ra ndomized controlled trial, evaluation of individual steps of the treatment strategies negates randomization and thus, requires an epidemiologic analysis approach similar to an observational study. Its larg e sample size and high level of data quality make the INVEST an appr opriate setting for the si multaneous evaluation of time-dependent treatment and time-dependent surrogate measure. Research Questions and Hypotheses The first research question aims to evalua te whether the ability to predict adverse cardiovascular outcomes in the INVEST is increa sed when blood pressure is operationalized as a multi-category time-dependent variable, as compared to a single, fixed estimate (such as baseline or average over follow-up). However, the estimati on of the association of systolic blood pressure presented in research question 1 does not contro l for concurrent use of antihypertensive drugs. Thus, research question 2 will estimate the effect of blood pressure control on clinical outcome over time controlling for time-dependent treat ment (operationalized as the number of antihypertensive INVEST study drugs as well as the total number of antihypertensive drugs), while research question 3 eval uates whether the concurrent use of antihypertensive drugs confounds the association of systolic blood pressu re over time with primary outcome. Lastly, the fourth and fifth research questi ons address the problem of estima ting the effectiveness of a drug or treatment strategy (in our study, aggressive versus standard an tihypertensive th erapy) in the 18

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presence of time-dependent confounding by a surr ogate measure (in our study, SBP control). The a priori significance level for all re search questions is set at 0.05. Research Question 1: Does time-dependent operationaliza tion of systolic blood pressure increase the ability to predict primary outcome events in the INVEST as compared to the use of single, fixed blood pressure values? Hypothesis for Research Question 1: The null hypothesis for rese arch question 1 is that the generalized R2 for a model that updates the systolic blood pressure at each visit is not different from models with fixed systolic blood pressure values, specifically baseline systolic blood pressure, and average syst olic blood pressure over follow-up. The alternative hypothesis is that the generalized R2 is larger. Research Question 2: In the INVEST, does systolic bl ood pressure control over follow-up affect the risk of primary outcome c ontrolling for time-dependent confounding by concurrent antihypertensive drug use? Hypothesis for Research Question 2: The null hypothesis for rese arch question 2 is that the hazard ratio for systolic blood pressure co ntrol is not significantly different from 1.0. The alternative hypothesis is that the hazard ratio is significantly different from 1.0. Research Question 3: In the INVEST, does time-dependent treatment (i.e., the number of antihypertensive INVEST study drugs as well as the total number of antihypertensive drugs) confound the effect of systolic blood pressure control over the follow-up period. Hypothesis for Research Question 3: The null hypothesis for rese arch question 3 is that the hazard ratio for SBP control obtained fr om a marginal structural Cox proportional hazards model that incorporates time-dependent treatment, is not significantly different from the hazard ratio obtained from a sta ndard time-dependent Cox proportional hazards model that does not control for treatment after baseline. Research Question 4: In the INVEST, adjusting fo r time-dependent systolic blood pressure control, is there a difference in risk of primary outcome between patients receiving aggressive antihypertensive thera py compared to standa rd antihypertensive therapy over follow-up? Hypothesis for Research Question 4: The null hypothesis for rese arch question 4 is that the hazard ratio for patients re ceiving aggressive antihypertensive therapy (three or more concurrent total antihypertensive drugs) versus standard antihypertensive therapy (less than three concurrent total antihypertensive drugs ) is not significantly different from 1.0. The alternative hypothesis is th at the hazard ratio is significantly different from 1.0. Research Question 5: In the INVEST, does time-depende nt systolic blood pressure control confound the effect of treatment (agg ressive versus standard antihypertensive therapy) over the follow-up period? 19

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Hypothesis for Research Question 5: The null hypothesis for rese arch question 5 is that the hazard ratio for patients re ceiving aggressive antihypertensive therapy (three or more total antihypertensive drugs) vers us standard antihypertensive th erapy (less than three total antihypertensive drugs) obtaine d from a marginal structur al Cox proportional hazards model that controls for time-dependent conf ounding by systolic blood pressure control, is not significantly different from the hazard ra tio obtained from a standard time-dependent Cox proportional hazards model that does not control for systolic blood pressure over follow-up. 20

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CHAPTER 2 LITERATURE REVIEW Surrogates A surrogate is defined as a la boratory measurement or physical sign used as a substitute for a clinically meaningful endpoint th at measures directly how a patien t feels, functions or survives. Changes induced by a therapy on a surrogate meas ure are expected to reflect changes in a clinically meaningful endpoint.6 Although drug therapy is ultimately aimed at affecting clinically meaningful endpoints, the use of surrogate measur es offers important advantages. When clinical endpoints are rare or manifest af ter substantial periods of time, as is often the case in chronic disease states, the use of surroga te measures allows shorter, sm aller, and less costly clinical trials, which in turn allow more rapid approval of new therapies.7-9 Patient advocacy groups, interested in the rapid availability of new and promising therapies, as well as drug manufacturers, who save costs and patent life of their products, consequently support the use of surrogates in Phase III trials. The Food and Drug Administ ration (FDA) has responded to these demands by allowing the use of surrogate measures to demons trate the efficacy of new drug products as part of its accelerated approval process for serious or life-threatening illness.10 However, due to the concern that changes in the surroga te may not translate into changes in the clinical outcome, the use of surrogates is not without controversy.9, 11-14 In addition to their function in the evaluation of new therapies, surrogate measures play an important role in the evaluation of treatment re sponse in individual patie nts and the modification of individual pharmacotherapy, often following gui delines that recommend treatment towards specific target levels of the surrogate measure. However, the use of surrogate measures is problematic when a treatment also affects the clinical endpoints in ways not mediated by the surrogate, since such effects are not captured by the observed changes in the surrogate. Prentice 21

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formalized the definition of a valid surrogate measure by requiring two sufficient conditions, (1) the surrogate must correlate with the true clin ical endpoint, and (2) the surrogate must fully capture the treatments net effect (the aggregate effect accounting for all causal effects of the treatment on the true clinical outcome)8. Figures 2-1 to 2-3 illustra te Prentices conditions and potential deviations that may co mpromise the validity of surrogate measures. Figure 2-1 depicts a situation where Prentices conditio ns are met. In contrast, Figure 2-2 illustrates a scenario in which use of a surrogate would comp letely fail to predict the effect of an intervention on the true clinical outcome. While the surrogate is correlated with the true clinical outcome, and thus, satisfies the correlation condition, it does no t lie on the biological pathway by which the disease causes the clinical outcome. In conseque nce an intervention affecting the surrogate will have no effect on the clinical outcome. A situat ion somewhere between the scenarios depicted in the previous two figures may give a more accurate reflection of reality. A disease may affect the clinical outcome th rough more than one biologic pathway. If an intervention affects more than one biologic pathway (arrows A and B in Figure 2-3) and the surrogate lies only in one of these pathways, then only a part of the effects of the intervention will be captured by its effect on the surrogate. In addition, the interven tion may causally affect the clin ical outcome unrelated to the disease (arrow C in Figure 2-3), for example, through adverse effects. While Prentices conditions defi ne a surrogate in absolute te rms, Figure 2-3 illustrates a more common scenario where the second conditi on is not completely satisfied, but rather partially met. The statistical l iterature has approached this problem by introducing the proportion of treatment effect (PTE) explained by a surrogate marker which allows a more subtle evaluation of a surrogates validity fo r a specific intervention.15 22

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Importantly, when Prentices conditions are not fully met, the evaluation of the effect of a specific treatment on a clinical outcome by a ssessing the treatment effect on the surrogate measure (be it in an aggregate form in the contex t of a clinical trial, or on an individual level when assessing response to treatment) will not ca pture the full effect of the treatment on the clinical outcome and thus, be biased. In summary, the validation of surrogate measures is a challenging task. First, it requires the understanding of the biological pathway through which the surr ogate affects the clinical outcome. Only in the second step follows the sta tistical evaluation. The va lidation of a surrogate for a specific treatment requires larger sample sizes than are needed to dete rmine the effect of the treatment on the clinical outcome. Therefore meta-analysis of large clinical trials that document the effects of treatment on both surrogate and clin ical outcomes are usually necessary. Since the validity of a surrogate is treatment specific, validation should be repeated for different classes of drugs in the same disease state. The Epidemiology of Blood Pressure Co ntrol and Cardiovascular Outcomes Blood pressure (BP) is a str ong independent predictor of adverse cardiovascular (CV) outcomes and its control is one of the central goals in the prevention and treatment of cardiovascular disease.16, 17 Blood pressure is currently classified into normal (systolic blood pressure [SBP]/diastolic blood pressure [D BP] < 120/80 mm Hg), pr ehypertension (120/80 mm Hg < SBP/DBP < 140/90 mm Hg), stage 1 (140/ 90 mm Hg < SBP/DBP < 160/100 mm Hg) and stage 2 (SBP/DBP > 160/100 mm Hg) hypertensi on. The prevalence of hypertension in the United States between 1989 and 1991 has been estimated to reach almost 25%, and increases sharply with advancing age.18 Mortality from stroke and ischem ic heart disease (IHD) increases with higher blood pressure levels starti ng from 115mm Hg SBP and 75 mm Hg DBP, respectively (Figure 2-4).17 23

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While DBP is a more important risk factor fo r cardiovascular diseas e than SBP before the age of 50, the importance reverses in patients older than 50 years of age.19 Treatment of hypertension ultimately aims at the reduction of circulatory and renal mortality and includes lifestyle modifications as well as pharmacol ogic treatment. A large number of drugs from multiple drug classes are currently approved for the treatment of hypertension and more than two-thirds of treated hypertensiv e patients require two or more antihypertensive drugs to reach blood pressure control.16 Initial antihypertensive drug choi ce and following management are influenced by the presence of secondary diagnoses with compelling advantages of specific antihypertensive drug classes in regards to efficacy, tolerability, and blood pressure response. For most patients without comorbidities, thiazide -type diuretics are recommended as first line treatment. 16 An algorithm for treatment of hype rtension is shown in Figure 2-5. However, a number of questions regarding the optimal therapy of hypertension remain controversially discussed. Arguably the most important issue is whether differences exist in the beneficial effects on adverse cardiovascular outcomes between the major antihypertensive drug classes. Closely related to this problem is the question that if a comparison between two drug classes results in differences in cardiovascular outcomes, then are these differences fully accounted for by the level of achieved blood pr essure reduction or do non blood pressure mediated effects play a role in the effectivene ss of antihypertensive drugs? In other words: does it matter how blood pressure reduction is achieved? Over the last decades a plethora of antihypertensive drug trials have been conduc ted comparing various drugs from the major antihypertensive drug classes with placebo or active control treatments. Two recent metaanalyses have aggregated data from 29 trials with 162,341 patients20, and 42 trials with 192,478 patients21, respectively. Both studies found no differen ces in the reduction of all cause or 24

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cardiovascular mortality between the major an tihypertensive drug classes. However, some differences were shown in the effects on specifi c cardiovascular outcomes, most notably heart failure, with diuretics presenting th e most beneficial effects. One of the studies also reported that, with the exception of heart failure, differences in achieved blood pressure between trials randomized to the major antihyperten sive drug classes were proportiona l to differences in risk of cardiovascular outcomes.20 While some argue that it is re latively unimportant which specific agents are used to achieve blood pressure control22, the differences in the effectiveness on specific cardiovascular outcomes between drug classes suggest the exis tence of drug-specific mechanisms that affect cardiovascular outcomes independent of blood pressure. As mentioned earlier, the majority of hypert ensive patients will require two or more antihypertensive drugs to achieve blood pressure control according to current guidelines. While the comparative effectiveness of specific antihypertensive drugs is still not conclusively established, much less is known regarding th e comparative effectiv eness of different combination therapies. The underlying question is whether synergistic eff ects exist for specific antihypertensive drug combinations or whet her only achievable blood pressure reduction, tolerability, and cost should determine treatment. The comparative effectiveness is considerably harder to assess for combination therapy than fo r monotherapy because of the large number of antihypertensive drugs and drug cl asses (and thus, the large numb er of possible comparisons). Additionally, benefits may be associated with the more rapid control of blood pressure through immediate initiation of combination therapy vers us initial treatment with monotherapy followed by additional antihypertensive drugs if blood pressure cont rol has not been achieved. Lastly, it is not clear what the ideal blood pressure goal s hould be and when to begin treatment. For individuals with uncomplicated hypertension, current guidelines prescribe 25

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initiation of antihypertensive pharmacotherapy, if lifestyle mo difications alone do not lower blood pressure below 140/90 mm Hg [SBP/DBP] (lower recommendations apply to individuals with specific comorbidities).16 However, epidemiological evidence suggests a more than twofold difference in cardiovascular risk for blood pr essure values of 130-139/85-89 mm Hg as (currently defined as prehypertension) co mpared to values below 120/80 mm Hg. Thus, additional benefits may be achievable by lowering treatment goals. Recently, there has been considerable cont roversy about the f easibility to treat prehypertension.23 A recent randomized controlled tria l demonstrated that treatment of prehypertensive patients delayed progression to stage I hypertens ion, but to date no data is available for the effect of such treatmen t on cardiovascular morbidity and mortality.24 Time-Dependent Confounding in Pharmacoepidemiology Confounding occurs when the measure of the effect of an exposure is distorted because of an association of the exposure with other f actors that influence the outcome under study. Its control is one of the central issues in pharmaco epidemiological research. It is important to distinguish between measured and unmeasur ed confounding. The presen t study will focus on measured confounding. Measured confounding may be addressed by restriction or matching within the design of a study or by stratification or multivariate regression within the analysis stage of a study25. Traditionally such met hods would use variables at the beginning of the exposure period and then follow patients over time. Through the increasing use of timedependent methods in which exposure status can vary over the follow-up period in recent years, the problem of time-dependent confounding has become apparent. Time-dependent confounding occurs when a covariate predicts future treatment and future outcome and is itself predicted by past treatment (Figure 2-6). This poses uni que problems because standard methods of confounder adjustment do not suffice to produce unbias ed estimates. To illustrate why standard 26

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models fail to produce unbiased estimates unde r the aforementioned conditions, consider the following example. In Figure 2-6, if the time depe ndent confounder L is not controlled for in the analysis, then L1 confounds the association of treatment A1 with outcome Y, because it simultaneously affects both A1 and Y. Thus, any estimate of th e association of A with Y would be biased if L is not controlled for. However, if L is controlled in the analysis, then L1, a variable in the causal path of A0 on Y, is blocked, again, resulting in a biased estimate of the association of A with Y. Marginal Structural Models Marginal structural models (MSMs), first introduced by Robins, Hernan, and Brumback, aim to produce unbiased estimates in th e presence of time-dependent confounding.3 MSMs use inverse probability of treatment weights (IPTWs) and inverse probability of censoring weights (IPCWs) to create a pseudo-population in which treatment is unconfounded and no censoring occurs.26 MSMs are fitted in a two stage process. The first step estimates the individual IPTWs and IPCWs. The IPTWs are based on each subjec ts probability of having their own treatment history at each time point given the subjects covariates (with the time-dependent confounder as one of the covariates). The IPCWs are similarl y estimated based on each subjects probability at each time point to be censored based on his covariates. The second step uses the IPTWs and IPCWs as weights in a regression model of the effect of the treatment on the outcome. Because of the weighting, the regression now take s place in the pseudo-population andif all assumptions are metresults in a causal estimate of the treatments effect on the study outcome. The method assumes no unmeasured confounding factors and corre ct model specification for both the weights and the final regression model. Marginal structural models have been used in a number of disease states to obtain causal estimates of the effect of treatments in th e presence of time-depende nt confounding. In a recent 27

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observational study that aimed to estimate the cau sal effect of treatmen t with zidovudine on the survival of HIV-positive men, the inclusion of CD4 cell count into standard models was prohibited because it simultaneously predicted in itiation of zidovudine, was part of the pathway through which zidovudine is hypothesized to work, a nd was a risk factor for the study outcome.26 While a standard time-dependent Cox model, ad justed for baseline cova riates but not for CD4 cell count resulted in a hazard ratio of 2.3 (95% CI 1.9-2.8), the marginal structural Cox model showed a hazard ratio of 0.7 (0.6-1.0), revealing th e beneficial effect of the treatment. Similar results have been obtained for treatment with methotrexate in patients with rheumatoid arthritis,27 or the effect of aspirin on cardiovascular mortality.28 Figure 2-1. Prentice criteria satisf ied (adapted from Fleming et al.)13 Figure 2-2. The surrogate is correlated with the clinical outcome but captures no treatment effect (adapted from Fleming et al.)13 28

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Figure 2-3. Net effect of treatment is only par tially captured by the surrogate (adapted from Fleming et al.)13 A B Figure 2-4. Mortality from stroke (A) and isch emic heart disease (B) in each decade of age versus usual systolic blood pressure at the start of that decade. Reprinted with permission from Lewington S, Clarke R, Qizilbash N, Peto R, Collins R. Agespecific relevance of usual blood pressure to vascular mortality: a meta-analysis of individual data for one million adults in 61 prospective studies. Lancet. Dec 14 2002;360(9349):1903-1913 (Figures 2 and 4, pages 1906 and 1908).17 29

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Figure 2-5. Algorithm for the treatment of hypertension. Repr inted with permission from Chobanian AV, Bakris GL, Black HR, et al. The Seventh Report of the Joint National Committee on Prevention, Detecti on, Evaluation, and Treatment of High Blood Pressure. Jama. May 21 2003;289(19):2560-2572 (Figure 1, page 2564).16 Figure 2-6. Directed acyclic gr aph for time-dependent confounding. causal effect; L0, vector of measured c onfounders at time 0; L1, vector of measured confounders at time 0; A0, treatment at time 0; A1, treatment at time 1; Y, outcome of interest. 30

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CHAPTER 3 METHODS The methods for this study are presented in f our parts: (1) a description of the dataset including operationalization of ke y variables, (2) a section detail ing descriptive statistics, (3) a section describing several statisti cal models used to determine th e association be tween systolic blood pressure over time and the risk of a primar y outcome event, and (4) a section describing the methods used to determine the relation betw een time-dependent treatment and the risk of a primary outcome event. Sections 3 and 4 include both standard methods (Cox-regression with and without time-dependent covariates) and nove l, causal methods (marginal structural Cox regression) to address potential bias introduced by time-dependent confounding. The INVEST and the INVEST Dataset The International Verapamil-Trandolapril SR Study (INVEST) was a large, international, randomized controlled antihypertensive trial invo lving patients with hypertension and coronary artery disease from 862 sites in 14 countries.4 After an extensive car diovascular history and physical exam the INVEST random ly assigned 22,576 CAD patients 50 years old to either a verapamil SRor an atenolol-based multidr ug antihypertensive strategy. Trandolapril and hydrochlorothiazide (HCTZ) were specified as added agents, if needed for blood pressure control, with trandolapr il added first in the verapamil SR strategy and HCTZ added first in the atenolol strategy. In both st rategies, trandolapril was reco mmended for patients with heart failure, diabetes, or renal impairment (Fi gure 3-1). Between 1997 and 2003, 61,835 patient-years follow-up were accumulated and each strategy pr ovided excellent BP control (>70% of patients achieved BP <140/90 mm Hg) without differences in BP between the strategies. The strategies were equivalent in preventing the primary outcome defined as all-cause death, nonfatal myocardial infarction (MI), or nonfatal stroke. All components of the primary outcome (defined 31

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as first occurrence of all-cause death, nonfatal MI, or nonfatal st roke) were fully adjudicated by an independent adjudication committee. Further details on the design and results have been published.4, 5 The INVEST and all subsequent studies in cluding the study at hand were approved by the institutional review board (IRB) of the University of Florida, whic h acted as the central IRB for all participating sites. During the INVEST patients had scheduled visits every six weeks for the first six months and every six months thereafter. At each vis it, patients were assessed for occurrence of symptoms, adverse events, and response to trea tment. SBP and DBP were measured twice at each visit (at least two minutes apart) with a standard mercur y sphygmomanometer in a sitting position. In a given patient througho ut the trial all measurements were taken on the same arm, and, when possible, approximately the same tim e of day to minimize measurement error. In addition, all antihypertensive drug use was recorded at each vis it. Throughout the remainder of the manuscript we refer to the antihypertensive dr ugs included in either of the INVEST treatment strategies (Atenolol, Verapamil, HCTZ, and Trandolapril) as study drugs and all other antihypertensive drugs as nonstudy drugs The term total antihypertensive drugs refers to both study and nonstudy antih ypertensive drug use. Follow-up continued until a patient was lost to follow up, died, or the end of the study. In the online data acquisition system, protocol visits were numbered consecutively from 1 (baseline) to 14 (maximum follow up of 5 years). Visits outside of the pr otocol schedule were also recorded and numbered 0. These visits were onl y included in the analysis if a protocol visit was not observed but an unscheduled visit was r ecorded in a time interval close to the omitted protocol visit. If patients did not return for one or multiple protocol visits and did not have suitable non-schedule visits to replace the unobserved protocol visit(s), values (e.g., SBP, 32

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antihypertensive drug use) from the last observed vi sit were carried forward. If a patient was lost to follow-up (i.e., does not have another observe d visit or final assessment), the patient was censored at the time of the last observed visit. For patients who experienced an event on the day of the recorded visit, BP and treatment measures from the last recorded visit before the event were used instead of the measures from the even t visit to avoid the possibility that the observed measures on the event date were affected by the event (reverse causation). Descriptive Statistics The following basic descriptive statistics were computed at each visit: Number and percentage of patients on each INVEST study drug Number and percentage of patie nts by number of INVEST st udy drugs and number of total antihypertensive drugs used Mean SBP, and percentage of patients in 10 mm Hg SBP categories Change in number and percentage of patient s between number of INVEST study, and total antihypertensive drugs between visits Change in percentage of patients with in 10 mm Hg categories between visits Blood Pressure and CV Outcomes The association of systolic blood pressure with the risk of primary outcome event was first assessed unadjusted for time-dependent antihype rtensive treatment using Poissonand Cox proportional hazards regression. Incidence Rates by Categories of Systolic Blood Pressure Incidence of primary outcome events per cate gory of systolic blood pressure was expressed as number of primary outcome events per 1000 patient years of follow-up. Blood pressure categories were defined as <110, 110-119, 120-129, 130-139, 140-149, 150-159, and 160 mm Hg. Adjusted incidence rates we re calculated using Poisson regression. The model adjusted for following baseline covariates that include predictors of CV-outcomes in the INVEST29, as well 33

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as basic demographic variables: sex, ethnicity, age, residency (US vs. non-US), smoking status, history of heart failure, history of diabetes, history of renal impai rment, prior stroke or transient ischemic attack, prior myocardial infarction, hist ory of peripheral vascular disease, and prior coronary revascularization. Adjusted inciden ce rates are presented for female sex, White ethnicity, age at baseline between 60 and 70 years, US residency, and in absence of other risk factors (these values reflect the medi an values of the included variables). Cox Proportional Hazards Models The potential association of sy stolic blood pressure with the risk of primary outcome event unadjusted for treatment (other than at baseline) was assessed using standa rd and time-dependent Cox models. The models included the following st atic covariates measured at baseline (sex, ethnicity, age, residency (US vs. non-US), smoking status, history of heart failure, history of diabetes, history of renal impairment, prior stroke or transient ischemic attack, prior myocardial infarction, history of peripheral vasc ular disease, and prior coronary revascularization) as well as SBP. All Cox models categorized SBP in seven 10 mm Hg categories as defined above and used SBP 130 to 139 mm Hg as reference category. SB P categories were operationalized either as static variables (Equatio n 3-1) or as a time-dependent vari ables (Equation 3-2), depending on the respective model. The Cox models were specified as follows: Cox Proportional Hazards model: ikk i i ix xxtt ... exp)()(2211 0 (3-1) Cox model with time-dependent covariate: ikk i i ix xtxtt ... )(exp)()(22 11 0 (3-2) )( ti = individual is hazard to e xperience an event at time t )(0t = baseline hazard function at time t 34

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1 = association parameter for the SBP categ ory (in the actual model, there are six parameters, one for each SBP category dummy variable) = individual is SBP category (in the actual model, six dummy variables are used) 1 ix k 2 = association parameters for indi vidual is k-1 static covariates = k-1 static covariates for individual i ikixx 2 = individual is SBP category at time t (six dummy variables) )(1txi Six Cox models using different operationaliz ations of systolic blood pressure were evaluated: (1) baseline, (2) average over follo w-up (fixed average), (3) average over follow-up weighted by follow-up time, (4) time-dependent us ing values from the pr evious visit (updated previous), (5) time-dependent using values fr om the next visit (updated next) and (6) timedependent using an average updated at every visit (updated mean). Models 1 to 3 used a single, static value of SBP over the time of follow up. In contrast, models 4 to 6 are time-dependent and SBP values were updated at each observation (duri ng the remainder of the study we refer to these models as updated models). Figure 3-2 shows how these different models conceptionalize SBP over follow-up for a sample INVEST patient. The sample patient has a baseline SBP of 160 mm Hg (visit 1), observed scheduled visits 2, 3, a nd 5 (with measured SBPs of 140, 130, and 155 mm Hg, respectively), and experienced an event after 32 weeks (before scheduled visit 6). Importantly, Figure 3-2 shows continuous SBP values for each model, while the Cox models utilized categorized data as described above (i.e ., for the Cox models the resulting SBP values are converted into dummy variables representing the 7 SBP categories). The baseline model simply used the SBP observed at baseline to represent the patients SBP throughout follow-up. Like the baseline model, the average model used a static SBP value to represent the patients SBP over the entire follow-up, however, instead of the baseline SBP, it 35

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used the average SBP calculated over the obser ved follow up period. The average was calculated as follows: 1 1 1 1 n n i n i iit tSBP PBS (3-3) PBS = average SBP over follow-up i = SBP at visit i SBP n = total number of observed visits = time between visit i and visit i+1 it Note that, because visit 4 was not observed, the calculation assigned the SBP value observed at visit 3 to the entire time period between visits 3 and 5 (see Figure 3-2 for a numerical example of the calculation). The time-weighted average model used the same fixed average value calculated in the equa tion above, but weighted each indi viduals observation by his or her respective total follow-up time. This model thus weighted a subjects contribution according to the total follow up-time the subject provided. Fo r each time period betwee n two observed visits, the updated previous model assigned the SBP value measured at the visit at the beginning of the respective time-period (i.e., it carr ies the value forward), while the updated next model assigned the SBP value from the visit that marked th e end of the time period. Since no observations existed after an event is observed, the update d next model used the last available SBP measurement before the event for the time period fr om the last observed visit before the event up to the event (i.e., it used the same value as the updated previous model). Lastly, the updated mean model used an SBP average calculated as in equation 3-3, but instead of calculating a single average at the end of follow-up (as in th e average, and time-weighted average models), 36

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calculated a new (updated) average at each observed visit. Note that the updated mean SBP at the end of follow-up is equivalent to the average SBP over the entire follow-up. A generalized R2 was calculated for each of the six m odels and used to assess and compare the strength of associatio n of the predictor variables with the outcome.30 n G R2 2exp1 (3-4) G2 = likelihood-ratio chi-squared statistic for testing the null hypothesis that all covariates have coefficients of 0 n = sample size Marginal Structural Cox Model A marginal structural Cox mode l was used to estimate the effect of SBP control (SBP less than 140 mm Hg) over the course of follow-up on primary outcome controlling for potential time-dependent treatment. Because SBP control, the independent variable of interest, is a binary variable (a requirement of the marginal structural model) all patients with SBP of less than 110 at any visit were excluded. This was necessary because a previous report31 and preliminary data from our analysis showed a J-shaped relations hip between SBP and the risk for cardiovascular outcomes, with substantially increased risk for cardiovascular outcomes associated with SBP of less than 110 mm Hg. T hus, if patients with such low SBP (that would be included in the category of less than 140 mm Hg) were not excluded, the estimate of the benefit of controlled SBP would be skewed towards the null. The remainder of this section describes the estimation of the marginal structural Cox model. First, the stabilized i nverse probability of treatment and inverse probability of censoring weights were estimated (Equations 3-5 to 3-7). Stabilized weights have been shown to produce more narrow confidence intervals with better cove rage rates. Note that in this instance treatment 37

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refers to having controlled versus uncontrolled systolic blood pressure In addition, the method requires the intend-to-treat like assumption that once treatment is initiated (here, SBP control is reached), patients remain on it until the end of th eir follow-up. Thus, the datasets used for the marginal structural Cox models are adjusted accordingly and all observations after treatment initiation areregardless of observed exposure statusrecoded as exposed to treatment. Inverse probability of treatment weight (IPTW): t k i i i iklkLkakAkakApr tw0)]()(),1()1(|)()([ 1 (3-5) Stabilized IPTW: t k i i i i i i iklkLkakAkakApr vVkakAkakApr tsw0)]()(),1()1(|)()([ ]),1()1(|)()([ (3-6) Stabilized Inverse probability of censoring weight (IPCW): t k i i i i iklkLkakAkCkCpr vVkakAkCkCpr tsw0 )]1()1(),1()1(,0)1(|0)([ ]),1()1(,0)1(|0)([ (3-7) Model parameters (uppercase letters represen t random variables, lowercase letters denote specific realizations of that random variable): probability of individual i to have experienced his or her own observed treatment history from time 0 to time t )( twi stabilized form of )( tswi ) ( twi A(k) = 1 if SBP < 140 mm Hg, 0 otherwise L(k) = vector of all measured risk factor s for Y at time k (number of antihypertensive drugs) Y = 1 if the INVEST primary outcome occurred V = vector of all baseline risk factors for Y = stabilized weight for the probability of censoring for individual i )(tswi 38

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C(k) =1 if a subject was lost to follow up by time k The IPTWs were estimated using a pooled logi stic regression model for the probability of having controlled systolic blood pressure at vis it (k) conditional on baseli ne covariates (all measured baseline variables were included) a nd antihypertensive treatment (number of both study and total antihypertensive drug s) at baseline and visit (k-1). The IPCWs were estimated in the same fashion using a pooled logistic regression model for the probability of being censored at visit (k). Second, combin ed stabilized weights x were calculated for each patient visit. ) ( tswi )(tswi Lastly, the combined stabilized weights were used in a weighted Cox proportional hazards model. To overcome computational limitations of standard software (most available programs including SAS do not allow subj ect specific time-varying weight s), the Cox proportional hazards model was estimated by fitting a pooled logistic regression that included the weights, baseline covariates and the time-dependent syst olic blood pressure control variable.26, 32 The model was specified as follows: logit pr VtAtVtAtDtD2 1 0)1()(]),1(,0)1(|1)([ (3-8) D ( t ) = 1 if the subject had an event in month t and D ( t ) = 0 otherwise. To assess whether antihypertensive treatmen t acted as a time-dependent confounder, we compared the hazard ratio for SBP control obtain ed from the marginal structural Cox model ( from equation 3-8 with each patien t visit weighted by the combined stabilized weights) with the estimate obtained from a standard time-dependent Cox model (i.e., a model that did not adjust for time-dependent confounding). The hazard ratio for SBP control in the standard timedependent Cox model was estimated simply by us ing equation 3-8 without the combined weights 1e 39

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( from equation 3-8). Statistical significance of the difference was assessed by comparing the 95% confidence intervals of both estimates. 1e Antihypertensive Treatment and CV Outcomes The time-dependent effect of treatment on the risk of primary outcome event was assessed both adjusted and unadjusted for time-dependent SBP, using Cox proportional hazards regression with and without combined stabilized weights (i .e., using a marginal structuralas well as a standard time-dependent Cox mode l as in the section above). Marginal Structural Cox Models A marginal structural Cox model similar to th e one described before was used to estimate the effect of time-dependent treatment (aggr essive antihypertensive treatment versus conventional antihypertensive treatment) on prim ary outcome controlling for SBP at each visit. Aggressive antihypertensive trea tment was defined as being simultaneously exposed to three or more total antihypertensive drugs. To assess the sens itivity of the results to this rather arbitrary definition (that is necessitated by the methods restriction to a bina ry independent variable), the analyses were also conducted using the four following addition al definitions for aggressive treatment: (1) more than one total antihype rtensive drug, (2) more than three total antihypertensive drugs, (3) more than one anti hypertensive study drug, and (4) more than two antihypertensive study drugs. Because of the U-shap ed relationship between SPB and the risk for cardiovascular outcomes in INVEST, time dependent SBP was categorized into three categories, low (<120 mm Hg), normal (120 mm Hg to <140 mm Hg), and high ( 140 mm Hg). As in the model for SBP control, the stabilized inverse probability of treatment and inverse probability of censoring weights were estimated (Equations 3-6 and 3-7). The IPTWs were estimated using a pooled logistic regression model for the probability of being exposed to aggressive versus standard anti hypertensive therapy at visit (k) conditional on baseline covariates 40

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(all measured baseline variables were included ) and systolic blood pre ssure (low, normal, or high) at baseline, visit (k) and vi sit (k-1). The IPCWs were estima ted in the same fashion using a pooled logistic regression model for the pr obability of being censored at visit (k). Equations 3-5 to 3-8 apply as before w ith treatment now defined as aggressive antihypertensive treatment and SBP acting as a potential tim e-dependent confounder, thus: A(k) = 1 if the number of total antihyperte nsive drugs was greater than 2, 0 otherwise L(k) = vector of all measured risk factors for the outcome at vis it k (including the three previously defined SBP categories) As in the previous section, combined stabi lized weights was computed and used in a weighted Cox proportional hazards model that is estimated through pooled logistic regression including the combined weights, baseline covari ates, and the time-dependent treatment variable (aggressive antihypert ensive treatment). Cox Proportional Hazards Models In addition to the marginal structural Cox model, a standard time-dependent Cox model was estimated analogous using the same pooled logi stic regression model that was used in the marginal structural Cox model above (equation 38) but without weighting. The hazard ratio for SBP control obtained by the standard time-depende nt Cox model was then compared to the one obtained from the marginal structural Cox mode l to determine whether a confounding effect of SBP on the hazard ratio for aggressive versus standard antihypertensive treatment exists. 41

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Figure 3-1. Treatment strategi es in the INVEST. Reprinted w ith permission from Elliott WJ, Hewkin AC, Kupfer S, Cooper-DeHoff R, Pepine CJ. A drug dose model for predicting clinical outcomes in hypertensi ve coronary diseas e patients. J Clin Hypertens (Greenwich). Nov 2005;7( 11):654-663 (Figure 1, page 656).33 42

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Figure 3-2. Operationalization of SBP: Examples for a sample patient. 43

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CHAPTER 4 RESULTS A total of 22,576 patients satisfied all requireme nts for inclusion into the original INVEST analysis.4 Total follow-up time for the cohort wa s 61,845 patient years with 2,269 patients experiencing a primary outcome event during th is period. For the present study, 906 patient years of follow-up were excluded from the analysis because they accrued af ter the occurrence of a nonfatal primary outcome event and thus, a tota l of 60,939 patient years of follow-up remained available for analysis. Descriptives Baseline characteristics of the INVEST cohort relevant to the present study are presented in Table 1. Briefly, the cohort ha d a mean age of 66.1 (.8) year s and included slightly more women than men. The majority of patients were White, followed by large proportions of Hispanics and Blacks. Considerable proportions of patients had a hist ory of cardiovascular events, or conditions recognized as cardiovascular risk fa ctors. No breakdown by INVEST treatment strategy is provided since randomization is not relevant to the analyses presented in this study. Average follow-up time to primary outcome ev ent or censoring (end of follow-up or loss to follow up) was 2.7 (.9) years, ranging from 1 day (a patient who expe rienced a PO event on the day of the first visit) to a maximum of 5.4 years. Of a maximum of 14 possible physician visits designated for data colle ction and treatment adjustments, the average number of visits during INVEST follow up (including last encounter) was 7.3 (.7). After missed visits prior to censoring were imputed by carrying forward values from the last observed visit, this number increased to 9.5 (.8). 44

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The number of patients at risk at each visit is depicted in Figure 4-1. All figures display follow-up over only 48 months (visits 1 to 12) due to the low numbers of uncensored patients at the last two visits (2583 patie nts after 54 months, and 792 patients after 60 months). However, all analyses are conducted using data of all 60 months (visits 1to14). Ninety five percent of patients remained in the trial at 24 months, slightly less than 50% at 36 months and only about 12% at 48 months. Depending on th e visit number, between 64% and 85% of uncensored patients had an observed visit. Visit f our (week 18) shows the lowest percentage of observed visits, with only 64% of uncensored patients assessed at this visi t. For the remainder of this study, all results are reporte d for the imputed data (with values carried forward for missed visits as described above) unless noted otherwise. Blood Pressure Mean SBP at the baseline visit was 150.9 mm Hg (.5). After 24 months, the mean SBP was reduced by 17.2 mm Hg to 133.7 mm Hg (.8). This reduction occurred mainly early in the trial with 52%, and 80% of the reduction obs erved at the six week and 12-week visits, respectively (Figure 4-2). When only observed visits were evalua ted, SBP values at each visit were on average about 2.5 mm Hg lower than in the imputed dataset. For the majority of the analyses in this study, SBP was categorized in to 7 categories, each spanning 10 mm Hg and ranging from smaller than 110 mm Hg to greater or equal to 160 mm Hg (Figure 4-3). At baseline 75% of patients had uncontrolled SBP ( 140 mm Hg) and 33% had a SBP of greater or equal to 160 mm Hg. Forty-four and 31% of patients showed uncontrolled SBP after three and 24 months, respectively, with 15% and 9% of patients in the ra nge of greater than 160 mm Hg. Figure 4-4 depicts the proportions of patients within each SBP category and at each visit (starting with visit two) who wher e not in the same category at th e visit before (i.e., had changed SBP category between visits). The early drop in mean SBP shown in Figure 4-2 is mirrored at 45

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the first data points (six week visit) in Figur e 4-4. Between 70% and 85% of patients in the lowest four SBP categories had no t been in the same category at baseline. With the exception of the highest SBP category that throughout followup at each visit included between 25% and 40% of patients who were in lower SBP categories at the visit before, all other categories show between 40% and slightly above 60% of patients with changed SBP category at each visit. Overall, at any given visit, only about half of all patients did not change blood pressure categories. Antihypertensive Drugs At the baseline visit, patients received on average 2.9 antihypertensive drugs, 1.5 of which were INVEST study drugs (Figure 4-5). After si x months of follow-up the number of study drugs had increased to 1.9 while the total number of drugs had decreased to 2.6. These numbers remained relatively stable throughout month 30, af ter which the total number of drugs and the number of study drugs dropped to about 2 and 1.5, respectively. The proportions of patients receiving each individual study dr ug over follow-up are depicted in Figure 4-6. At baseline, the first line study drugs verapamil and atenolol were utilized by 50% and 45% of patients, with 20% and 33%, respectively, receiving the add-on drugs HCTZ and trandolapril. Over the followup period the percentage of patients on first line study drugs continuously dropped to 40% and 30% of patients on verapamil and atenolol after 24 months, respectively, and 38% and 28% after 48 months. Over the initial six months of fo llow-up, the proportion of patients on add-on study drugs increased to 42% and 44% for HCTZ and tr andolapril, respectively. Starting at week 12, trandolapril was the most commonly used study drug within INVEST, with atenolol becoming the second most commonly used study drug after one year. From 30 months to the end of followup, the proportion of patients on study add-on dr ugs dropped to about 40% to 45% for HCTZ and trandolapril, after remaining relatively constant at 47% to 55% from 12 to 30 months. 46

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Proportions of INVEST patients categor ized by the number of study and total antihypertensive drugs are shown in Figures 4-7 and 4-8. At baseline 62% of patients received one, 28% two, and the remaining 10 percent thre e study antihypertensive drugs. After the first six months, the number of patients on one study drug had more than halved to 29%, while 41% and 25% of patients were placed on two and thre e study drugs, respectively, and 5% of patients did not receive any study antihypertensive trea tment. Over the following months, the proportion of patients on one study drug continued to decr ease to 19% at month 30, with 20% having no study antihypertensive drug at this time point. Over the sa me time period the proportion of patients on three study drugs increased to 30% while the proportion of patients on two study drugs dropped to 31%. After 30 months the perc entages of patients on study drugs continued to drop slightly with the proporti on of patients without study drugs increasing to 34% by month 48. Similar trends can be observed when examin ing the data for all an tihypertensive drugs. From baseline to 24 months most patients (between 33% and 39%) received two antihypertensive drugs followed by patients on th ree antihypertensive dr ugs. From month 30 to the end of follow-up, patients on three antihypert ensive drugs contributed the largest proportion with 27% to 30%. Starting at month 36 and th roughout the remainder of follow-up about one quarter of patients did not receive any antihype rtensive drugs. Throughout the follow-up period a stable proportion of between 5% and 10% of pa tients each received five and more than five antihypertensive drugs. Compared to the high proportion of patient s who experienced changes in their SBP categories between visits (Figure 4-4), antihypertensive drug use was relatively stable. Figure 4-9 shows by visit and starting at the second visit th e proportion of patients w ho had a change in the number of prescribed antihypertensive study drug s from the prior visit. After 18 months this 47

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proportion stabilized at around 10% for patients on one to three study drugs, but ranging from 30% to 50% for patients who did not have a prescription for a study drug. Compared to the changes reported for the num ber of antihypertensive study drugs (Figure 4-9), changes in the number of total antihypert ensive drugs were more pronounced. Figure 4-10 shows by visit and starting at the second visit th e proportion of patients w ho had a change in the number of prescribed total anti hypertensive drugs compared to the prior visit. Patients with no antihypertensive drugs are most lik ely to report a change from th e visit before (depending on the visit, 50% to 90% of patients who did not take any antihypertensive drug s were on at least one antihypertensive drug at the pr ior visit. After vi sit two and for thos e patients who had a prescription for at least one an tihypertensive drug, the proportion who reports changes in the total number of antihypertensive drugs ranges fr om 10% to 45% with patients on five total antihypertensive drugs generally repor ting the highest propo rtion of change. Primary Outcome Events Figure 4-11 displays a consta nt slope for the cumulative number of INVEST primary outcome events over the initial th ree years of follow-up, followed by a slightly steeper slope for the remaining years, indicating that the event rate in INVEST is initially constant with only a small increase after more th an three years of follow-up. Hazard Ratios The following section shows plots of hazard ratios (HR) by categories of SBP, obtained by conventional and time-dependent Cox PH regression. All hazard ratios show the hazard for primary outcome event in a specific SBP category compared to the hazard for a primary outcome event in the category of SBP 130-140 mm Hg (reference category). Oper ationalization of SBP was varied and included baseline, mean over follow-up, mean over follow-up weighted by time 48

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of follow-up, actual value at prio r visit (time-dependent), actual value at the following visit (time-dependent), and updated mean over follow up (time-dependent). Baseline SBP Model Figure 4-12 shows the hazard ratios and 95% confidence intervals for a primary outcome event by categories of baseline SBP. The relationship between baseline SBP and the hazard for an outcome event follows a reverse J-shape with a nadir at the reference category of 130 to < 140 mm Hg. The lowest and two highest SBP categories show significan tly increased risk, while the remaining three categories show no difference. Th e distribution of patien ts within each SBP category was as follows: Almost 33% of patients ha d a baseline SBP of gr eater than 160 mm Hg with relatively few patients c ontributing to categories of 110 and 110 to 120 mm Hg (3%) and smaller than 110 mm Hg (0.9%). The remaining categories of baseline SBP included between 8% (SBP 120 to <130 mm Hg) and 22% (SBP 140 to <150 mm Hg) of the 22576 INVEST patients. Average SBP Model Calculation of the average SBP over follow up for each subject resulted in 7259 patients (32%) with an average between 130 mm Hg a nd 140 mm Hg, followed by 6403 subjects (28%) with an average follow-up SBP between 120 mm Hg and 130 mm Hg. The two extreme SBP categories of less than 110 mm Hg and greater than 160 mm Hg, included fewer subjects with 190 (.8%) and 1500 subjects (6.6%), respectively. The relationship between risk for primary outcome and average SBP categories over followup follows a J-curve with the nadir at 120 mm Hg to 130 mm Hg (Figure 4-13). Patients with an average SBP over follow-up between 120 mm Hg and 130 mm Hg show no difference in the risk for an outcome event (HR 0.96, 95% CI 0.851.09) compared to the reference category, while all remaining categories show significantly higher risk. Different from the h azard ratios obtained for baseline SBP the increase in the hazard 49

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is larger for the highest two categories of average SBP (with a maximum increase of 180%, 95% CI 44%-221%, at SBP greater or equal 160 mm Hg ) than for the lowest category (80%, 95% CI 25%-158%). In comparison, the estimates for SBP of greater or equal 160 mm Hg and lower than 110 mm Hg were a 17% increase (95% CI 2-33%) and a 64% increase (95% CI, 17-130%) when the baseline SBP was used. Average SBP Weighted by Follow-up Time Model Individual follow-up time in INVEST was used to weight each individuals average follow-up SBP (Figure 4-14) to avoid over-repr esentation of patients who contributed little follow-up time due to an early event or loss to follow-up early in the trial. The resulting curve shows a similar shape as Figure 4-13 but is genera lly flatter. Its maximum hazard ratio occurs at an average SBP greater or equal to 160 mm Hg and with 2.11, 95% CI 1.76 2.54, is about one third lower than the hazard ratio for the un-we ighted average at the same SBP category (HR 2.80, 95% CI 2.44-3.21). The risk at the lowest SBP category of less than 110 mm Hg is not different from the risk at the next higher categor y and shows a very wide confidence interval due to the low number of patients with low average SBP. Time-Dependent SBP Models Figure 4-15 shows the relationship between the SBP category observed at the last recorded visit of a given time interval in the Cox model and the risk for a primary outcome event. SBP categories were continuously updated over the co urse of follow-up. Figure 4-15 shows a flat Vshape with its nadir at SBP between 130 mm Hg and 140 mm Hg. All but the category between 120 to 130 mm Hg show a significantly increased risk for a primary outcome event compared to the reference category. The lowest and the two highest SBP categories sh ow slightly over 50% increase in risk while the remain ing two categories are at about 20%. 50

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In contrast to Figure 4-15, Figure 4-16 s hows hazard ratios for the primary outcome by category of time-dependent SBP from the next observed visit. Here, SBP for each given time interval is taken from the first observed visit after this time interval. One exception was made: For the time period immediately preceding an event, the SBP from the last observed visit was used since there was no observation available af ter the patient was censored. Figure 4-16 shows a J-shaped curve with nadir for the hazard ratio at 120 mm Hg to 130 mm Hg, significantly lower than the reference category (HR 0.73, 95% CI 0.650.83). Departing from the curves J-shape the two lowest SBP categories show a lmost identical hazard ratios. Updated Mean SBP Model The hazard ratios for Figure 4-17 were deri ved calculating at each observed visit an updated mean SBP that was used as a time-depende nt covariate in the model. This produced a nearly symmetric V-shaped curve with its na dir at SBP 130-140 mm Hg. With the exception of updated mean SBP values between 120 mm Hg and 130 mm Hg (H R 1.09, 95% CI 0.96-1.23), all remaining SBP categories showed significan tly higher hazard ratios than the reference category. The lowest and highest categories show ed the greatest increase in risk with hazard ratios of 1.61 (95% CI, 1.12-2.32), and 1.80 (95% CI, 1.56 2.06), respectively. Compared to the analysis using the unweighted average, th e highest three categories using the updated mean showed between 13% (SBP between 140 mm Hg and 150 mm Hg) and 35% (SBP larger than 160 mm Hg) lower risk for a primary outcome event. Compared to the time dependent SBP model (prior visit) the results of the updated mean model show only small differences ranging from a 5% lower estimate (SBP between 150 mm Hg and 160 mm Hg) to a 25% overestimation (SBP between 110 mm Hg and 120 mm Hg) with th e lowest and highest SBP category within 3% and 13% respectively. 51

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Incidence While the previous section presented numerous estimates of the hazard for an outcome event in a specific SBP category relative to the reference category of 130 to 140 mm Hg, absolute risks for patients in specific SBP cat egories have thus far not been presented. The following section shows both unadjusted and adjusted incidence rates presen ted as the number of primary outcome events per 1000 person years spen t in the seven respective SBP categories. Figure 4-18 presents unadjusted incidence rates for the primary outcome events by category of SBP. Each subjects follow-up period could contribute person time to multiple SBP categories. Person time was accrued for the last observed SBP category until a change in SBP category, the occurrence of an event, or censorin g. Likewise, events were attributed to the SBP category observed at the last visit prior to th e event. Most person years of follow-up were accrued in the category of 130-140 mm Hg (16188 person years), while the category of <110 mm Hg contributed the lowest number (1678 person years). The crude incidence of the INVEST primary outcome by SBP category was V-shaped a nd consequently highest in the extremely low and high SBP categories <110 mm Hg (53.6 primary outcome events/1000 person years) and 160 mm Hg (53.8 primary outcome events/1000 pers on years). The crude incidence rates in the categories of 130 to 140 mm Hg, and 120 to130 mm Hg were more than 40% lower with 30.6 primary outcome events/1000 person years for these SBP categories. The respective adjusted incidence rates, calculated by Poisson regression for White, US, female patients without co-morbi dities and between the ages of 60 and 70 years, displayed in Figure 4-19 show a similar V-shape and range from 14.1 primary outcome events/1000 person years for the SBP category between 130 to140 mm Hg to 18.8 primary outcome events/1000 patient years for the category greater than 160 mm Hg. 52

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Comparisons The two previous sections pres ent several approaches to determine relative and absolute risks to experience an outcome event for pa tients of the INVEST depending on their SBP category. The following section compares the resu lts of these approaches and provides a brief description of the assumptions implied in each of the modeling approaches. Table 4-2 presents a summary of the result s obtained by the modeli ng approaches of the previous two sections. For each model, Table 4-2 shows the hazard ratios (relative risks for the Poisson regression model) for the lowest SBP cat egory (<110 mm Hg), th e category with the lowest risk for an outcome event, and the highest SBP category ( 160 mm Hg). Hazard ratios and relative risks for the lowest and highest SBP category are presented both in comparison to the reference category (130 to140 mm Hg) and the SBP category with the lowest risk (in parenthesis) if that is not the reference category in the re spective model. Add itionally, Table 4-2 shows the generalized R2 for each model. Compared to th e reference category, the hazard ratios/relative risks for the SBP category of lower than 110 mm Hg range from 1.16 (timedependent next) to 1.80 (average ov er follow up). At the same time hazard ratios/ relative risks for the highest SBP category (>160 mm Hg) range from 1.17 (baseline) to 2.80 (average). Notably, the most extreme estimates for both the lowest and highest SBP categories were obtained from the average SBP model. Generalized R2 values for the presented models were small, ranging from 0.039 to 0.070, with little difference between models. Average SBP and Bias Table 4-3 illustrates in a much simplified scenar io that the use of an average of a measure (e.g., controlled versus uncontrolled SBP averaged over follow-up) can lead to biased estimates if (1) the duration follow-up time is not fixed but ra ther determined by the occurrence of an event and (2) there is a directed change of the measur e over the course of follow-up (i.e., mean SBP is 53

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lowered during the course of INVEST, especially early). Of note, condi tions (1) and (2) are typically met in the context of clinical trial da ta that treat a surrogate over follow-up and have a primary outcome at which patients are censored, su ch as the INVEST data. It also applies to observational studies where a surrogate show s a time-dependent upward or downward trend. Notably a directed change in a mean over follow-up can also occur as the re sult of regression to the mean if inclusion of subjects in the study is dependent on extreme values of the surrogate. The simplified scenarios (A to F) below make the following assumptions: Patients start with eith er controlled or uncontro lled blood pressure Duration of follow-up is three years Measures are taken after the first and third years The event rate is constant at 10% per year and independent of blood pressure control Events occur at the time of measurement At the end of follow up the average is calcula ted as high and low, respectively, for those patients who remained in their BP category over follow up and for those who changed BP category after the first year as the value of the second (longer) measurement period. Scenarios A to F show the effects of varyi ng longitudinal changes in BP (A to D), and different patient distributions between controlle d and uncontrolled BP at baseline (E to F): Scenario A: 100 patients each start with controlled and uncontrolled BP respectively. Patients do not change BP cat egories throughout follow-up. Scenario B: 100 patients each start with controlled and uncontrolled BP respectively. 30% of patients with uncontrolled blood pressure wi ll be controlled after the first follow-up year. Patients with controlled BP will continue to have controlled BP. Scenario C: 100 patients each start with controlled and uncontrolled BP respectively. 60% of patients with uncontrolled blood pressure wi ll be controlled after the first follow-up year. Patients with controlled BP will continue to have controlled BP. 54

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Scenario D: 100 patients each start with controlled and uncontrolled BP respectively. 60% of patients with uncontrolled blood pressure wi ll be controlled after the first follow-up year. 60% of patients with controlled blood pr essure will have uncontrolled BP after the first follow-up year and over th e remainder of follow-up. Scenario E: Equivalent to scenario D except that 200 patients have uncontrolled BP and 100 patients have controlled BP at baseline. Scenario F: Equivalent to scenario D except that 100 patients have uncontrolled BP and no patients have controlled BP at baseline. Scenario A (no changes in BP categories over follow-up) results, as expected, in an event rate of 10 events per 100 patient years. Ov erall, 28 events occurred, 10 (35.7%) of which occurred after the first year. The number is sligh tly higher than one third because only 90 of the original 100 patients were still at risk for an event in the second, two-year long, follow-up period. Scenario B, which has 30% of patients sw itch from uncontrolled to controlled BP after one year, deviates from the expected event rates. It results in an event ra te of 11.6% for patients with average uncontrolled BP ove r follow-up and 9.2% for patients with average controlled BP. The percentage of all events of the categories stemming from patients whose average BP was based on only the first year of follow-up is a bout 10 percentage points higher, at 45.5%, as expected for patients with uncontrolled BP and about 6% lower than expected for those who average controlled BP (29.4%). Of note, the num ber of events after one year of follow up is constant throughout all four scenarios at 10 ea ch for controlled and uncontrolled patients, respectively. Scenario C, which doubles the percentage of patients who, starting as uncontrolled, achieve BP control after the one year visit, results in an even larger deviation from the true event rate. This scenario results in a 16% event rate for those patients averaging uncontrolled BP and an 8.7% event rate for those averaging contro lled BP. Simultaneously, th e percentage of all events per category contributed by patients whos e average was only based on the first year of follow-up diverged further from the expected 35.7%, with 62.5% of all events within patients 55

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whose average BP over follow-up was uncontrolled resulting from patients who had an event at the end of the first year, and onl y 25% of all events in patients with an average controlled BP attributable to patients who had their event af ter one year. Model D demonstrates, that when patients switch BP categories evenly, that is wh en as many patients beco me uncontrolled after one year as achieve BP control, calculated even t ratesas in scenario A where patients do not switch between categories at allma tch expected event rates. Scenario E demonstrates that not the proportional change between cate gories is responsible for the proportion of events that occur in the first year but rather the absolute number of patients with a change in BP categories. While the proportions of patients who swit ch categories in scenario E are identical (60% in each group), the absolute number of patient s who switch from uncontrolled to controlled is double the number of patients that switch from controlled to uncontrolled since twice as many patients started follow-up in the uncontrolled group. Overall, model E results in 45.5% of all events within the uncontrolled group from the first year of follow-up. Lastly, Scenario F, in which all patients start with uncontrolled BP and thus, change is by defin ition directed for the first year of follow up, results in 62.5% of all events within the uncontrolled group resulting from the first visit compared to 0% of all events in the controlled group from the same time period (since no patients with uncontrolled BP were at risk during the first year). To show the consequences of using the averag e BP control over follow-up as the predictor of cardiovascular risk, we calcula ted the relative risks to experience an event comparing patients with an uncontrolled average over follow-up to patients with a controlled average over follow up. The relative risks were calculated by dividing the absolute risk (e vent rate per patient year) of uncontrolled patients over the absolute risk of patients with controlled SBP over follow-up. Absolute risk estimates were obtained by dividi ng the number of events that occurred in each 56

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group by the person years of follow-up in the respective BP category based on the average BP over follow up (e.g., a patient who was uncontrolle d during year one and controlled for the remaining two years contribute s all 3 years of follow-up to the uncontrolled SBP group). Of note, the true relative risk is 1.0, since the even t rates used for the simulation were identical between groups at 10% per patient per year. Scenarios A and D, the scenarios that show equal numbers of patients in both average groups after follow-up (i.e., lack directed change of the measure) accurately show relative risks of 1.0. In contrast, scenarios B and C, that both simulate a directed change of patients from uncontrolled to controlled average BP over follow-up as a result of higher rates of change between groups from uncontro lled to controlled BP, show relative risks of 1.26 and 1.84, respectively. However, scenario E in which pati ents change between groups in equal proportions as in scenario D, but shows a directed net cha nge of subjects resulting from regression to the mean (since twice as many patients start followup in the uncontrolled group with both groups having equal rates of change), es timates a relative risk of 1.59, similar to scenarios B and C. Lastly, scenario F, that at baseline only includes patients with uncontrolled BP and thus shows the strongest possible directed change of patient s between groups, estimates the largest relative risk with 2.39. Scenarios A to F show that even w ith identical true event rates per year of followup, the mere fact that a directed change in BP cont rol exists, leads to an ov erestimation of risk in the categories that lose patients and to an underes timation of risk in thos e categories that gain patients. In contrast, Table 4-4 shows the results of the equivalent six simulations, when the denominator (person time) of the absolute risk estimates for each BP category is time-dependent. In these simulations, a patient who started with uncontrolled BP at baseline and achieved blood 57

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pressure control for years two and three, contribu tes one person year to the total person time in uncontrolled BP and two person years to the total person time in controlled BP (in the average calculation the same patient contri butes all three years to the total person time in controlled BP since his average over the entire follow-up is cont rolled). Notably, when using this updated mean SBP, the simulations under all scenarios correct ly estimate the true relative risk of 1.0. The results of these simple simulations help explain the observed differences between the Cox proportional hazards regressions with av erage SBP over follow-up (Figure 4-15) and updated mean SBP (Figure 4-19). In the simulation we observe a correlation between the magnitude of the observed bias in Scenarios B and C and the proportion of total events within each category that resulted from the patients with only one year of follow-up at their event time. The higher this proportion, the higher was the observ ed relative risk (i.e., bias, since the true RR is 1.0). Figure 4-20 illustrates within INVEST the calculation of bias introduced by the Cox model using the average SBP, expressed as the percent difference from the hazard ratio obtained by the time-dependent Cox model using the update d mean SBP. The largest bias exits in the highest two SBP categories where the C ox model using the average over follow-up overestimates the hazard ratios by 34% and 56%. Figure 4-21 shows for INVEST within categories of average blood pressure over followup the proportion of total events that were contributed by patients based on thei r number of observed visits at the time of the event. Figure 4-21 shows that patients in the highest two and the lowest average SBP categories were considerably more likely to have their average based on only the baseline visit (i.e., their event occurred before the second visit). Figure 4-22 combines data generated by Figures 4-20 and 4-21 and plots the bias of the Cox model using the average SBP (Figure 4-20) and the proportion of events resulting from 58

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patients with only two observed visits (Figure 4-21) in the same graph by SBP category. As observed in the simulation, the bias resulting from using an average over follow-up correlates with the percentage of events after the first follow-up period, st rongly suggesting, that the higher hazard ratios obtained from the Cox model using average SBP over-follow up are indeed resulting from a bias analogous to the bias simula ted in scenarios B, C, E, and F of Table 4-2. Of note, the time-weighted average is equally affected by this suggested bias. However, the impact of the bias is likely attenuated since observations who c ontribute strongest to the bias (patients who experience events early) receive small weights compared to patients with longer follow-up times. Marginal Structural Models The first part of this section intends to e xpand on the analyses of the prior sections by using a marginal structural Cox model to estimate the effect of SBP on the risk for cardiovascular events control ling for potential time-dependent confounding by antihypertensive drug use. However, instead of the seven SBP categories used in the previously presented models, a binary operationalization of SB P (controlled vs. uncontrolled, with controlled defined as SBP< 140 mm Hg) was used to accommodate current limitations in the method. Note that 2038 patients with extremely low SBP values (< 110 mm Hg at any visit during follow-up) were excluded to allow the use of a binary SBP variable (required by the marginal structural Cox model) even though the relationship between SBP and cardiovas cular outcomes follows a U shape (Figures 412 to 4-19). Time-dependent use of antihypertensi ve drugs was operationaliz ed by the number of total antihypertensive drugs a nd the number of study antihyper tensive drugs (defined as antihypertensive drugs that were part of the INVEST protocol) at baseline, each follow-up visit, as well as lagged drug variables that, at each visit other than baseline, represent the values of the respective prior visit. The second part of th e section aims to estimate the effect of 59

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antihypertensive drug use contro lling for time-dependent confounding by SBP. Antihypertensive drug use was operationalized as a ggressive (more than two total antihypertensive drugs) versus standard (two or less total an tihypertensive drugs) antihyperten sive therapy, with additional definitions used in a sensitivity analysis. SBP was operationalized as lo w (lower than 120 mm Hg); normal (120 mm Hg to lower than 140 mm Hg ); and high (equal or higher than 140 mm Hg). Effect of Systolic Blood Pressure Control Table 4-5 shows the result of the inverse probability of tr eatment weighted Cox model (marginal structural Cox model) compared to the equivalent standard time-dependent Cox model. Both models show a significantly re duced hazard for patients with controlled SBP compared to patients with uncontrolled SBP. Th e standard model estimates a 46% (95% CI 40%52%) reduction in the hazard for a cardiovasc ular event while the inverse probability of treatment weighted model estimates an almost identical reduction of 45% (95% CI 39%-50%). There was no significant difference between the estimates of both models. A significant difference between the models would support the presence of a time-dependent confounding effect of antihypertensive treatment (i.e., a non SBP mediated eff ect of aggressive antihypertensive treatment as defined). Effects of Antihypertensive Drugs Tables 4-6 provides an inverse probability of treatment weighted estimate for the effect of aggressive (more than two concurrent tota l antihypertensive drugs ) versus standard antihypertensive treatment (two or less concurrent total antihyper tensive drugs), compared with estimates from the equivalent standard time-d ependent Cox model. The standard Cox model estimated no difference in cardiovascular risk between the treatment with aggressive and standard antihypertensive therapy (HR 0.96, 95% CI 0.87-1.07). In contrast, the inverse 60

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probability of treatment weighted Cox model estimated a significant 19% (95% CI 8%-29%) reduction in the hazard of an outcome event for patients treated with aggressive antihypertensive therapy. However, the two results have overlap ping 95% confidence interv als and thus, are not significantly different from each other. A signifi cant difference between the two estimates would suggest that time-dependent confounding by SBP control substantially alters the estimate of the effect of receiving aggressive antihypertensive treatment. Table 4-6 shows the results of a sensitivity analysis conducte d to assess whether and by how much the results were influenced by the de finition of aggressive antihypertensive therapy. As in the original analysis (Table 4-6), the eff ect of aggressive versus standard antihypertensive treatment was assessed by estimating both a standa rd Cox model and a marginal structural Cox model. Four additional definitions of aggressi ve antihypertensive therapy were assessed, (1) more than one total antihypertensive drug, (2) more than three total anti hypertensive drugs, (3) more than one antihypertensive study drug, and (4 ) more than two antihypertensive study drugs. Regardless of the definition used for aggressive antihype rtensive treatment, all four comparisons estimated a larger beneficial effect for aggres sive antihypertensive ther apy from the marginal structural Cox model compared to the standard model. As in the primary analysis, the difference be tween the models failed to reach significance in three of the four models. The analyses that de fine aggressive antihyper tensive treatment as the concomitant use of more than three total anti hypertensive drugs found the hazard ratio estimated from the marginal structural Cox model (H R 0.79, 95% CI 0.71-0.89) to be significantly lower than the one estimated by the standard model (HR 0.98, 95% CI 0.90-1.07). The analysis defining aggressive antihyperten sive therapy as the concomitant use of more than one study antihypertensive drug found a borderline significant difference between the models with an HR 61

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estimate of 0.61 (95% CI 0.54-0.68) for the margin al structural Cox model and 0.73 (95% CI 0.67-0.80) for the standard time-dependent Cox model, respectively. Table 4-1. Composition of the INVEST Cohort at Baseline Variable N=22576 Demographic Age, mean (SD), years 66.1 (9.8) Women 11770 (52.1) Race/Ethnicity White 10925 (48.4) Black 3029 (13.4) Hispanic 8045 (35.6) Other 577 (2.6) Calcium Antagonist Strategy 11267 (49.9) Condition Myocardial infarction 7218 (32.0) Stroke/transient ischemic attack 1629 (7.2) Congestive Heart Failure 1256 (5.6) Diabetes 6400 (28.4) Renal impairment 424 (1.9) Peripheral vascular disease 2699 (12.0) CABG 6166 (27.3) Smoking (ever) 10454 (46.3) Abbreviations: SD, Standard deviation; CABG, Coronary artery bypass graft. Unless indicated otherwise, values express numbers (percentage). 62

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63 Table 4-2. Comparison of models Model Hazard Ratio at SBP <110 mm Hg Minimum Hazard Ratio (at SBP category) Hazard Ratio at SBP 160 mm Hg Generalized R2 Baseline 1.64 1.00 (130 to <140 mm Hg) 1.17 0.059 Average over follow-up 1.80 (1.88*) 0.96 (120 to <130 mm Hg) 2.80 (2.92*) 0.070 Time-weighted average 1.41 1.00 (130 to <140 mm Hg) 2.54 0.039 Time-dependent (prior) 1.57 1.00 (130 to <140 mm Hg) 1.59 0.061 Time-dependent (next) 1.16 (1.59*) 0.73 (120 to <130 mm Hg) 2.26 (3.10*) 0.071 Updated mean 1.61 1.00 (130 to <140 mm Hg) 1.80 0.062 RR from Poisson 1.50** 1.00** (130 to <140 mm Hg) 1.57** n/a *Compared to the lowest risk category, ** Relative risk

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Table 4-3. Simulation of six scenarios using average over follow-up BP Status 1st Year of Follow-up 2nd & 3rd Years Average Over Follow-up N (baseline) Events Change in BP status No change in Bp status N (year 2) Events Total Person Time* Total Events Event rate per patient year Percentage of events from 1st year Relative Risk Scenario A Uncontrolled 100 10 0 90 90 18 280 28 10% 35.7 1.0 Controlled 100 10 0 90 90 18 280 28 10% 35.7 1.0 Scenario B Uncontrolled 100 10 30 60 60 12 190 22 11.6% 45.5 1.26 Controlled 100 10 0 90 120 24 370 34 9.2% 29.4 1.0 Scenario C Uncontrolled 100 10 60 30 30 6 100 16 16% 62.5 1.84 Controlled 100 10 0 90 150 30 460 40 8.7% 25 1.0 Scenario D Uncontrolled 100 10 60 30 90 18 280 28 10% 35.7 1.0 Controlled 100 10 60 30 90 18 280 28 10% 35.7 1.0 Scenario E Uncontrolled 200 20 120 60 120 24 380 44 13.8% 45.5 1.59 Controlled 100 10 60 30 150 30 460 40 8.7% 25 1.0 Scenario F Uncontrolled 100 10 60 30 30 6 100 16 16% 62.5 2.39 Controlled 0 0 0 0 60 12 180 12 6.7% 0 1.0 64 *in average over follow-up controlled vs. uncontrolled

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65 Table 4-4. Simulation of six scenarios using updated mean BP Status 1st Year of Follow-up 2nd & 3rd Years Average Over Follow-up N (baseline) Events Change in BP status No change in Bp status N (year 2) Events Total Person Time* Total Events Event rate per patient year Percentage of events from 1st year Relative Risk Scenario A Uncontrolled 100 10 0 90 90 18 280 28 10% 35.7 1.0 Controlled 100 10 0 90 90 18 280 28 10% 35.7 1.0 Scenario B Uncontrolled 100 10 30 60 60 12 220 22 11.6% 45.5 1.0 Controlled 100 10 0 90 120 24 340 34 9.2% 29.4 1.0 Scenario C Uncontrolled 100 10 60 30 30 6 160 16 16% 62.5 1.0 Controlled 100 10 0 90 150 30 400 40 8.7% 25 1.0 Scenario D Uncontrolled 100 10 60 30 90 18 280 28 10% 35.7 1.0 Controlled 100 10 60 30 90 18 280 28 10% 35.7 1.0 Scenario E Uncontrolled 200 20 120 60 120 24 440 44 13.8% 45.5 1.0 Controlled 100 10 60 30 150 30 400 40 8.7% 25 1.0 Scenario F Uncontrolled 100 10 60 30 30 6 160 16 16% 62.5 1.0 Controlled 0 0 0 0 60 12 120 12 6.7% 0 1.0 updated mean controlled vs. uncontrolled

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Table 4-5. Inverse probabil ity of treatment weighted estimates fo r the causal effect of controlled SBP on primary INVEST primary outcome event Hazard Ratio 95% Confidence Interval Standard Cox model 0.54 0.48-0.60 Marginal Structural Cox Model 0.55 0.50-0.61 SBP control is defined as SBP < 140 mm Hg; patien ts who had SBP of <110 mm Hg at any visit were excluded from the analysis (n=2038) Table 4-6. Inverse probability of treatment weighted estimates for the effect of receiving more than two total antihypertensive drugs on primary INVEST primary outcome event Hazard Ratio 95% Confidence Interval Standard Cox model 0.96 0.87-1.07 Marginal Structural Cox Model 0.81 0.71-0.92 Table 4-7. Inverse probability of treatment weighted estimates for the causal effect of receiving various numbers of total an tihypertensive drugs on INVEST primary outcome event Hazard Ratio 95% Confidence Interval > 1 total antihypertensive drug Standard Cox model 0.89 0.70-1.13 Marginal structural Cox model 0.83 0.64-1.06 > 3 total antihypertensive drugs Standard Cox model 0.98 0.90-1.07 Marginal structural Cox model 0.79 0.71-0.89 > 1 study antihypertensive drug Standard Cox model 0.73 0.67-0.80 Marginal structural Cox model 0.61 0.54-0.68 > 2 study antihypertensive drugs Standard Cox model 0.78 0.71-0.85 Marginal structural Cox model 0.72 0.64-0.81 66

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0 5000 10000 15000 20000 25000 0612182430364248 Time [months] N observed & imputed observed Figure 4-1. Patients remaini ng in the study at each visit 130 135 140 145 150 155 0612182430364248 Time [months]SBP [mm Hg] observed & imputed observed Figure 4-2. Mean systolic blood pressure over follow-up (observe d vs. imputed data) 67

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0% 5% 10% 15% 20% 25% 30% 35% 0612182430364248 Time [months]Percentage <110 mm Hg 110 <120 mm Hg 120 <130 mm Hg 130 <140 mm Hg 140 <150 mm Hg 150 <160 mm Hg >160 mm Hg Figure 4-3. Percentage of patients w ithin each SBP category over follow-up 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 0612182430364248 Time [months]Percentage <110 mm Hg 110 <120 mm Hg 120 <130 mm Hg 130 <140 mm Hg 140 <150 mm Hg 150 <160 mm Hg >160 mm Hg Figure 4-4. Percentage of patient s within each SBP category who were not within the same SBP category at the prior visit 68

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0 1 2 3 4 0612182430364248 Time [months]Number total antihypertensive drugs study antihypertensive drugs Figure 4-5. Number of total antihypertensive drugs and antihypertensive study drugs over follow-up 0% 10% 20% 30% 40% 50% 60% 0612182430364248 Time [months]Percentage Atenolol HCTZ Verapamil Trandolapril Figure 4-6. Percentage of patients on each individual study drug over follow-up 69

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0% 10% 20% 30% 40% 50% 60% 70% 0612182430364248 Time [months]Percentage 0 study drug 1 study drug 2 study drugs 3 study drugs Figure 4-7. Number of INVEST study drugs over follow-up 0% 5% 10% 15% 20% 25% 30% 35% 40% 45% 0612182430364248 Time [months]Percentage 0 antihypertensive drug 1 antihypertensive drug 2 antihypertensive drugs 3 antihypertensive drugs 4 antihypertensive drugs 5 antihypertensive drugs >5 antihypertensive drugs Figure 4-8. Number of total anti hypertensive drugs over follow-up 70

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0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% 0612182430364248 Time [months]Percentage 0 study drug 1 study drug 2 study drugs 3 study drugs Figure 4-9. Percentage of patients on a speci fic number of antihypert ensive study drugs who were not on the same number of antihype rtensive drugs at the prior visit 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% 0612182430364248 Time [months]Percentage 0 antihypertensive drug 1 antihypertensive drug 2 antihypertensive drugs 3 antihypertensive drugs 4 antihypertensive drugs 5 antihypertensive drugs >5 antihypertensive drugs Figure 4-10. Percentage of patie nts on a specific number of anti hypertensive drugs who were not on the same number of antihyperten sive drugs at the prior visit 71

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Figure 4-11. Cumulative incidence of the primary outcome event over follow-up 0.5 1 1.5 2 2.5 <110 (n=205) 110 to <120 (n=667) 120 to <130 (n=1777) 130 to <140 (n=3117) 140 to <150 (n=4892) 150 to <160 (n=4514) 160 (n=7404) Systolic Blood Pressure Category [mm Hg]Hazard Ratio Figure 4-12. Hazard ratios for an INVEST pr imary outcome event by categories of baseline systolic blood pressure. 72

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0.5 1 1.5 2 2.5 3 3.5 <110 (n=190) 110 to <120 (n=1500) 120 to <130 (n=6403) 130 to <140 (n=7259) 140 to <150 (n=3983) 150 to <160 (n=1761) 160 (n=1480) Systolic Blood Pressure Category [mm Hg]Hazard Ratio Figure 4-13. Hazard ratios for an INVEST pr imary outcome event by categories of average systolic blood pressure over follow-up. 0.5 1 1.5 2 2.5 <110 (n=190) 110 to <120 (n=1500) 120 to <130 (n=6403) 130 to <140 (n=7259) 140 to <150 (n=3983) 150 to <160 (n=1761) 160 (n=1480) Systolic Blood Pressure Category [mm Hg]Hazard Ratio Figure 4-14. Hazard ratios for an INVEST primary outcome event by categories of average systolic blood pressure over follo w-up, weighted by time of follow-up. 73

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0.5 1 1.5 2 2.5 <110110 to <120120 to <130130 to <140140 to <150150 to <160 160 Systolic Blood Pressure Category [mm Hg]Hazard Ratio Figure 4-15. Hazard ratios for an INVEST prim ary outcome event by categories of systolic blood pressure (updated; carried fo rward from last observed visit) 0.5 1 1.5 2 2.5 <110110 to <120120 to <130130 to <140140 to <150150 to <160 160 Systolic Blood Pressure Category [mm Hg]Hazard Ratio Figure 4-16. Hazard ratios for an INVEST prim ary outcome event by categories of systolic blood pressure (updated; fr om next observed visit) 74

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0.5 1 1.5 2 2.5 <110110 to <120120 to <130130 to <140140 to <150150 to <160 160 Systolic Blood Pressure Category [mm Hg]Hazard Ratio Figure 4-17. Hazard ratios for an INVEST pr imary outcome event by categories of updated mean systolic blood pressure (time-dependent; updated at each visit) 0 10 20 30 40 50 60 <110 (1678 pt yrs) 110 to <120 (7289 pt yrs) 120 to <130 (22433 pt yrs) 130 to <140 (38621 pt yrs) 140 to <150 (48250 pt yrs) 150 to <160 (53815 pt yrs) 160 (60939 pt yrs)Systolic Blood Pressure Category [mm Hg]Incidence /1000 pt yrs Figure 4-18. Crude incidence of primary outcome events by SBP category 75

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0 5 10 15 20 25 30 <110110 to <120120 to <130130 to <140140 to <150150 to <160 160 Systolic Blood Pressure Category [mm Hg]Incidence / 1000 pt yrs Figure 4-19. Adjusted incidence of primary outcome events for White, female, US patients between the ages of 60 to 70 years by SBP category 11% -3% -11% 0% 14% 34% 56%-20% 0% 20% 40% 60% 80% 100% 120% 140% 160%<110110 to <120120 to <130130 to <140140 to <150150 to <160 160Systolic Blood Pressure Category [mmHg]Percent Bias0 0.5 1 1.5 2 2.5 3Hazard Ratio percent bias average over follow-up updated mean Figure 4-20. Bias of outcome event hazard rati os obtained average SBP compared to updated mean SBP 76

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0% 10% 20% 30% 40% 50% 123456789101112 Number of VisitsPercentage <110 mm Hg 110 <120 mm Hg 120 <130 mm Hg 130 <140 mm Hg 140 <150 mm Hg 150 <160 mm Hg >160 mm Hg Figure 4-21. Proportion of events within categor y of average SBP by number of observed visits at the occurrence of the event 0 10 20 30 40 50 60<110110 to <120120 to <130130 to <140140 to <150150 to <160 160Systolic Blood Pressure Category [mm Hg]Percentage of events from first follow-up period-20 -10 0 10 20 30 40 50 60Percent Bias average versus updated average Event % Bias % Figure 4-22. Bias and timing of events by category of SBP 77

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CHAPTER 5 DISCUSSION The present study shows that, in the Inte rnational Verapamil SR/Trandolapril Study (INVEST), estimates for the effect of SBP on cardiovascular morbidity and mortality vary significantly depending on the met hod of SBP operationalization. It further demonstrates that using the average SBP over follow-up as a predic tor of cardiovascular events systematically overestimates the risk associated with extreme SBP categories. Causal analyses suggest that time-dependent confounding by SBP may bias estimates of treatment effects, but provides no evidence of time-dependent confounding by treatment in the estimation of risk associated with SBP control. However these analyses are consid erably restricted by limitations imposed by the statistical method, which necessitated significant simplifications of the data. Consequently, these results are only exploratory in nature. La stly, our study provides detailed longitudinal descriptions of SBP and antihypert ensive treatment patterns over the course of INVEST, which facilitate better understanding and interpreta tion of the presented inferential analyses. Descriptive Analyses: Antihypertensive Treatment and SBP in the INVEST Several observations from the descriptive an alyses deserve note. First, when choosing specific time points of follow-up to report BP or other variables (e .g., percentage of patients with BP control at month 24),4 a proportion of patients (those who are uncensored but do not have an observation at the time-point) is not included in the estimate. Figur e 4-1 shows that for the first 24 months of follow-up this proportion is rather significant ranging from a bout 20% to more than 35% of patients depending on the sp ecific visit chosen to report. As shown in Figure 4-2 there may be differences between results reported for patients with an observation compared to the entire uncensored cohort (with imputed values carried forward from the last observation for patients who do not have an observation at the tim e-point of interest). A decision between the 78

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two approaches resembles a trade off between a possi ble selection bias that occurs if the actually observed patients at a specifi c point of follow-up differ syst ematically from the uncensored patients who lack this observation, and a measurem ent bias that would occur if the imputed data for patients who lack the observation of interest is systematically different from the actual, unmeasured value for the variable of interest (e.g., if there is reducti on in mean SBP for the cohort including those lacking sp ecific observations, then imputation of missing values from the last observation would systematically overestim ate the true SBP value). If feasible, both approaches should be presented to best reflect the true situation at specific points of follow-up. Another consideration may involve choosing the descriptiv e approach that is in line with the inferential statistical methods to be used. In th e present study, all inferential analyses implicitly or explicitly use imputed data and thus the majo rity of descriptive information was presented for these data. Second, after mean SBP for the INVEST cohort dropped about 15 mm Hg over the first six months of follow up, it remained rather stable throughout the remaining 42 months, never diverging more than two to three mm Hg from the value observed at si x months (Figure 4-2). Consequently, the proportion of patients within th e respective SBP categories was stable after the initial six months. However, the proportion of individual patients who experienced a change in SBP categories between visits was continuous ly high and remained between 30% and 60%, depending on SBP category, throughout the enti re follow-up. Thus, the rather stable SBP displayed by the INVEST cohort as a whole afte r the initial six month of follow-up, was not the result of equally stable SBP on the individual level but rather the result of a constant undirected change (steady state) between categories. This ob servation likely reflects natural variation as well as measurement error in the assessment of SBP and shows that careful examination of the 79

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data is necessary to distinguish between a stable mean over follow-up that is based on a stable value on the patient level and significant undirected individual variation as observed in the INVEST. This distinction has profound consequences for the choice of an appropriate method of analysis. Standard regression methods using fixed values for SBP may be used when there is little individual variation or measurement error, while time-dependent methods are likely more appropriate to capture and incorporate short term individual variation and its potential effects on outcomes. Third, descriptive analyses as presented in th e first section of Chapter 4 illustrate the limitation of intend to treat (ITT) analyses in randomized controlled trials. While ITT is necessary to preserve randomization, it does introduce misclassification (e.g., at the 24 month visit less than 80% of uncensored patients were still receiving one of the first line study drugs atenolol or verapamil (Figure 4-6)). The widespread utiliza tion of nonstudy antihypertensive drugs (more than a quarter of all antihypertensive medication in INVEST were nonstudy drugs) will likely also result in the attenuation of diffe rences between treatment strategies. Thus, an as treated analysis as performed in the present study should be c onsidered complementary to the original ITT analysis, es pecially when the nature of the results suggesting noninferiority are considered. Operationalization of SBP The present study confirms findings from a prior report which suggested that in the INVEST both low and high blood pressures are associ ated with an increase in the risk for the primary outcome.31 While varying in the magn itude of the risk associated with high and low SBP categories, all SBP models pr esented in our study support this observation. The previously published report, which modeled the average syst olic and diastolic BP over follow-up, suggests that the relationship between BP and the INVEST primary outcome event follows a J-shape with 80

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its nadir for SBP at 120 to 130 mm Hg. However, it is important to note that our study presents evidence suggesting that the use of average BPs over follow-up may lead to biased estimates of association. Depending on the SBP model used, our study finds the relationship between SBP and cardiovascular outcomes varyin g between a J, V, and a revers e-J-shape with the nadir at either 120 to 130 mm Hg, or 130 to 140 mm Hg. These findings di ffer significantly from other reports that have consistently suggested a l og linear increase of car diovascular risk with increasing SBP (Figure 2-4). However, the INVEST study population differs significantly from a general hypertensive po pulation by including only patients wi th documented CAD. In patients with CAD low SBP (and more importantly DBP, which was not included in the analyses of our study) may compromise coronary perf usion and cause cardiac ischemia.31 While it is important to note that neither the prev ious INVEST report nor our st udy, both post hoc observational analyses, can establish that lo w blood pressures causes cardiova scular outcomes, they do show that CAD patients with low SBP are at an increa sed risk to experience cardiovascular outcomes and thus suggest caution in lowering SBP in hypertensive patients with CAD. Modeling Assumptions The 7 models presented in Table 4-2 make implicit assumptions about the mechanism by which SBP affects the risk for cardiovascular ev ents. The following section will summarize and contrast these assumptions of how SBP over time affects cardiovasc ular outcomes. At one end of the spectrum is the baseline SBP model. By ig noring any changes in SBP after the beginning of follow-up, the baseline SBP model assumes that SBP at a single historic poi nt in time (baseline) acts as a proxy for a patients cardiovascular risk, while short te rm changes in SBP after patient enrollment do not significantly ch ange the cardiovascular risk th at has been defined by numerous years of SBP history. In contrast, the average SBP model assume s that both historic and actual SBP values affect cardiovascular risk. The resp ective contributions of historic and actual SBP 81

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values, however, are difficult to quantify sin ce they are dependent on the length of follow-up. Specifically, the contribution of recent SBP values diminishes as follow up time increases. In order to adjust for the fact that the average SB P model would apply the sa me weight to patients who were followed over multiple years as to patients who were followed for only a short period of time, the time-weighted average SBP model was introduced by weighing each subjects observation by its individual follow-up time. As opposed to the previous models that rely either completely (baseline model) or partially (both average SBP models) on historic SBP values the two short term time-dependent models lie at the other end of the spectrum of possible assu mptions. These models assume that there is no effect of SBP history but rather assume that SB P at each specific point in time determines the risk for a cardiovascular even t at this moment in time. The short term time-dependent SBP models do not differ in these modeling assumptions but rather in the choice of the best available SBP measurement at a given point of follow-up. Th e prior visit model assumes that SBP at each time point is best approximated by the last m easured SBP observation prior to this time point while the following visit model assumes that the best approximation of SBP for the same time point is the first observed measurement after this point in time (Figure 32). The rationale for the prior model is straightforward: for each time point it simply uses the last measured SBP value. The rationale for the next visit model is slightly more complex: since antihypertensive treatment is potentially changed at each vi sit (after response to treatment has been assessed by measuring BP), SBP may change shortly afte r the visit and thus, true SBP at a given point after this visit may actually be better reflected by the SBP observed at the next visit. Howe ver, this approach is potentially biased because for patients who experience an event, no SBP values are available after the event. As a consequence the next visit model treats time periods directly before events 82

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systematically different than all other time pe riods between visits a nd therefore may produce a biased estimate. The updated average model combines aspects of th e previous models in that it incorporates SBP history by using an average SBP but also allows change over time by calculating a new (thus time-dependent) average at each observe d follow-up time. Last, the Poisson model makes assumptions that closely resemble those of the time-dependent prior visit model as it assigns patient time to the last observed SBP category. The remainder of this section discusses the SBP models presented in Figures 4-14 to 4-19 in more detail. Several comparisons between SBP models are of specific interest. Baseline SBP Model Compared to all other models, the base line SBP model (Figure 4-14) estimates a substantially smaller risk associated with the tw o highest SBP categories, while its risk estimates for low SBP categories are of a similar magnitude as the other models. This observation can be explained by considering what happened to the average SBP during the INVEST. Since the INVEST protocol was aimed at controlling pati ents SBP, most patients who had high SBP at baseline experienced a reduction in SBP in the first months follow up as shown in Figures 4-2 and 4-3. Thus, for patients with high SBP at baseline, the baseline SBP value poorly represents the true SBP over follow-up (which is likely to be lower than baseline) and as a consequence models that use the baseline value to predict th e risk of an outcome ev ent will underestimate the risk for patients with high baseline SBP. In contrast, this systematic misclassification affects patients with a low baseline SBP to a much lesser extend since these patients were likely to remain in a low SBP category. It is therefore not surprising that the baseline SBP model is comparable in its risk estimates for low SBP categories to the other presented models but it results in much lower estimates for the highest SBP categories. 83

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Average SBP Models On the surface, the use of an average of a surrogate over follow-up to predict the risk of an outcome of interest has many appealing featur es. Averages over follow-up allow simple modeling without the need to e xplicitly incorporate time-dependent changes in the measure. They incorporate implicitly and to some exte nd intuitively such timedependent changes and create a single value for every subject that al lows straightforward incorporation in standard regression models. As a result, averages over followup have been used to estimate the effects of surrogates on clinical outcomes in various disease states such as diabetes, hyperlipidemia, and hypertension.31, 34, 35 However, the simulations presented in Chapter 4 demonstrate that the apparent simplicity of this approach comes at a price. Consider able bias may be introduced when modeling an outcome with an average over follow-up (Table 4-3). Specifically, for SB P categories that (1) include a large proportion of pa tients at baseline and (2) include fewer and fewer patients over the course of follow up, overestimation of the true risk associated with these SBP categories is likely. In the INVEST, the above conditions are met for the highest three SBP categories. Table 4-3 shows that these three SBP categories at baseline include th e largest proportions of patients (with SBP >160 mm Hg including the single largest propo rtion) and include continuously fewer patients over the subsequent six months of fo llow-up (with the most significant reduction in patients observed in the category of SBP >160 mm Hg). As a result, the risk for the highest three SBP categories is systematically overestimat ed by the average SBP model. Specifically, compared to the updated-mean model, the fixe d average model overestimates the risk for a cardiovascular event by 56%, 34%, and 14% for SBP >160 mm Hg, SBP 150 to 160 mm Hg, and SBP 140 to 150 mm Hg, respectively. The update d mean model is selected as the comparator because like the average model, it uses an averag e of SBP to predict ca rdiovascular outcomes, 84

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but as opposed to the average model does not introduce bias as shown by the second set of simulations in Chapter 4 (Table 4-4). The weighted average model (Figure 4-16) estim ates results that lie between the average model and the updated mean model. This is ex pected since the weighted average model is subject to the same bias as the average model (it uses the identical averages) but reduces the impact of the bias by weighti ng observations according to the length of their follow up time. Since observations with events in the first follow-up period (a nd thus rather short follow-up time) are most responsible for the bias as discussed above, such weighting will, while not eliminating the bias, reduce its magnitude. Short Term SBP Models (Time-Dependent) The two short term time-dependent SBP mode ls differ substantially in their results. Compared to the model that for each period betw een visits carries forward the SBP value from the first visit (updated previous model), the model that utilizes the SBP fr om the latter visit for the same interval (updated next model) estimat es higher risks associated with SBP categories above 140 mm Hg and lower risks for SBP categor ies below 130 mm Hg. Considering that mean SBP in the INVEST was lowered substantially over follow-up, this pattern is expected. The timedependent Cox model used in our analyses compar es at each time an event occurs, the SBP of a patient who experiences this even t with all other patients SBP at the same time. Thus, a shift from the SBP measured at the visit prior to th e event time to the SBP measured at the visit following the event will on average reduce the SBP of the patients at risk (i.e., those who have not experienced an event and are uncensored). Ho wever, the SBP of patients with events are unaffected by the shift because (see Figure 3-2) pa tients are censored at the time of the event and therefore no post-event SBP measurements exis t. Consequently, compared to the updated previous model, the updated next model compares identical SBP values for patients with events, 85

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to on average lower SBP values for patients without events and therefore overestimates the risk for high SBP categories and underestimates the risk for low SBP categories. When comparing the two short term time-depe ndent models to the updated mean model it becomes apparent, that the prior models results ar e very similar to the up dated mean model. The similarity of results is somewhat surprising considering the significan t differences in SBP operationalization. While the updated prior model incorporates only the most recently observed SBP values, the updated mean model does incorpor ate both historic and current SBP values. Both models would therefore be expected to pr ovide differing results. The similarity of both approaches in the INVEST may result from the limited follow-up time and the relative stability of mean SBP after the initial six months of fo llow-up, but may not generalize to different followup periods or disease states. Even so, in the INVEST it is reassuring that both unbiased timedependent models provide similar estimates for th e association of SBP w ith the cardiovascular risk. More complex modeling approaches that combine short term time-dependent SBP measures with one or more lagged historic SBP values (i.e., BP at each time point would be represented by the most recent SBP as well as SBP measures from fixed time intervals prior to the most recent visit) are possible, however, su ch models are more difficult to interpret since SBP values with different lag times may be associ ated with different estimates of risk, the and thus limited in their clinical utility. Model Selection The question arising from the presented m odels is which of the presented modeling approaches should ultimately be us ed to estimate the effects of SB P on the risk of cardiovascular outcomes, or more generally the effects of a surrogate on clinical outcomes? While no single correct answer to this question existsany sp ecific decision will always be influenced by a 86

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multitude of factorsa number of points deserve consideration and should guide the selection of modeling approaches. First and foremost, the assumptions underlying the modeling approach should be closely aligned with the hypothesi zed biological mechanism. If the hypothesized biological mechanism suggests that a surrogate ex erts its effect on clinical outcomes in an immediate fashion, a short term time-dependent model may be pref erable. However, the absence of established biological models as well as lim itations in data availability and quality may complicate this decision. If no established biological models exist, multiple models with varying assumptions should be produced and compared. If da ta availability or quality does not allow the selection of a preferred model, the consequences and limitations of choosing a different model should be explicitly discussed. When data availability permits, our study sugge sts that an updated mean model should be considered over more extreme (baseline or short term time-dependent) models since it incorporates both historic and current values of the surrogate. More complex models that use both current and lagged surrogate values may also be appropriate (especially if overall follow-up is extremely long and as a consequence recent SB P values would contribu te less and less to the updated mean as time progresses), but results obtained from such models are commonly difficult to interpret and communicate. A second general consideration should be the avoidance of models that likely introduce bias. As discussed above this will generally be the case for baseline models if an intervention or natural progression of the diseas e leads to a directed change of the surrogate over follow-up, which in turn leads to a systematic overor und erestimation of the true value of the surrogate over follow-up. Even without such directed change the use of a single measurement at baseline 87

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may introduce an estimate that, due to the effect of measurement error, is biased towards the null (regression dilution bias).36, 37 The use of a fixed average over follow-up w ill under most conditions introduce bias and should be generally avoided. If the data allow calcu lation of an average (i.e., surrogate values are not limited to baseline), a time-dependent updated mean model should be used instead of a fixed average model. Lastly, the choice between the two short term time-dependent models is difficult. While the updated next model may provide more precise approximation of a surrogate than the updated previous model, especially when change s in drug therapy are co mmon at visits and timeintervals between visits are long, the differentia l treatment of time peri ods before events may introduce bias. Whether the potentia l bias introduced in the updated next model through this differential treatment of time periods preceding events or the potential bias resulting from systematic measurement error in troduced by the updated next mode l is a greater threat to the validity of the estimate has to be evaluated in the context of each specific study. Unfortunately, the comparison of model diagnostics such as generalized R2 (a proxy for the fit of the model), is not helpful in the process of model selection. Unlike the R2 in linear regression models, the generalized R2 cannot be interpreted as the proportion of variation in the dependent variable that is e xplained by the covariates incl uded in the model but is only interpretable as a number between 0 and 1 that ge ts larger when the covariates are associated more strongly with the outcome.30 More importantly, the generalized R2, as all measures of model fit, does not distinguish between true associations and associations resulting from bias. Consequently, a biased model will gene rally produce a larger generalized R2 than an equivalent unbiased model. In our study, for instance, th e biased average model produces a larger generalized R2 than the unbiased updated mean model. 88

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These considerations regarding th e selection of models to estim ate the effect of a surrogate on a clinical outcome are not mere academic but rather have profound consequences for the establishment of treatment guidelines and clinical practice. Time-dependent Confounding The previous section suggests that the sele ction of a modeling approach for a surrogate measure has substantial consequences for the re sulting estimates of risk and shows that timedependent modeling approaches ar e preferable under most circumstances. However, the use of a time-dependent surrogate may introduce time-de pendent confounding by any type of treatment that has nonsurrogate mediated e ffects on the clinical outcome, affects the surrogate, and whose initiation is not independent of the surroga te. Such time-dependent confounding by treatment was not considered in the previously presented modeling approaches. Specifically, the previously presented time-dependent modeli ng approaches do not include ad justments for the concurrent use of antihypertensive medication and thus, may produce biased estimates of the effects of SBP on cardiovascular outcomes. Time dependent co nfounding would occur if antihypertensive drug use has effects on cardiovascular outcomes wh ich are not mediated by SBP control since initiation and change of antihypert ensive treatments is dependent on SBP control. For example, an increase in the number of antihypertensive dr ugs will at the same time increase the likelihood of SBP control and (assuming non-SBP mediated be neficial effects of an tihypertensive drugs on outcome) reduce the patients risk to experience an outcome event. Thus, a model that does not control for time-dependent confounding by antihyper tensive drug use will likely overestimate the beneficial effects of SBP control by attributing both the effects of SBP control and the beneficial effects of an increased number of antihypertensi ve drugs to SBP control. Controlling for timedependent confounding by antihypertensive drug use would therefore reduce the estimated beneficial effect of SBP control compared to the estimate obtained from a standard model. 89

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However, our results do not support the pres ence of a time-dependent confounding effect of antihypertensive treatment. Both the standard time-dependent Cox model and the marginal structural Cox model estimate an almost identical, strong benefici al effect of SBP control with HRs of 0.54 (95% CI 0.48-0.60) and 0.55 (95% CI 0.50-0.61), respec tively. If time-dependent confounding by treatment (i.e., a non-SBP mediated beneficial or detrimental effect of antihypertensive drugs) had been present, the HR estimated by the marginal structural model would have been expected to be closer to 1.0, (i.e., show a weaker association between SBP control and outcome). In other words, the two co mplementary analyses suggest that the type of antihypertensive treatment does not affect cardiovascular outcomes, as long as SBP is adequately controlled. However, it is important to note, that the drug effect was onl y operationalized as the number of antihypertensive total, and study drugs with no regard for drug class or dose, and that trandolapril, an antihypertensive with demonstrated outcome bene fits for patients with specific comorbidities, was per INVEST protocol prescribed to all patients with an indication. To our knowledge this is the first time that inverse probab ility of treatment weighting was used to obtain an estimate of the effects of a surrogate controlling for time-dependent confounding by treatment. Additional marginal structural models were cr eated to estimate the effects of aggressive versus standard antihypertensive treatment (mor e than two versus less two or less concurrent total antihypertensive drugs), controlling for time-dependent confounding by SBP. In this scenario, the fact that the aggressive treatment is more likely to be initiated in patients with uncontrolled SBP (confounding by indication), w ould lead to an unde restimation of the beneficial effect of antihyperten sive therapy (or, if the eff ects of such negative selection outweigh the beneficial e ffects of aggressive treatment, in th e estimation of a harmful effect of 90

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aggressive treatment) because uncontrolled SBP would at the same time increase the likelihood of treatment with aggressive antihypertensive ther apy and increase the risk for a cardiovascular event. The estimate for aggressive antihypertensive treatment obtained from the marginal structural model is lower than the estimate from the standard Cox model but the 95% CIs of both estimates overlap (HR 0.81, 95% CI 0.71-0.92 and HR 0.96, 95% CI 0.87-1.07 for marginal structural and the standard Cox models, resp ectively). However, while the models are not significantly different from each other, it is notew orthy that the marginal structural Cox model shows a significant benefit of aggressive antihype rtensive therapy, while the standard Cox model fails to show such benefit. Sensitivity analyses were conducted to assess the influence of the definition of aggressive antihype rtensive therapy on th e results. The marginal structural Cox models consistently estimate lower point estimates for the HR associated with aggressive antihypertensive therapy than the standard Cox models for all four a dditional definitions of aggressive antihypertensive therapy. Of the four definitions the differences between the two models were significant for one definition (aggres sive antihypertensive th erapy defined as more than three concurrent to tal antihypertensive drugs) borderline significant for another (aggressive antihypertensive therapy defined as more than one concurrent study anti hypertensive drug) and not significant for the remaining two definitions. Although the differences between the standard Cox models and the marginal structural Cox models did not reach statis tical significance in the main an alysis and three of the four additional analyses, the trend for a larger beneficial effect of aggressive antihypertensive treatment versus standard an tihypertensive treatment was consistent across all analyses. Assuming correct model specification and no viol ation of the assumptions necessary for the 91

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marginal structural Cox model, the estimate for the beneficial effect of aggressive versus standard antihypertensive therapy can be interpreted as the effect that would have been observed in a RCT that compared aggressive to standard antihypertensive treatme nt over the course of follow-up. Thus the estimate is causally interpre table and includes all pathways (including SBP mediated pathways) through which aggressive antihypertensive therapy tends to improve the clinical outcome, regardless of SBP valu es preceding the initia tion of aggressive antihypertensive therapy. These results are in both magn itude and direction comparable to prior studies that have used inverse probability of treatment weighted estimates to estimate unbiased effects of treatments in observational studies in the presence of time-dependent confounding. Specifically, an observational study that asse ssed the effectiveness of met hotrexate in patients with rheumatoid arthritis estimated a mortality HR of 0.6 (95% CI 0.4-0.8) using a standard timedependent Cox model and an mortality HR of 0.4 (95% CI 0.2-0.8) using a marginal structural Cox model that controlled for time-depende nt confounding by several prognostic factors. Another observational study evalua ted the aspirin component of the Physicians Health Study, a randomized controlled trial that evaluated the effectiv eness of aspirin in the prevention of cardiovascular disease. While the trial establ ished a strong reduction in first myocardial infarction in patients treated with aspirin, and was stopped early because of it, it failed to detect a significant beneficial effect of aspirin on cardiovascular mortality. At the time of the Physicians Health Study, the effectiveness of aspirin in th e prevention of secondary cardiovascular mortality already had been established and lead to increased use of aspirin in patients that had experienced a nonfatal cardiovascular event. The observational study reanalyzed the clinical trial data (similar to our study) disregarding the original random ization and controlling for time-dependent 92

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confounding by nonfatal cardiovascula r events using a marginal structural Cox model. The standard as treated model controlling for predicto rs of aspirin exposure at baseline as well as cardiovascular risk factors estimated a mort ality HR of 0.81 (95% CI 0.57-1.15), while the marginal structural Cox model that additiona lly controlled for time-dependent confounding by nonfatal cardiovascular events reduced the es timated HR to 0.74 (95% CI 0.48-1.15). Lastly, a study that assessed the effectiven ess of zidovudine in reducing mo rtality in patients with HIV found a significant detrimental effect of zidovudine using standard methods that did not control for time-dependent confounding by CD4 cell count (HR 2.3, 95% CI 1.9-2.8), but was able to show a beneficial effect of zidovudine using a marginal structural Cox model (HR 0.7, 95% CI 0.6-1.0). Of these three studies, on ly the study that investigated the effectiveness of zidovudine found a statistically significant difference betwee n the HR estimates obtained from a standard time dependent Cox model and a marginal structur al Cox model, but as in our study, all three studies estimated consistently higher effectiv eness of the treatment under study when a using marginal structural Cox model that controlled for time-dependent confounding by a risk factor for the clinical outcome that was at the same time a predictor of treatment initiation and subsequently affected by the treatment. Limitations The present study has several noteworthy lim itations. All analyses were conducted in a retrospective, observational de sign. While our study utilized the dataset of INVEST, a large international randomized controlle d clinical trial, the presente d analyses are post hoc and are independent of the initial randomization. Therefore our analysis of SBP cannot establish a causal association between SBP and cardiovascular ri sk. Unmeasured confounding factors may exist that affect SBP as well as cardiovascular risk. In addition, the generalizability of our study is limited to elderly hypertensive patie nts with CAD. Specifically, the increase in risk associated 93

PAGE 94

with lower SBP categories is likely not representative of a healthier popu lation of patients with uncomplicated hypertension. However, the INVEST population represents a large and important high risk population that has not been at the center of antihypertensive research efforts and therefore warrants compre hensive investigation. Another limitation of our study is the meas urement error inherent in the study of hypertension. Measurement error has been widely reported as a problem in the analysis of hypertension studies.38-40 While the INVEST protocol tried to minimize measurement error by providing standardized BP measur ement instructions following JNC-VI to all providers, a certain extend of measurement error is unavoidable. However, it is unlikely that the remaining measurement error is systematic. Random measur ement error may affect our results in ways other than reducing the precision of the provided results. If the absolu te magnitude of SBP variation increases with higher SBP values then the categorization of SBP into 10 mm Hg categories may affect our results in that the ob served variability in the continuous SBP measure would lead to a larger extend of variation in SBP categories at larger values of SBP. The use of marginal structural Cox models to adjust for time-dependent confounding through inverse probability of treatment weightin g introduces another set of limitations to the causal analyses in our study. Invers e probability of treatment weighti ng as to date established in statistical theory requires a numbe r of assumptions and a rather simple data structure. First, the independent variable of interest has to be binary. As clearly shown in Figures 4-12 to 4-19 the relationship between SBP and clin ical outcomes is more complex than our categorization of SBP into controlled versus uncontrolled. Although we excluded patients with very low SBP to account for the observed J-shape, our operationaliza tion of SBP is a rather poor representation of the data. The same applies to the complementar y analysis of antihypertensive drug use. Our 94

PAGE 95

study categorized antihypertensive drug use in a ggressive versus standard antihypertensive therapy defined as the use of three or more concurrent total antihypertensive drugs. This definition does not distinguish between specific drugs and drug classes and does not take dosing of each specific drug into account If treatment effects vary be tween specific drugs and doses, our model will not show these differences and rather produce an estimate reflective of the average treatment combinations used in the aggr essive and standard an tihypertensive therapy groups. Thus, our results are of limited value in aiding in the selection of specific antihypertensive drugs. However, we conducted f our additional analyses varying the definition of aggressive antihypertensive therapy to assess how sensitive our results are to the treatment definition and results were consis tent across all analyses. The fact that the marginal structural Cox model estimates a larger benefit for aggressi ve antihypertensive ther apy than the standard Cox model regardless of the drug number cutoff used to define aggressive antihypertensive therapy, shows that more antihypertensive drugs te nd to produce more beneficial outcomes than less antihypertensive drugs, when preceding SBP values that may influence the addition of antihypertensive drugs to an indi viduals treatment regimen are c ontrolled for. This beneficial effect is likely mediated through a more pronounced effect on SBP, since the results presented in Table 4-5 suggest the absence of nonSBP mediated treatment effects. Second the method requires the assumption, that once initiated, exposur e (in our analyses either SBP control, or aggressi ve antihypertensive therapy) is not discontinued until the end of follow-up or censoring. This assumption is not me t in the INVEST (Figures 4-4, 4-9, and 4-10). We therefore artificially altered the data in or der to meet the assumpti on of the model by keeping BP controlled after BP control was first achieved or keeping patients on aggressive antihypertensive therapy once the respective cutoff was reached. This was necessary, because 95

PAGE 96

the marginal structural model, at present, is not able to incorporate complex modeling approaches that allow reversion of exposure. La stly, the pooled logistic regression model that was used to estimate the marginal structural Cox model assumes that observations are equally spaced, which was not the case in the INVEST where the initial five visits occurred in six week intervals while the remaining visi ts occurred in six month interv als. Thus, the pooled logistic regression model may not be fully equiva lent to the Cox model it replaces. The estimation of a surrogate (S BP control in our study) in the presence of time-dependent confounding by treatment raises concerns about it s interpretability. While controlling for time dependent confounding by a surrogate is, if all as sumptions are fully met and all models are correctly specified, essentially equivalent to a RCT where treatment initia tion is independent of the surrogate, the same thought experiment does not hold for the analysis of time-dependent confounding of a surrogate by treatment. C ontrolling for time-dependent confounding by treatment in the estimation of th e effect of a surrogate on a cl inical outcome wouldas a thought experimentassume that values of the surrogate are randomized to subj ects regardless of their treatment pattern (in our study, SBP control status would be randomly assigned to patients regardless of the number of antihypertensive drug s they are taking). While this obviously would not be possible in reality, and the estimate is therefore more difficult to communicate, we do believe in the validity of the presented approach. Future Research The marginal structural models presented in our study demonstrate, in principle, the importance of considering time-dependent confoundi ng in the analysis of chronic disease drug studies involving surrogates. However, the lim itations described above presently limit the clinical utility of marginal structural models in the analysis of disease states with complex treatment patterns such as hypertension. In order to make more clinica lly useful inferences, 96

PAGE 97

future research will have to extend causal methods such as marginal structural models, to allow a more realistic representation of the observed da ta. Specifically, the method should be extended to allow multi-category independent variables and both initiation as well as discontinuation of exposure. Another important area of research is the evaluation of dynamic treatment regimens from observational data. While our analysis compared nondynamic regimens (e.g., aggressive antihypertensive treatment thr oughout follow-up versus standa rd treatment throughout followup), questions involving dynamic treatment regimens (e.g., initiation of antihypertensive therapy at SBP of greater than 135 mm Hg versus initiation of antihyper tensive therapy at 145 mm Hg) may be equally important for clinical practice. Such analyses require artificial censoring of patients once they deviate from the defined treatment regimens followed by weighting by the inverse probability of censoring to adjust for the potential biased intr oduced by the artificial censoring.41 Summary and Conclusions The complex interplay of surrogate measures pharmacological treatments, and clinical outcomes makes the analysis of observational studies of chronic diseases challenging. Our study shows that the estimation of surrogate effects on a clinical outcome is highly dependent on the operationalization of the surrogate and that se veral commonly used approaches may introduce severe bias to the analysis. While it is conceptually clear that tim e-dependent confounding by a surrogate is problematic for the estimation of treatment effects in observational studies, our study is the first to empirically support the presence of such time-dependent confounding in the context of hypertension. Our results suggest that timedependent confounding by SBP, leads to an underestimation of the effectiv eness of antihypertensive treat ment. No evidence for timedependent confounding of the effect of SBP c ontrol by antihypertensiv e treatment was found, 97

PAGE 98

suggesting, that antihypertensive treatment as modeled in our anal ysis does not affect cardiovascular outcomes in pathways other than SBP. However, limitations in the methods that were used to allow the inclusion of time-de pendent confounders in th e analysis required considerable simplification of the data structure and thus, these methods at present have only limited practical utility. As such causal methods are further developed, they may become more useful in the analysis of large observational hypertension studies. 98

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LIST OF REFERENCES 1. World Health Organization. Preventing chronic diseases: a vital investment: WHO global report. World Health Organi zation, Geneva, Switzerland. 2005. 2. Centers for Disease Control and Preventi on. Chronic disease overview. Centers for Disease Control and Preventi on, Atlanta, GA. Revised 2005. http://www.cdc.gov/nccdphp/overvie w.htm. Accessed January 2007. 3. Robins JM, Hernan MA, Brumback B. Margin al structural models and causal inference in epidemiology. Epidemiology. Sep 2000;11(5):550-560. 4. Pepine CJ, Handberg EM, Cooper-DeHoff RM et al. A calcium antagonist vs a noncalcium antagonist hypertension treatment stra tegy for patients with coronary artery disease. The International Verapamil-Tr andolapril Study (INVEST): a randomized controlled trial. Jama. Dec 3 2003;290(21):2805-2816. 5. Pepine CJ, Handberg-Thurmond E, Marks RG et al. Rationale and design of the International Verapamil SR/Trandolapril Study (INVEST): an Internet-based randomized trial in coronary artery disease patients with hypertension. J Am Coll Cardiol. Nov 1998;32(5):1228-1237. 6. Temple R. A regulatory authority's opini on about surrogate endpoints. In: Nimmo WS TG, ed. Clinical Measurement in Drug Evaluation New York: Wiley; 1995. 7. Fleming TR, DeGruttola V, De Mets DL. Surrogate endpoints. AIDS Clin Rev. 1997:129143. 8. Prentice RL. Surrogate endpoints in clinical trials: definition and operational criteria. Stat Med. Apr 1989;8(4):431-440. 9. Psaty BM, Weiss NS, Furberg CD, et al. Surro gate end points, health outcomes, and the drug-approval process for the treatment of risk factors for cardiovascular disease. Jama. Aug 25 1999;282(8):786-790. 10. Code of Federal Regulations. Approval based on a surrogate endpoint or on an effect on a clinical endpoint other than survival or irreversible morbidity.: Code of Federal Regulations, Title 21, Volume 5, (21CFR314.410), Revised 2006. 11. D'Agostino RB, Jr. Debate: The slippery slope of surrogate outcomes. Curr Control Trials Cardiovasc med. 2000;1(2):76-78. 12. Fleming TR. Surrogate endpoints and FDA's accelerated approval process. Health Aff (Millwood). Jan-Feb 2005;24(1):67-78. 13. Fleming TR, DeMets DL. Surrogate end points in clinical trials: are we being misled? Ann Intern Med. Oct 1 1996;125(7):605-613. 99

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14. Sobel BE, Furberg CD. Surrogates, se mantics, and sensible public policy. Circulation. Mar 18 1997;95(6):1661-1663. 15. Lin DY, Fleming TR, De Gruttola V. Es timating the proportion of treatment effect explained by a surrogate marker. Stat Med. Jul 15 1997;16(13):1515-1527. 16. Chobanian AV, Bakris GL, Black HR, et al The Seventh Report of the Joint National Committee on Prevention, Detection, Evaluati on, and Treatment of High Blood Pressure: the JNC 7 report. Jama. May 21 2003;289(19):2560-2572. 17. Lewington S, Clarke R, Qizilbash N, Peto R, Collins R. Age-specific relevance of usual blood pressure to vascular mortality: a meta-analysis of individual data for one million adults in 61 prospective studies. Lancet. Dec 14 2002;360(9349):1903-1913. 18. Burt VL, Whelton P, Roccella EJ, et al. Prevalence of hypertension in the US adult population. Results from the Third National He alth and Nutrition Examination Survey, 1988-1991. Hypertension. Mar 1995;25(3):305-313. 19. Franklin SS, Larson MG, Khan SA, et al. Does the relation of blood pr essure to coronary heart disease risk change with aging? The Framingham Heart Study. Circulation. Mar 6 2001;103(9):1245-1249. 20. Turnbull F. Effects of different bloo d-pressure-lowering regimens on major cardiovascular events: results of prospectively-designed overviews of randomised trials. Lancet. Nov 8 2003;362(9395):1527-1535. 21. Psaty BM, Lumley T, Furberg CD, et al. Health outcomes associated with various antihypertensive therap ies used as first-line agen ts: a network meta-analysis. Jama. May 21 2003;289(19):2534-2544. 22. LeLorier J. The value of lowering blood pressure. Can J Cardiol. Jan 2006;22(1):63-64. 23. Mitka M. Experts ponder treating prehypertension. Jama. May 10 2006;295(18):21252126. 24. Julius S, Nesbitt SD, Egan BM, et al. Feas ibility of treating prehypertension with an angiotensin-receptor blocker. N Engl J Med. Apr 20 2006;354(16):1685-1697. 25. Hartzema AG, Tilson HH, Chan KA, ed. Pharmacoepidemiology: An Introduction. 4th ed. Cincinnati, OH: Harvey Wh itney Books; 2007; in press. 26. Hernan MA, Brumback B, Robins JM. Margin al structural models to estimate the causal effect of zidovudine on the survival of HIV-positive men. Epidemiology. Sep 2000;11(5):561-570. 100

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27. Choi HK, Hernan MA, Seeger JD, Robins JM, Wolfe F. Methotrexate and mortality in patients with rheumatoid ar thritis: a prospective study. Lancet. Apr 6 2002;359(9313):1173-1177. 28. Cook NR, Cole SR, Hennekens CH. Use of a ma rginal structural model to determine the effect of aspirin on cardiovascular mort ality in the Physicians' Health Study. Am J Epidemiol. Jun 1 2002;155(11):1045-1053. 29. Pepine CJ, Kowey PR, Kupfer S, et al. Predictors of adverse outcome among patients with hypertension and coronary artery disease. J Am Coll Cardiol. Feb 7 2006;47(3):547551. 30. Allison PD, SAS Institute. Survival analysis using the SAS system: a practical guide Cary, NC: SAS Institute; 1995. 31. Messerli FH, Mancia G, Conti CR, et al. Dogma disputed: can aggressively lowering blood pressure in hypertensive patients with coronary artery disease be dangerous? Ann Intern Med. Jun 20 2006;144(12):884-893. 32. D'Agostino RB, Lee ML, Belanger AJ, Cupples LA, Anderson K, Kannel WB. Relation of pooled logistic regression to time dependent Cox regression analysis: the Framingham Heart Study. Stat Med. Dec 1990;9(12):1501-1515. 33. Elliott WJ, Hewkin AC, Kupfer S, Cooper-D eHoff R, Pepine CJ. A drug dose model for predicting clinical outcomes in hypert ensive coronary disease patients. J Clin Hypertens (Greenwich). Nov 2005;7(11):654-663. 34. Henricsson M, Nilsson A, Groop L, Heijl A, Janzon L. Prevalence of diabetic retinopathy in relation to age at onset of the diabetes, treatment, dur ation and glycemic control. Acta Ophthalmol Scand. Dec 1996;74(6):523-527. 35. Matsuzaki M, Kita T, Mabuchi H, et al Large scale cohort st udy of the relationship between serum cholesterol conc entration and coronary events with low-dose simvastatin therapy in Japanese patients with hypercholesterolemia. Circ J. Dec 2002;66(12):10871095. 36. MacMahon S, Peto R, Cutler J, et al. Blood pr essure, stroke, and coronary heart disease. Part 1, Prolonged differences in blood pr essure: prospective observational studies corrected for the regression dilution bias. Lancet. Mar 31 1990;335(8692):765-774. 37. Rosner B, Spiegelman D, Willett WC. Corr ection of logistic regression relative risk estimates and confidence intervals for measurement error: the case of multiple covariates measured with error. Am J Epidemiol. Oct 1990;132(4):734-745. 101

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38. Hypertension Detection and Fo llow-up Program Co-operative Group. Variability of blood pressure and the results of screening in the hyperten sion detection and follow-up program. J Chronic Dis. 1978;31(11):651-667. 39. Bennett S. Blood pressure measurement error: its effect on cross-sectional and trend analyses. J Clin Epidemiol. Mar 1994;47(3):293-301. 40. Marshall T. Misleading measurements: modeling the effects of blood pressure misclassification in a United States population. Med Decis Making. Nov-Dec 2006;26(6):624-632. 41. Hernan MA, Lanoy E, Costagliola D, R obins JM. Comparison of dynamic treatment regimes via inverse probability weighting. Basic Clin Pharmacol Toxicol. Mar 2006;98(3):237-242. 102

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BIOGRAPHICAL SKETCH Tobias Gerhard was born and raised in Ha mmelburg, Germany. He holds a Bachelor of Pharmacy degree from Albert-Ludwigs Univer sity in Freiburg. In 2002, he joined the Department of Pharmacy Health Care Administrati on at the University of Florida as an Alumni Fellow to pursue a PhD in pharmacoepidemiology. Tobias has authored and coauthored several peer-reviewed publications and presented at national and international conferences. He is interested in the pharmacoepidemiology and pharm acogenetics of cardiovascular and mental health drugs. 103


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Title: Time-Dependent Confounding in Antihypertensive Drug Studies
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Copyright Date: 2008

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TIME-DEPENDENT CONFOUNDING IN
ANTIHYPERTENSIVE DRUG STUDIES













By

TOBIAS GERHARD


A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA

2007

































Copyright 2007

by

Tobias Gerhard

































To my parents, Gertrud and Albrecht Gerhard









ACKNOWLEDGMENTS

I want to thank my adviser, Almut Winterstein, for her continuous support. She has been a

terrific mentor and has never stopped challenging me to do my best. I would also like to thank

my supervisory committee members Julie Johnson, Abraham Hartzema, Carl Pepine, and

Jonathan Shuster for their expertise, advice, and encouragement. I thank Yan Gong and Rhonda

Cooper-DeHoff for their help with the INVEST dataset. Finally, I thank my fellow graduate

students for their support and friendship.









TABLE OF CONTENTS

page
pM.ge

A C K N O W L E D G M E N T S .............................................................................................. ........... ..... 4

LIST OF TABLES.............................................................7

LIST OF FIGURES .............................................................8

A B ST R A C T .............................................................. ................................ .. .................. 10

1 IN TRODU CTION ............... .............................................. ...............12

B background .......................................................................................... ......................... 12
Need for Study ............... .. .... ..... ........ .... ..... .. ... ...............13
Association of a Surrogate with Clinical Outcome: Surrogates are Time-Dependent
Variables .............. .. .... .... . ... .... .. .. .. ... ... .. ............... 13
Association of a Surrogate with Clinical Outcome: Confounding by Treatment ...........14
Estimation of Drug Effectiveness in Observational Research ......................................15
Purpose of the Study ....................................................................................... .............. 16
R research Q questions and H ypotheses ...................... ............................................ ...............18

2 LITERA TURE REVIEW ................................................................................................. 21

Su rrog ates .................. .. .. ............................................. ........... ..... ......................2 1
The Epidemiology of Blood Pressure Control and Cardiovascular Outcomes ......................23
Time-Dependent Confounding in Pharmacoepidemiology................................... ...............26
M arginal Structural M odels...........................................................................................27

3 M E TH O D S .......................................................................................... ..........................31

The INVEST and the INVEST Dataset................................................................................31
D descriptive Statistics ............................................................ .................... ...............33
Blood Pressure and CV Outcomes .............................................33
Incidence Rates by Categories of Systolic Blood Pressure...........................................33
Cox Proportional H azards M odels ................................................................................34
M arginal Structural Cox M odel.....................................................................................37
Antihypertensive Treatment and CV Outcomes...................................................................40
M arginal Structural Cox M odels ...................................................................................40
Cox Proportional H azards M odels ................................................................................41

4 R E SU L T S .............. ......... ................................................ .......................................... . 4 4

D escriptives ........................................................................................ .......................... 44
B lood Pressure ............................................................... .................... ...............45
A ntihypertensive D rugs.................................................................................................46
Prim ary O utcom e Events...............................................................................................48









H azard R atios............................................. ............. .............................................................48
Baseline SBP M odel................ ..................................................... .... ...............49
Average SBP Model ................. .... ......... ...... ..............................49
Average SBP W eighted by Follow-up Time M odel .....................................................50
Tim e-D dependent SBP M odels.......................................................................................50
U pdated M ean SB P M odel ............................................................................................51
In cid en ce ............... .......... ................................................ .......................................... . 5 2
C om prisons ....................................................................................... ......................... 53
Average SBP and Bias.................. ....................................................... ................53
M arginal Structural M odels ....................................................................................................59
Effect of Systolic Blood Pressure Control............................................................................60
Effects of A ntihypertensive D rugs .......................................................................................60

5 D ISCU SSIO N ...................................................................................... ..........................78

Descriptive Analyses: Antihypertensive Treatment and SBP in the INVEST.......................78
O perationalization of SBP .............. ............................................... .................. ....80
M modeling A ssum options .......... .. ...... ................................. .................8 1
Baseline SBP M odel................ ..................................................... .... ...............83
Average SBP M models .............................. .......... ............. ...............84
Short Term SBP M odels (Time-Dependent).................................................................85
M odel Selection ............................................................ ................... ...............86
Tim e-dependent Confounding ..............................................................................................89
L im stations ........................................................................................... ......................... 93
Future R research ................................................................................... .........................96
Su m m ary an d C on clu sion s .....................................................................................................97

L IS T O F R E F E R E N C E S ...............................................................................................................99

B IO G R A P H IC A L SK E T C H .......................................................................................................103






















6









LIST OF TABLES


Table page

4-1 Composition of the INVEST Cohort at Baseline............................................................62

4-2 Com prison of m models ................................................................................................. 63

4-3 Simulation of six scenarios using average over follow-up.............................. ...............64

4-4 Simulation of six scenarios using updated mean. ................ ....................................65

4-5 Inverse probability of treatment weighted estimates for the causal effect of controlled
SBP on primary INVEST primary outcome event .......................................... ...............66

4-6 Inverse probability of treatment weighted estimates for the effect of receiving more
than two total antihypertensive drugs on primary INVEST primary outcome event........66

4-7 Inverse probability of treatment weighted estimates for the causal effect of receiving
various numbers of total antihypertensive drugs on INVEST primary outcome event.....66









LIST OF FIGURES


Figure page

2-1 Prentice criteria satisfied..............................................................................................28

2-2 The surrogate is correlated with the clinical outcome but captures no treatment effect....28

2-3 Net effect of treatment is only partially captured by the surrogate..............................29

2-4 Mortality from stroke (A) and ischemic heart disease (B) in each decade of age
versus usual systolic blood pressure at the start of that decade......................................29

2-5 A lgorithm for the treatm ent of hypertension .....................................................................30

2-6 Directed acyclic graph for time-dependent confounding................................. ...............30

3-1 Treatm ent strategies in the INVEST...............................................................................42

3-2 Operationalization of SBP: Examples for a sample patient............................. ...............43

4-1 Patients remaining in the study at each visit.................... ...................................67

4-2 Mean systolic blood pressure over follow-up (observed vs. imputed data) ......................67

4-3 Percentage of patients within each SBP category over follow-up..................................68

4-4 Percentage of patients within each SBP category who were not within the same SBP
category at the prior visit .................. ...................................................... ...............68

4-5 Number of total antihypertensive drugs and antihypertensive study drugs over
follow -up ....................................................................................... ......................... 69

4-6 Percentage of patients on each individual study drug over follow-up...............................69

4-7 Number of INVEST study drugs over follow-up ............................................ ...............70

4-8 Number of total antihypertensive drugs over follow-up..................................................70

4-9 Percentage of patients on a specific number of antihypertensive study drugs who
were not on the same number of antihypertensive drugs at the prior visit........................71

4-10 Percentage of patients on a specific number of antihypertensive drugs who were not
on the same number of antihypertensive drugs at the prior visit....................................71

4-11 Cumulative incidence of the primary outcome event over follow-up ...............................72

4-12 Hazard ratios for an INVEST primary outcome event by categories of baseline
systolic blood pressure ............ .... .. ................................... .. .............. ..72









4-13 Hazard ratios for an INVEST primary outcome event by categories of average
systolic blood pressure over follow -up. ..........................................................................73

4-14 Hazard ratios for an INVEST primary outcome event by categories of average
systolic blood pressure over follow-up, weighted by time of follow-up...........................73

4-15 Hazard ratios for an INVEST primary outcome event by categories of systolic blood
pressure (updated; carried forward from last observed visit) .........................................74

4-16 Hazard ratios for an INVEST primary outcome event by categories of systolic blood
pressure (updated; from next observed visit)..................................................................74

4-17 Hazard ratios for an INVEST primary outcome event by categories of updated mean
systolic blood pressure (time-dependent; updated at each visit) ....................................75

4-18 Crude incidence of primary outcome events by SBP category.......................................75

4-19 Adjusted incidence of primary outcome events for White, female, US patients
between the ages of 60 to 70 years by SBP category .....................................................76

4-20 Bias of outcome event hazard ratios obtained average SBP compared to updated
m ean SB P ..................................................................................... ........................... 76

4-21 Proportion of events within category of average SBP by number of observed visits at
the occurrence of the event .............................................................................................77

4-22 Bias and timing of events by category of SBP ...............................................................77









Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy

TIME-DEPENDENT CONFOUNDING IN
ANTIHYPERTENSIVE DRUG STUDIES

By

Tobias Gerhard

May 2007

Chair: Almut Winterstein
Major Department: Pharmacy Health Care Administration

Accurate estimation of blood pressure (BP) effects on the risk for cardiovascular outcomes

has important implications for the treatment of hypertension. The extent to which

operationalization of BP affects these risk estimates is unclear. Furthermore, the presence of a

time-dependent confounder may lead to biased estimates for the risk of BP on cardiovascular

outcomes and can not be adjusted for by standard statistical methods. The same bias may occur

in the estimation of drug effects in the presence of time-dependent confounding by BP.

To examine the impact of systolic blood pressure (SBP) operationalization on risk

estimates for myocardial infarction, stroke, or all cause death (primary outcome) we estimated

the hazard ratios of 7 SBP categories for six different Cox proportional hazards models in

patients of the International Verapamil-Trandolapril Study (INVEST), a randomized study of

22,576 hypertensive coronary artery disease patients. To test for the presence of time-dependent

confounding by antihypertensive treatment (or, alternatively, SBP control), we estimated both

standard Cox models and marginal structural Cox models (causal models) for the effect of SBP

control (or, respectively, aggressive antihypertensive treatment), adjusting for the number of

concurrently used antihypertensive drugs (or, respectively, SPB).









Estimates of the effect of SBP on primary outcome vary significantly depending on the

method of SBP operationalization. Some of the operationalization approaches, most notably the

use of average SBP, may lead to systematically biased estimates. Causal analyses suggest that

time-dependent confounding by SBP may bias estimates of treatment effects (Hazard ratio [HR]

standard model: 0.96; 95% confidence interval [CI] 0.87-1.07; HR marginal structural model:

0.81; 95% CI 0.71-0.92), but provides no evidence of time-dependent confounding by treatment

in the estimation of risk associated with SBP control (HR standard model: 0.54; 95% CI 0.48-

0.60; HR marginal structural model: 0.55; 95% CI 0.50-0.61).

Our results suggest that time-dependent confounding by SBP, leads to an underestimation

of the effectiveness of antihypertensive treatment. No evidence for time-dependent confounding

of the effect of SBP control by antihypertensive treatment was found, implying, that

antihypertensive treatment as modeled in our analysis does not affect cardiovascular outcomes in

pathways other than through SBP.









CHAPTER 1
INTRODUCTION

Background

In 2005, chronic diseases, such as cardiovascular disease, diabetes, or cancer were

estimated to be responsible for 60% of the total global mortality (35 million deaths). In the

United States alone, chronic diseases affect the lives of over 90 million Americans and account

for 70% of all deaths.2 Treatment of patients suffering from chronic diseases occurs over

extended periods of time, frequently involves multi-drug regimens, and often relies on surrogates

(i.e., intermediate markers of health) to evaluate the effectiveness of treatment in the individual

patient.

Clinically relevant outcomes of chronic diseases such as myocardial infarction, stroke, or

death often occur only in a proportion of affected patients and often after years or even decades

of the disease. As a consequence, immediately observable surrogate measures such as blood

pressure, low density lipoprotein (LDL) level, or CD4 cell count (a marker of circulating T

helper cells) play an important role in the treatment of patients suffering from chronic disease as

they predict the risk for manifestation of adverse outcomes. In addition, surrogate measures

typically facilitate shorter clinical trials with smaller sample sizes. Accurate estimation of the

association between the surrogate measure and the risk of clinically relevant outcomes over time

is a prerequisite for the informed use of a surrogate measure in treatment and research.

Furthermore, to avoid confounding, the influence of the surrogate has to be carefully considered

in the planning and analysis of observational studies of drug effects, because surrogate measures

play an important role in the determination and management of drug therapy.









Need for Study

Association of a Surrogate with Clinical Outcome: Surrogates are Time-Dependent
Variables

Surrogate measures are rarely constant over time. Disease progression, life-style

modification, pharmacologic and nonpharmacologic treatments may all contribute to changes in

a surrogate measure over time. Thus, any analysis that aims to quantify an association of a

surrogate with a relevant clinical outcome (i.e., morbidity or mortality) over a prolonged period

of time and uses a single, fixed value to represent the true surrogate values over the course of

time will lead to misclassification. Inclusion of multiple values of the surrogate over time (i.e.,

its inclusion as a time-dependent variable) can significantly reduce misclassification bias.

However, it is often unclear to what extend bias introduced by such misclassification will alter

estimates of the effect of a surrogate on a clinical outcome in practice. Since, time-dependent

modeling of surrogates involves more complex statistical methods and requires regularly

measured data-points for the surrogate over time, study results are frequently based on single,

fixed surrogate values (such as baseline, or average over follow-up).

Another problem closely related to the time-dependent nature of surrogate measures is the

potential lag time of a surrogate's effect on the clinical outcome. Depending on the

pathophysiological mechanism through which the surrogate affects the clinical outcome,

associations between the surrogate and the clinical outcome may be immediate or delayed. This

has profound consequences for analysis because it determines whether current or historical

values (or a combination of the two) of the surrogate should be used to model the risk for the

clinical outcome (e.g., it would affect to what extend BP history, as opposed to current BP

values, should be included in risk models for cardiovascular disease).









Association of a Surrogate with Clinical Outcome: Confounding by Treatment

Surrogate measures are routinely used to guide clinical practice. Physicians will for

example, increase the dose of an antihypertensive medication or add an additional agent, if a

patient's blood pressure is considered uncontrolled, and patients with elevated cholesterol may

be treated with increasing doses of stations until recommended LDL levels are achieved. The

validity of this approach relies on unbiased estimation of the causal effect of the surrogate on the

clinical outcome. Several factors make this estimation difficult. As mentioned above, surrogate

measures are not constant over time, and thus, estimation of the causal effect of the surrogate on

clinical outcome needs to account for these time-dependent changes. In addition, surrogate

measures are rarely observable in untreated patients, because changes in a surrogate are expected

to result in changes in clinical outcomes, and thus, once identified, patients with elevated values

of a surrogate are routinely receiving treatment. This treatment may confound the estimation of a

causal effect between surrogate and clinical outcome in a treated cohort. Specifically, only if the

effect of a given drug is entirely mediated by the surrogate, which rarely is the case in practice,

will an estimate of the causal effect of the surrogate on a clinical outcome in the presence of the

drug be unconfounded. If a drug affects clinical outcome in parts through pathways different

from the surrogate measure of interest, the drug acts as a confounder and needs to be controlled

for in any analysis that aims to estimate the causal effect of the surrogate on the clinical outcome.

However, since drug use is commonly affected by a prior value of the surrogate, and thus is

simultaneously a direct cause for subsequent values and a direct result of prior values of the

surrogate, assumptions for standard methods of confounder adjustments, such as inclusion in

regression models are violated, and such methods fail to produce unbiased, causally interpretable

estimates.3









In summary, the evaluation of the causal effect of surrogate measures must incorporate

changes of the surrogate observed over time and account for time-dependent confounding by

treatment. To the best of our knowledge, time-dependent confounding by treatment has never

been accounted for in the analysis of surrogate measures.

Estimation of Drug Effectiveness in Observational Research

Pharmacoepidemiological research, particularly when it relates to drugs used in the

treatment of chronic diseases, commonly deals with the risks and benefits of drugs used over

prolonged periods of time. More often than not, treatment will not be stable over time but rather

will doses be adjusted and drugs added or removed from the treatment regimen. Such

adjustments of therapy over time do not occur at random and thus, control of factors that

influence both treatment changes and treatment outcome (i.e., confounders) is necessary to

obtain unbiased estimates of risks and benefits for the various treatment choices. However, as

detailed in the previous section, when factors that predict changes in treatment are also affected

by the change in the treatment regimen, as is common for surrogate measures of chronic disease

states (e.g., BP, HDL/LDL, HbA1C), assumptions for standard methods of confounder

adjustments are violated and these methods fail to produce unbiased estimates. Conventional

evaluation of drug effects in the presence of a time-dependent confounder therefore may produce

biased estimates.

For a number of reasons evidence from randomized clinical trials alone is often

insufficient to provide the evidence needed for optimal selection of individual treatment

strategies. First, randomized clinical trials are typically conducted over short periods of time and

take place in narrow study populations defined by explicit inclusion and exclusion criteria. In

contrast, drug use in clinical practice will occur over extended periods of time in less

homogeneous populations. Second, and more importantly in the context of this study, the









comparisons made in clinical trials are limited, frequently involving comparisons of single

therapeutic agents with each other or placebo. In practice however, many chronic disease

patients will require a combination of two or more drugs to be adequately treated. While clinical

trials comparing specific combination therapies or flexible treatment strategies are possible, and

have been conducted, the number of possible drug (and dose) combinations will likely exceed

what can be feasibly tested in a clinical trial setting.

Thus, observational pharmacoepidemiological research, which is able to explore the

broad spectrum of treatments occurring in practice over extended periods of time, could play an

important role in evaluating the long-term effectiveness of complex multi-drug strategies.

However, careful control of treatment decisions that determine the exposure of individual

patients to specific drug regimens over the course of a study and that may lead to time-dependent

confounding is necessary to avoid biased estimates of regimen effectiveness.

Purpose of the Study

Our study used a dataset from a large international antihypertensive trial to estimate the

association of systolic blood pressure (surrogate measure) over time on the risk for

cardiovascular morbidity and mortality (clinical outcome) and to assess whether time-dependent

changes in treatment confound this association. In addition, this study will evaluate the effects of

treatment on clinical outcome, when initiation of treatment is partly conditional on inadequate

response to prior treatment and thus, confounded by a surrogate measure. Our study will

illustrate problems arising from the presence of time-dependent confounding in such a setting

and use newly developed statistical methods to obtain estimates of unbiased effects for both the

surrogate and treatment on clinical outcome in the presence of time-dependent confounding.

Specifically, this study will describe blood pressure and antihypertensive drug use patterns

for patients participating in the International Verapamil SR/Trandolapril Study (INVEST)4'5 over









the time of follow-up. It will then evaluate how systolic blood pressure over time associates with

the incidence of primary outcome events (nonfatal myocardial infarction, nonfatal stroke, or all

cause death) and compare this time-dependent approach to analytic approaches that use single,

fixed SBP estimates (e.g., baseline SBP, average SBP over treatment period). Using marginal

structural Cox models, the present study will then assess whether time-dependent treatment with

antihypertensive drugs confounds the association of blood pressure control (SBP <140 mm Hg

versus >140 mm Hg) with clinical outcome and to what extend failure to consider this in

traditional methods biases these estimates. Lastly, adjusting for SBP control over time using

marginal structural Cox models, this study will derive an unbiased estimate for the effect of

antihypertensive therapy (aggressive versus standard antihypertensive therapy) on the clinical

outcome. Of note, the necessity to dichotomize the independent variables of interest (SBP

control, aggressive antihypertensive therapy) is a limitation inherent in the use of current

marginal structural models and will likely produce estimates of association that are of limited

clinical utility.

More complex and specific comparisons between individual drug combinations or use of

multiple BP categories may be possible and should be addressed in future research. The present

study will use hypertension to illustrate the aforementioned problems arising from time-

dependent confounding when treatment initiation and choice are affected by the prior surrogate

and the surrogate lies on the hypothesized pathway through which the treatment affects the risk

for the clinical outcome. Blood pressure is an important and widely used surrogate measure that

plays an essential role in the selection and management of antihypertensive treatment and is

likely to be the major pathway through which antihypertensive drugs affect the risk of clinical

outcome. Causal methods such as marginal structural models may indirectly contribute to better









answer the question to which extent the effects of specific antihypertensive drugs and drug

classes are mediated by blood pressure and may ultimately contribute to the identification of

optimized combination therapies.

The INVEST cohort provides the opportunity to investigate the independent effects of

antihypertensive drug use and a surrogate measure (blood pressure) on a clinical outcome

(INVEST primary outcome) in a rich and validated clinical dataset with independently

adjudicated outcomes. Although INVEST is a randomized controlled trial, evaluation of

individual steps of the treatment strategies negates randomization and thus, requires an

epidemiologic analysis approach similar to an observational study. Its large sample size and high

level of data quality make the INVEST an appropriate setting for the simultaneous evaluation of

time-dependent treatment and time-dependent surrogate measure.

Research Questions and Hypotheses

The first research question aims to evaluate whether the ability to predict adverse

cardiovascular outcomes in the INVEST is increased when blood pressure is operationalized as a

multi-category time-dependent variable, as compared to a single, fixed estimate (such as baseline

or average over follow-up). However, the estimation of the association of systolic blood pressure

presented in research question 1 does not control for concurrent use of antihypertensive drugs.

Thus, research question 2 will estimate the effect of blood pressure control on clinical outcome

over time controlling for time-dependent treatment (operationalized as the number of

antihypertensive INVEST study drugs as well as the total number of antihypertensive drugs),

while research question 3 evaluates whether the concurrent use of antihypertensive drugs

confounds the association of systolic blood pressure over time with primary outcome. Lastly, the

fourth and fifth research questions address the problem of estimating the effectiveness of a drug

or treatment strategy (in our study, aggressive versus standard antihypertensive therapy) in the









presence of time-dependent confounding by a surrogate measure (in our study, SBP control). The

a priori significance level for all research questions is set at 0.05.

* Research Question 1: Does time-dependent operationalization of systolic blood pressure
increase the ability to predict primary outcome events in the INVEST as compared to the
use of single, fixed blood pressure values?

* Hypothesis for Research Question 1: The null hypothesis for research question 1 is that
the generalized R2 for a model that updates the systolic blood pressure at each visit is not
different from models with fixed systolic blood pressure values, specifically baseline
systolic blood pressure, and average systolic blood pressure over follow-up. The
alternative hypothesis is that the generalized R2 is larger.

* Research Question 2: In the INVEST, does systolic blood pressure control over follow-up
affect the risk of primary outcome controlling for time-dependent confounding by
concurrent antihypertensive drug use?

* Hypothesis for Research Question 2: The null hypothesis for research question 2 is that
the hazard ratio for systolic blood pressure control is not significantly different from 1.0.
The alternative hypothesis is that the hazard ratio is significantly different from 1.0.

* Research Question 3: In the INVEST, does time-dependent treatment (i.e., the number of
antihypertensive INVEST study drugs as well as the total number of antihypertensive
drugs) confound the effect of systolic blood pressure control over the follow-up period.

* Hypothesis for Research Question 3: The null hypothesis for research question 3 is that
the hazard ratio for SBP control obtained from a marginal structural Cox proportional
hazards model that incorporates time-dependent treatment, is not significantly different
from the hazard ratio obtained from a standard time-dependent Cox proportional hazards
model that does not control for treatment after baseline.

* Research Question 4: In the INVEST, adjusting for time-dependent systolic blood
pressure control, is there a difference in risk of primary outcome between patients
receiving aggressive antihypertensive therapy compared to standard antihypertensive
therapy over follow-up?

* Hypothesis for Research Question 4: The null hypothesis for research question 4 is that
the hazard ratio for patients receiving aggressive antihypertensive therapy (three or more
concurrent total antihypertensive drugs) versus standard antihypertensive therapy (less than
three concurrent total antihypertensive drugs) is not significantly different from 1.0. The
alternative hypothesis is that the hazard ratio is significantly different from 1.0.

* Research Question 5: In the INVEST, does time-dependent systolic blood pressure
control confound the effect of treatment (aggressive versus standard antihypertensive
therapy) over the follow-up period?









* Hypothesis for Research Question 5: The null hypothesis for research question 5 is that
the hazard ratio for patients receiving aggressive antihypertensive therapy (three or more
total antihypertensive drugs) versus standard antihypertensive therapy (less than three total
antihypertensive drugs) obtained from a marginal structural Cox proportional hazards
model that controls for time-dependent confounding by systolic blood pressure control, is
not significantly different from the hazard ratio obtained from a standard time-dependent
Cox proportional hazards model that does not control for systolic blood pressure over
follow-up.









CHAPTER 2
LITERATURE REVIEW

Surrogates

A surrogate is defined as a laboratory measurement or physical sign used as a substitute for

a clinically meaningful endpoint that measures directly how a patient feels, functions or survives.

Changes induced by a therapy on a surrogate measure are expected to reflect changes in a

clinically meaningful endpoint.6 Although drug therapy is ultimately aimed at affecting clinically

meaningful endpoints, the use of surrogate measures offers important advantages. When clinical

endpoints are rare or manifest after substantial periods of time, as is often the case in chronic

disease states, the use of surrogate measures allows shorter, smaller, and less costly clinical

trials, which in turn allow more rapid approval of new therapies.79 Patient advocacy groups,

interested in the rapid availability of new and promising therapies, as well as drug manufacturers,

who save costs and patent life of their products, consequently support the use of surrogates in

Phase III trials. The Food and Drug Administration (FDA) has responded to these demands by

allowing the use of surrogate measures to demonstrate the efficacy of new drug products as part

of its accelerated approval process for serious or life-threatening illness.10 However, due to the

concern that changes in the surrogate may not translate into changes in the clinical outcome, the

use of surrogates is not without controversy.9, 11-14

In addition to their function in the evaluation of new therapies, surrogate measures play an

important role in the evaluation of treatment response in individual patients and the modification

of individual pharmacotherapy, often following guidelines that recommend treatment towards

specific target levels of the surrogate measure. However, the use of surrogate measures is

problematic when a treatment also affects the clinical endpoints in ways not mediated by the

surrogate, since such effects are not captured by the observed changes in the surrogate. Prentice









formalized the definition of a valid surrogate measure by requiring two sufficient conditions, (1)

the surrogate must correlate with the true clinical endpoint, and (2) the surrogate must fully

capture the treatments net effect (the aggregate effect accounting for all causal effects of the

treatment on the true clinical outcome)8. Figures 2-1 to 2-3 illustrate Prentice's conditions and

potential deviations that may compromise the validity of surrogate measures. Figure 2-1 depicts

a situation where Prentice's conditions are met. In contrast, Figure 2-2 illustrates a scenario in

which use of a surrogate would completely fail to predict the effect of an intervention on the true

clinical outcome. While the surrogate is correlated with the true clinical outcome, and thus,

satisfies the "correlation" condition, it does not lie on the biological pathway by which the

disease causes the clinical outcome. In consequence an intervention affecting the surrogate will

have no effect on the clinical outcome. A situation somewhere between the scenarios depicted in

the previous two figures may give a more accurate reflection of reality. A disease may affect the

clinical outcome through more than one biologic pathway. If an intervention affects more than

one biologic pathway (arrows A and B in Figure 2-3) and the surrogate lies only in one of these

pathways, then only a part of the effects of the intervention will be captured by its effect on the

surrogate. In addition, the intervention may causally affect the clinical outcome unrelated to the

disease (arrow C in Figure 2-3), for example, through adverse effects.

While Prentice's conditions define a surrogate in absolute terms, Figure 2-3 illustrates a

more common scenario where the second condition is not completely satisfied, but rather

partially met. The statistical literature has approached this problem by introducing the proportion

of treatment effect (PTE) explained by a surrogate marker which allows a more subtle evaluation

of a surrogate's validity for a specific intervention.15









Importantly, when Prentice's conditions are not fully met, the evaluation of the effect of a

specific treatment on a clinical outcome by assessing the treatment effect on the surrogate

measure (be it in an aggregate form in the context of a clinical trial, or on an individual level

when assessing response to treatment) will not capture the full effect of the treatment on the

clinical outcome and thus, be biased.

In summary, the validation of surrogate measures is a challenging task. First, it requires the

understanding of the biological pathway through which the surrogate affects the clinical

outcome. Only in the second step follows the statistical evaluation. The validation of a surrogate

for a specific treatment requires larger sample sizes than are needed to determine the effect of the

treatment on the clinical outcome. Therefore meta-analysis of large clinical trials that document

the effects of treatment on both surrogate and clinical outcomes are usually necessary. Since the

validity of a surrogate is treatment specific, validation should be repeated for different classes of

drugs in the same disease state.

The Epidemiology of Blood Pressure Control and Cardiovascular Outcomes

Blood pressure (BP) is a strong independent predictor of adverse cardiovascular (CV)

outcomes and its control is one of the central goals in the prevention and treatment of

cardiovascular disease.16, 17 Blood pressure is currently classified into normal (systolic blood

pressure [SBP]/diastolic blood pressure [DBP] < 120/80 mm Hg), prehypertension (120/80 mm

Hg < SBP/DBP < 140/90 mm Hg), stage 1 (140/90 mm Hg < SBP/DBP < 160/100 mm Hg) and

stage 2 (SBP/DBP > 160/100 mm Hg) hypertension. The prevalence of hypertension in the

United States between 1989 and 1991 has been estimated to reach almost 25%, and increases

sharply with advancing age.18 Mortality from stroke and ischemic heart disease (IHD) increases

with higher blood pressure levels starting from 115mm Hg SBP and 75 mm Hg DBP,

respectively (Figure 2-4).17









While DBP is a more important risk factor for cardiovascular disease than SBP before the

age of 50, the importance reverses in patients older than 50 years of age.19 Treatment of

hypertension ultimately aims at the reduction of circulatory and renal mortality and includes

lifestyle modifications as well as pharmacologic treatment. A large number of drugs from

multiple drug classes are currently approved for the treatment of hypertension and more than

two-thirds of treated hypertensive patients require two or more antihypertensive drugs to reach

blood pressure control.16 Initial antihypertensive drug choice and following management are

influenced by the presence of secondary diagnoses with compelling advantages of specific

antihypertensive drug classes in regards to efficacy, tolerability, and blood pressure response.

For most patients without comorbidities, thiazide-type diuretics are recommended as first line

treatment. 16 An algorithm for treatment of hypertension is shown in Figure 2-5.

However, a number of questions regarding the optimal therapy of hypertension remain

controversially discussed. Arguably the most important issue is whether differences exist in the

beneficial effects on adverse cardiovascular outcomes between the major antihypertensive drug

classes. Closely related to this problem is the question that if a comparison between two drug

classes results in differences in cardiovascular outcomes, then are these differences fully

accounted for by the level of achieved blood pressure reduction or do non blood pressure

mediated effects play a role in the effectiveness of antihypertensive drugs? In other words: does

it matter how blood pressure reduction is achieved? Over the last decades a plethora of

antihypertensive drug trials have been conducted comparing various drugs from the major

antihypertensive drug classes with placebo or active control treatments. Two recent meta-

analyses have aggregated data from 29 trials with 162,341 patients20, and 42 trials with 192,478

patients21, Spectively. Both studies found no differences in the reduction of all cause or
patients respectively. Both studies found no differences in the reduction of all cause or









cardiovascular mortality between the major antihypertensive drug classes. However, some

differences were shown in the effects on specific cardiovascular outcomes, most notably heart

failure, with diuretics presenting the most beneficial effects. One of the studies also reported that,

with the exception of heart failure, differences in achieved blood pressure between trials

randomized to the major antihypertensive drug classes were proportional to differences in risk of

cardiovascular outcomes.20 While some argue that it is 'relatively unimportant' which specific

agents are used to achieve blood pressure control22, the differences in the effectiveness on

specific cardiovascular outcomes between drug classes suggest the existence of drug-specific

mechanisms that affect cardiovascular outcomes independent of blood pressure.

As mentioned earlier, the majority of hypertensive patients will require two or more

antihypertensive drugs to achieve blood pressure control according to current guidelines. While

the comparative effectiveness of specific antihypertensive drugs is still not conclusively

established, much less is known regarding the comparative effectiveness of different

combination therapies. The underlying question is whether synergistic effects exist for specific

antihypertensive drug combinations or whether only achievable blood pressure reduction,

tolerability, and cost should determine treatment. The comparative effectiveness is considerably

harder to assess for combination therapy than for monotherapy because of the large number of

antihypertensive drugs and drug classes (and thus, the large number of possible comparisons).

Additionally, benefits may be associated with the more rapid control of blood pressure through

immediate initiation of combination therapy versus initial treatment with monotherapy followed

by additional antihypertensive drugs if blood pressure control has not been achieved.

Lastly, it is not clear what the ideal blood pressure goal should be and when to begin

treatment. For individuals with uncomplicated hypertension, current guidelines prescribe









initiation of antihypertensive pharmacotherapy, if lifestyle modifications alone do not lower

blood pressure below 140/90 mm Hg [SBP/DBP] (lower recommendations apply to individuals

with specific comorbidities).16 However, epidemiological evidence suggests a more than twofold

difference in cardiovascular risk for blood pressure values of 130-139/85-89 mm Hg as

(currently defined as prehypertension) compared to values below 120/80 mm Hg. Thus,

additional benefits may be achievable by lowering treatment goals.

Recently, there has been considerable controversy about the feasibility to treat
23
prehypertension.23 A recent randomized controlled trial demonstrated that treatment of

prehypertensive patients delayed progression to stage I hypertension, but to date no data is

available for the effect of such treatment on cardiovascular morbidity and mortality.24

Time-Dependent Confounding in Pharmacoepidemiology

Confounding occurs when the measure of the effect of an exposure is distorted because of

an association of the exposure with other factors that influence the outcome under study. Its

control is one of the central issues in pharmacoepidemiological research. It is important to

distinguish between measured and unmeasured confounding. The present study will focus on

measured confounding. Measured confounding may be addressed by restriction or matching

within the design of a study or by stratification or multivariate regression within the analysis

stage of a study25. Traditionally such methods would use variables at the beginning of the

exposure period and then follow patients over time. Through the increasing use of time-

dependent methods in which exposure status can vary over the follow-up period in recent years,

the problem of time-dependent confounding has become apparent. Time-dependent confounding

occurs when a covariate predicts future treatment and future outcome and is itself predicted by

past treatment (Figure 2-6). This poses unique problems because standard methods of

confounder adjustment do not suffice to produce unbiased estimates. To illustrate why standard









models fail to produce unbiased estimates under the aforementioned conditions, consider the

following example. In Figure 2-6, if the time dependent confounder L is not controlled for in the

analysis, then Li confounds the association of treatment A, with outcome Y, because it

simultaneously affects both A, and Y. Thus, any estimate of the association of A with Y would

be biased if L is not controlled for. However, if L is controlled in the analysis, then Li, a variable

in the causal path of Ao on Y, is blocked, again, resulting in a biased estimate of the association

of A with Y.

Marginal Structural Models

Marginal structural models (MSMs), first introduced by Robins, Hernan, and Brumback,

aim to produce unbiased estimates in the presence of time-dependent confounding.3 MSMs use

inverse probability of treatment weights (IPTWs) and inverse probability of censoring weights

(IPCWs) to create a pseudo-population in which treatment is unconfounded and no censoring

occurs.26 MSMs are fitted in a two stage process. The first step estimates the individual IPTWs

and IPCWs. The IPTWs are based on each subject's probability of having their own treatment

history at each time point given the subject's covariates (with the time-dependent confounder as

one of the covariates). The IPCWs are similarly estimated based on each subjects probability at

each time point to be censored based on his covariates. The second step uses the IPTWs and

IPCWs as weights in a regression model of the effect of the treatment on the outcome. Because

of the weighting, the regression now takes place in the pseudo-population and-if all

assumptions are met-results in a causal estimate of the treatment's effect on the study outcome.

The method assumes no unmeasured confounding factors and correct model specification for

both the weights and the final regression model.

Marginal structural models have been used in a number of disease states to obtain causal

estimates of the effect of treatments in the presence of time-dependent confounding. In a recent









observational study that aimed to estimate the causal effect of treatment with zidovudine on the

survival of HIV-positive men, the inclusion of CD4 cell count into standard models was

prohibited because it simultaneously predicted initiation of zidovudine, was part of the pathway

26
through which zidovudine is hypothesized to work, and was a risk factor for the study outcome.26

While a standard time-dependent Cox model, adjusted for baseline covariates but not for CD4

cell count resulted in a hazard ratio of 2.3 (95%CI 1.9-2.8), the marginal structural Cox model

showed a hazard ratio of 0.7 (0.6-1.0), revealing the beneficial effect of the treatment. Similar

results have been obtained for treatment with methotrexate in patients with rheumatoid

arthritis,27 or the effect of aspirin on cardiovascular mortality.28



Disease ~ Surrogate C-----
Disease C-- --- Clinical
/ Outcome



Intervention


Figure 2-1. Prentice criteria satisfied (adapted from Fleming et al.)13




10
Disease Clinical
Suiiogale Outcome





Intervento


Figure 2-2. The surrogate is correlated with the clinical outcome but captures no treatment
effect (adapted from Fleming et al .)13
*1



Intervention


Figre2-1 Peffie ct iei aife (adapted from Fleming et al.)13














Disease Clinical
Surrogate Outcome



A; BIX C -


Interve
* I /

Intervention -'


Figure 2-3. Net effect of treatment is only partially captured by the surrogate (adapted from
Fleming et al.)13


Age at risk:
80-89
years

70-79
years


Age at risk:
80-89
years

70-79
years
60-69
years

50-59
years

/ 40-49
years


120 140 160
Usual systolic blood
pressure (mm H&)


120 140 160
Usual systolic blood
pressure (mm Hg)


Mortality from stroke (A) and ischemic heart disease (B) in each decade of age
versus usual systolic blood pressure at the start of that decade. Reprinted with
permission from Lewington S, Clarke R, Qizilbash N, Peto R, Collins R. Age-
specific relevance of usual blood pressure to vascular mortality: a meta-analysis of
individual data for one million adults in 61 prospective studies. Lancet. Dec 14
2002;360(9349):1903-1913 (Figures 2 and 4, pages 1906 and 1908)."17


Figure 2-4.


180


^


^


r.













Lifestyle Modifications


Not at Goal BP
(<140/90 mm Hg or <1 30/80 mm Hg for Those With Diabetes
or Chronic Kidrey Disease)

............................_................... ................................
Irii inl C-1r iCnO C--I


T


H f.i1. rp on .r:.Virin AIil
q-r n.llll A .ll ,)g I, l N",ll. .I N -.


Hypertension With
Compelling Indications


7
Stage 1 Hypertension
(Systolic BP 140-159 mm Hg
or Diastolic BP 90-99 mnm Hg)
Thiazide-Type Diuretics for Most
May Consider ACE Inhibitor, ARB,
O-Blocker. CCB, or Combination


T
7
Slage 2 Hynerfernio.r
<\ -.V -l 1;FP 1tu- o.r.. i H .| *,i
Diastolic BP >100 mm Hg)
2-Drug Combinatiofn for Most
(Usually -tc,, r-T-.1 -. Ols..el
and ACE Inhibitor or ARB or
P-Blocker or CCB)


T
Druaqrst tir the
Compelling Indications
(See Table 6)
Other inr, enrn 'i. e 1ni 1,.
(Diuretics, ACE Inhibitor, ARB,
P-Blocker, CCB) as Needed


Not at Goal BP
T
Optimize Dosages or A-.i 1 Iii.n.:II Cwiii 'TJhiiiC,.il B 13 : r:ni .i
Consider Consultation '.*iir. H,p.qrt.,n-,i-r. Sp'-rii;iI


Algorithm for the treatment of hypertension. Reprinted with permission from
Chobanian AV, Bakris GL, Black HR, et al. The Seventh Report of the Joint
National Committee on Prevention, Detection, Evaluation, and Treatment of High
Blood Pressure. Jama. May 21 2003;289(19):2560-2572 (Figure 1, page 2564).16


Lo Ao


Figure 2-6.


-0 L -. Al


Directed acyclic graph for time-dependent confounding.
causal effect; Lo, vector of measured confounders at time 0; Li, vector of
measured confounders at time 0; Ao, treatment at time 0; Ai, treatment at time 1; Y,
outcome of interest.


Figure 2-5.









CHAPTER 3
METHODS

The methods for this study are presented in four parts: (1) a description of the dataset

including operationalization of key variables, (2) a section detailing descriptive statistics, (3) a

section describing several statistical models used to determine the association between systolic

blood pressure over time and the risk of a primary outcome event, and (4) a section describing

the methods used to determine the relation between time-dependent treatment and the risk of a

primary outcome event. Sections 3 and 4 include both standard methods (Cox-regression with

and without time-dependent covariates) and novel, causal methods (marginal structural Cox

regression) to address potential bias introduced by time-dependent confounding.

The INVEST and the INVEST Dataset

The International Verapamil-Trandolapril SR Study (INVEST) was a large, international,

randomized controlled antihypertensive trial involving patients with hypertension and coronary

artery disease from 862 sites in 14 countries.4 After an extensive cardiovascular history and

physical exam the INVEST randomly assigned 22,576 CAD patients >50 years old to either a

verapamil SR- or an atenolol-based multidrug antihypertensive strategy. Trandolapril and

hydrochlorothiazide (HCTZ) were specified as added agents, if needed for blood pressure

control, with trandolapril added first in the verapamil SR strategy and HCTZ added first in the

atenolol strategy. In both strategies, trandolapril was recommended for patients with heart

failure, diabetes, or renal impairment (Figure 3-1). Between 1997 and 2003, 61,835 patient-years

follow-up were accumulated and each strategy provided excellent BP control (>70% of patients

achieved BP <140/90 mm Hg) without differences in BP between the strategies. The strategies

were equivalent in preventing the primary outcome defined as all-cause death, nonfatal

myocardial infarction (MI), or nonfatal stroke. All components of the primary outcome (defined









as first occurrence of all-cause death, nonfatal MI, or nonfatal stroke) were fully adjudicated by

an independent adjudication committee. Further details on the design and results have been

published.4'5 The INVEST and all subsequent studies including the study at hand were approved

by the institutional review board (IRB) of the University of Florida, which acted as the central

IRB for all participating sites.

During the INVEST patients had scheduled visits every six weeks for the first six months

and every six months thereafter. At each visit, patients were assessed for occurrence of

symptoms, adverse events, and response to treatment. SBP and DBP were measured twice at

each visit (at least two minutes apart) with a standard mercury sphygmomanometer in a sitting

position. In a given patient throughout the trial all measurements were taken on the same arm,

and, when possible, approximately the same time of day to minimize measurement error. In

addition, all antihypertensive drug use was recorded at each visit. Throughout the remainder of

the manuscript we refer to the antihypertensive drugs included in either of the INVEST treatment

strategies (Atenolol, Verapamil, HCTZ, and Trandolapril) as study drugs, and all other

antihypertensive drugs as nonstudy drugs. The term total antihypertensive drugs refers to both

study and nonstudy antihypertensive drug use.

Follow-up continued until a patient was lost to follow up, died, or the end of the study. In

the online data acquisition system, protocol visits were numbered consecutively from 1

(baseline) to 14 (maximum follow up of 5 years). Visits outside of the protocol schedule were

also recorded and numbered 0. These visits were only included in the analysis if a protocol visit

was not observed but an unscheduled visit was recorded in a time interval close to the omitted

protocol visit. If patients did not return for one or multiple protocol visits and did not have

suitable non-schedule visits to replace the unobserved protocol visitss, values (e.g., SBP,









antihypertensive drug use) from the last observed visit were carried forward. If a patient was lost

to follow-up (i.e., does not have another observed visit or final assessment), the patient was

censored at the time of the last observed visit. For patients who experienced an event on the day

of the recorded visit, BP and treatment measures from the last recorded visit before the event

were used instead of the measures from the event visit to avoid the possibility that the observed

measures on the event date were affected by the event (reverse causation).

Descriptive Statistics

The following basic descriptive statistics were computed at each visit:

* Number and percentage of patients on each INVEST study drug

* Number and percentage of patients by number of INVEST study drugs and number of total
antihypertensive drugs used

* Mean SBP, and percentage of patients in 10 mm Hg SBP categories

* Change in number and percentage of patients between number of INVEST study, and total
antihypertensive drugs between visits

* Change in percentage of patients within 10 mm Hg categories between visits

Blood Pressure and CV Outcomes

The association of systolic blood pressure with the risk of primary outcome event was first

assessed unadjusted for time-dependent antihypertensive treatment using Poisson- and Cox

proportional hazards regression.

Incidence Rates by Categories of Systolic Blood Pressure

Incidence of primary outcome events per category of systolic blood pressure was expressed

as number of primary outcome events per 1000 patient years of follow-up. Blood pressure

categories were defined as <110, 110-119, 120-129, 130-139, 140-149, 150-159, and >160 mm

Hg. Adjusted incidence rates were calculated using Poisson regression. The model adjusted for

following baseline covariates that include predictors of CV-outcomes in the INVEST29, as well









as basic demographic variables: sex, ethnicity, age, residency (US vs. non-US), smoking status,

history of heart failure, history of diabetes, history of renal impairment, prior stroke or transient

ischemic attack, prior myocardial infarction, history of peripheral vascular disease, and prior

coronary revascularization. Adjusted incidence rates are presented for female sex, White

ethnicity, age at baseline between 60 and 70 years, US residency, and in absence of other risk

factors (these values reflect the median values of the included variables).

Cox Proportional Hazards Models

The potential association of systolic blood pressure with the risk of primary outcome event

unadjusted for treatment (other than at baseline) was assessed using standard and time-dependent

Cox models. The models included the following static covariates measured at baseline (sex,

ethnicity, age, residency (US vs. non-US), smoking status, history of heart failure, history of

diabetes, history of renal impairment, prior stroke or transient ischemic attack, prior myocardial

infarction, history of peripheral vascular disease, and prior coronary revascularization) as well as

SBP. All Cox models categorized SBP in seven 10 mm Hg categories as defined above and used

SBP 130 to 139 mm Hg as reference category. SBP categories were operationalized either as

static variables (Equation 3-1) or as a time-dependent variables (Equation 3-2), depending on the

respective model. The Cox models were specified as follows:

Cox Proportional Hazards model:

A (t)= AO(t)exp{,xI + 2(,8 +.+2 k-k)k (3-1)

Cox model with time-dependent covariate:

A (t) AO (t) exp{fixx,(t)+(f2X2 + ... + A k)} (3-2)

* A (t) = individual i's hazard to experience an event at time t

* AO (t) = baseline hazard function at time t









* f[A =association parameter for the SBP category (in the actual model, there are six
parameters, one for each SBP category dummy variable)

* x,1 = individual i's SBP category (in the actual model, six dummy variables are used)

* f2~ k = association parameters for individual i's k-1 static covariates

* x,2 x = k-1 static covariates for individual i

* x, (t) = individual i's SBP category at time t (six dummy variables)

Six Cox models using different operationalizations of systolic blood pressure were

evaluated: (1) baseline, (2) average over follow-up (fixed average), (3) average over follow-up

weighted by follow-up time, (4) time-dependent using values from the previous visit (updated

previous), (5) time-dependent using values from the next visit (updated next) and (6) time-

dependent using an average updated at every visit (updated mean). Models 1 to 3 used a single,

static value of SBP over the time of follow up. In contrast, models 4 to 6 are time-dependent and

SBP values were updated at each observation (during the remainder of the study we refer to these

models as 'updated models'). Figure 3-2 shows how these different models conceptionalize SBP

over follow-up for a sample INVEST patient. The sample patient has a baseline SBP of 160 mm

Hg (visit 1), observed scheduled visits 2, 3, and 5 (with measured SBPs of 140, 130, and 155 mm

Hg, respectively), and experienced an event after 32 weeks (before scheduled visit 6).

Importantly, Figure 3-2 shows continuous SBP values for each model, while the Cox models

utilized categorized data as described above (i.e., for the Cox models the resulting SBP values

are converted into dummy variables representing the 7 SBP categories).

The baseline model simply used the SBP observed at baseline to represent the patient's

SBP throughout follow-up. Like the baseline model, the average model used a static SBP value

to represent the patient's SBP over the entire follow-up, however, instead of the baseline SBP, it









used the average SBP calculated over the observed follow up period. The average was calculated

as follows:


SBP = Bt (3-3)
yn-1


* SBP = average SBP over follow-up

* SBP,= SBP at visit i

* n = total number of observed visits

* t = time between visit i and visit i+1

Note that, because visit 4 was not observed, the calculation assigned the SBP value

observed at visit 3 to the entire time period between visits 3 and 5 (see Figure 3-2 for a numerical

example of the calculation). The time-weighted average model used the same fixed average value

calculated in the equation above, but weighted each individual's observation by his or her

respective total follow-up time. This model thus weighted a subjects' contribution according to

the total follow up-time the subject provided. For each time period between two observed visits,

the updated previous model assigned the SBP value measured at the visit at the beginning of the

respective time-period (i.e., it carries the value forward), while the updated next model assigned

the SBP value from the visit that marked the end of the time period. Since no observations

existed after an event is observed, the updated next model used the last available SBP

measurement before the event for the time period from the last observed visit before the event up

to the event (i.e., it used the same value as the updated previous model). Lastly, the updated

mean model used an SBP average calculated as in equation 3-3, but instead of calculating a

single average at the end of follow-up (as in the average, and time-weighted average models),









calculated a new (updated) average at each observed visit. Note that the updated mean SBP at the

end of follow-up is equivalent to the average SBP over the entire follow-up.

A generalized R2 was calculated for each of the six models and used to assess and compare

the strength of association of the predictor variables with the outcome.30


R 2= 1- exp G (3-4)
I n )

* G2 = likelihood-ratio chi-squared statistic for testing the null hypothesis that all covariates
have coefficients of 0

* n = sample size

Marginal Structural Cox Model

A marginal structural Cox model was used to estimate the effect of SBP control (SBP less

than 140 mm Hg) over the course of follow-up on primary outcome controlling for potential

time-dependent treatment. Because SBP control, the independent variable of interest, is a binary

variable (a requirement of the marginal structural model) all patients with SBP of less than 110 at

any visit were excluded. This was necessary because a previous report31 and preliminary data

from our analysis showed a J-shaped relationship between SBP and the risk for cardiovascular

outcomes, with substantially increased risk for cardiovascular outcomes associated with SBP of

less than 110 mm Hg. Thus, if patients with such low SBP (that would be included in the

category of less than 140 mm Hg) were not excluded, the estimate of the benefit of controlled

SBP would be skewed towards the null.

The remainder of this section describes the estimation of the marginal structural Cox

model. First, the stabilized inverse probability of treatment and inverse probability of censoring

weights were estimated (Equations 3-5 to 3-7). Stabilized weights have been shown to produce

more narrow confidence intervals with better coverage rates. Note that in this instance treatment









refers to having controlled versus uncontrolled systolic blood pressure. In addition, the method

requires the intend-to-treat like assumption that once treatment is initiated (here, SBP control is

reached), patients remain on it until the end of their follow-up. Thus, the datasets used for the

marginal structural Cox models are adjusted accordingly and all observations after treatment

initiation are-regardless of observed exposure status-recoded as exposed to treatment.

Inverse probability of treatment weight (IPTW):


wQ(t) = 1 (3-5)
k=0pr[A(k) = a, (k) I A(k 1) = ai (k 1), L(k)= (k)]

Stabilized IPTW:

w )= pr[A(k)= a, (k) I A(k-1) = ai (k -1),V = v,
swt Ht) = (3-6)
k= npr[A(k) = a, (k) I A(k 1) = at (k 1), L(k) = 1 (k)]

Stabilized Inverse probability of censoring weight (IPCW):

,t ( pr[C(k) = 0 | C(k 1) = 0, A(k -1) = a (k 1), V = v,
sW = ft) =(3-7)
k Opr[C(k)= 0 |C(k -1)= 0,A(k -1) a, (k 1),L(k -1) = (k -1)]

Model parameters (uppercase letters represent random variables, lowercase letters denote

specific realizations of that random variable):

* w, (t) = probability of individual ito have experienced his or her own observed treatment
history from time 0 to time t

* sw, (t) = stabilized form of w, (t)

* A(k) = 1 if SBP < 140 mm Hg, 0 otherwise

* L(k) = vector of all measured risk factors for Y at time k (number of antihypertensive
drugs)

* Y = 1 if the INVEST primary outcome occurred

* V = vector of all baseline risk factors for Y

* swl (t)= stabilized weight for the probability of censoring for individual i









* C(k) =1 if a subject was lost to follow up by time k

The IPTWs were estimated using a pooled logistic regression model for the probability of

having controlled systolic blood pressure at visit (k) conditional on baseline covariates (all

measured baseline variables were included) and antihypertensive treatment (number of both

study and total antihypertensive drugs) at baseline and visit (k-1). The IPCWs were estimated in

the same fashion using a pooled logistic regression model for the probability of being censored at

visit (k). Second, combined stabilized weights sw, (t) x sw, (t) were calculated for each patient

visit.

Lastly, the combined stabilized weights were used in a weighted Cox proportional hazards

model. To overcome computational limitations of standard software (most available programs

including SAS do not allow subject specific time-varying weights), the Cox proportional hazards

model was estimated by fitting a pooled logistic regression that included the weights, baseline

covariates and the time-dependent systolic blood pressure control variable.26'32 The model was

specified as follows:


logit pr[D(t) = 1 D(t -1)= 0,A(t 1),V]= A(t) + /1A(t -1) + 3,2V (3-8)


D(t) = 1 if the subject had an event in month t and D(t) = 0 otherwise.

To assess whether antihypertensive treatment acted as a time-dependent confounder, we

compared the hazard ratio for SBP control obtained from the marginal structural Cox model (eA

from equation 3-8 with each patient visit weighted by the combined stabilized weights) with the

estimate obtained from a standard time-dependent Cox model (i.e., a model that did not adjust

for time-dependent confounding). The hazard ratio for SBP control in the standard time-

dependent Cox model was estimated simply by using equation 3-8 without the combined weights









(e81 from equation 3-8). Statistical significance of the difference was assessed by comparing the

95% confidence intervals of both estimates.

Antihypertensive Treatment and CV Outcomes

The time-dependent effect of treatment on the risk of primary outcome event was assessed

both adjusted and unadjusted for time-dependent SBP, using Cox proportional hazards regression

with and without combined stabilized weights (i.e., using a marginal structural- as well as a

standard time-dependent Cox model as in the section above).

Marginal Structural Cox Models

A marginal structural Cox model similar to the one described before was used to estimate

the effect of time-dependent treatment (aggressive antihypertensive treatment versus

conventional antihypertensive treatment) on primary outcome controlling for SBP at each visit.

Aggressive antihypertensive treatment was defined as being simultaneously exposed to three or

more total antihypertensive drugs. To assess the sensitivity of the results to this rather arbitrary

definition (that is necessitated by the method's restriction to a binary independent variable), the

analyses were also conducted using the four following additional definitions for aggressive

treatment: (1) more than one total antihypertensive drug, (2) more than three total

antihypertensive drugs, (3) more than one antihypertensive study drug, and (4) more than two

antihypertensive study drugs. Because of the U-shaped relationship between SPB and the risk for

cardiovascular outcomes in INVEST, time dependent SBP was categorized into three categories,

low (<120 mm Hg), normal (120 mm Hg to <140 mm Hg), and high (> 140 mm Hg).

As in the model for SBP control, the stabilized inverse probability of treatment and inverse

probability of censoring weights were estimated (Equations 3-6 and 3-7). The IPTWs were

estimated using a pooled logistic regression model for the probability of being exposed to

aggressive versus standard antihypertensive therapy at visit (k) conditional on baseline covariates









(all measured baseline variables were included) and systolic blood pressure (low, normal, or

high) at baseline, visit (k) and visit (k-1). The IPCWs were estimated in the same fashion using a

pooled logistic regression model for the probability of being censored at visit (k).

Equations 3-5 to 3-8 apply as before with treatment now defined as aggressive

antihypertensive treatment and SBP acting as a potential time-dependent confounder, thus:

* A(k) = 1 if the number of total antihypertensive drugs was greater than 2, 0 otherwise

* L(k) = vector of all measured risk factors for the outcome at visit k (including the three
previously defined SBP categories)

As in the previous section, combined stabilized weights was computed and used in a

weighted Cox proportional hazards model that is estimated through pooled logistic regression

including the combined weights, baseline covariates, and the time-dependent treatment variable

(aggressive antihypertensive treatment).

Cox Proportional Hazards Models

In addition to the marginal structural Cox model, a standard time-dependent Cox model

was estimated analogous using the same pooled logistic regression model that was used in the

marginal structural Cox model above (equation 3-8) but without weighting. The hazard ratio for

SBP control obtained by the standard time-dependent Cox model was then compared to the one

obtained from the marginal structural Cox model to determine whether a confounding effect of

SBP on the hazard ratio for aggressive versus standard antihypertensive treatment exists.












Verapamil SR Strategy


I ---[


Diabetes, renal impairment, heart failure add trandolapril


Step 1
Cerapamil SR 240 mg

Step 2
Verapamil SR 240 mg +
trandolapril 2 mg

Step 3
Verapamil SR 180 mg b.i.d. +
trandolapril 2 mg b.i.d.


Step 1
Atenolol 50 mg


Addition of drug



Increase dose


Step 2
Atenolol 50 mg +
HCTZ 25 mg

Step 3
Atenolol 50 mg b.i.d. +
HCTZ 25 mg b.i.d.


# Step 4 -Addition of diu Step 4
Verapamil SR 180 mg b.i.d. + Atenolol 50 mg b.i.d. +
trandolapril 2 mg b.i.d. + HCTZ 25 mg HCTZ 25 mg b.i.d. + trandolapril 2 mg
Increase dose and/or add nonstrategy drugs)

Strategy drugs could be titrated: verapamil SR 120-480 mg/d; trandolapril 0.5-8 mg/d;
atenolol 25-200 mg/d; HCTZ 12.5-100 mg/d
Available verapamil SR/trandolapril combinations: 180/2 mg/d, 240/1 mg/d, 240/2 mg/d, 240/4 mg/d


Treatment strategies in the INVEST. Reprinted with permission from Elliott WJ,
Hewkin AC, Kupfer S, Cooper-DeHoff R, Pepine CJ. A drug dose model for
predicting clinical outcomes in hypertensive coronary disease patients. J Clin
Hypertens (Greenwich). Nov 2005;7(11):654-663 (Figure 1, page 656).33


Figure 3-1.


Atenolol Strategy


I
..











Visit 1 2 3 4 5 n/a

Observed SBP 160 140 130 n/a 155 n/a

Time [weeks] 0 6 12 18 24 32 (event)
I I III
f 1B5 i___________________________________
155
Baseline E 145- 10(visitl)
135 -
125-

165 -
E 155 143.75=(160'6+140'6+130'12+155'8j 132
Fixed Average E 145 -
135 -
5 125 -

165 160 (visit 1) 155 (visit 5)
155 2
Updated Previous 2 145 40visit2)
Z 135 130 (visit 31
125

Y 165 155 (visit 5)
2 155
Updated Next E 145 1- 40 (visit 2)
Z 135- i-- 130 Ivisit 3)
125

iS5 165 60 (visit 1) 150= 143.75=
E 155 (166140* 12 (160'6+140*6+130t12+1558)/32
Updated Mean E 145
135 -
125 140= {1606+140*C+13012)124

Figure 3-2. Operationalization of SBP: Examples for a sample patient.









CHAPTER 4
RESULTS

A total of 22,576 patients satisfied all requirements for inclusion into the original INVEST

analysis.4 Total follow-up time for the cohort was 61,845 patient years with 2,269 patients

experiencing a primary outcome event during this period. For the present study, 906 patient years

of follow-up were excluded from the analysis because they accrued after the occurrence of a

nonfatal primary outcome event and thus, a total of 60,939 patient years of follow-up remained

available for analysis.

Descriptives

Baseline characteristics of the INVEST cohort relevant to the present study are presented

in Table 1. Briefly, the cohort had a mean age of 66.1 (9.8) years and included slightly more

women than men. The majority of patients were White, followed by large proportions of

Hispanics and Blacks. Considerable proportions of patients had a history of cardiovascular

events, or conditions recognized as cardiovascular risk factors. No breakdown by INVEST

treatment strategy is provided since randomization is not relevant to the analyses presented in

this study.

Average follow-up time to primary outcome event or censoring (end of follow-up or loss

to follow up) was 2.7 (0.9) years, ranging from 1 day (a patient who experienced a PO event on

the day of the first visit) to a maximum of 5.4 years. Of a maximum of 14 possible physician

visits designated for data collection and treatment adjustments, the average number of visits

during INVEST follow up (including last encounter) was 7.3 (2.7). After missed visits prior to

censoring were imputed by carrying forward values from the last observed visit, this number

increased to 9.5 (1.8).









The number of patients at risk at each visit is depicted in Figure 4-1. All figures display

follow-up over only 48 months (visits 1 to 12) due to the low numbers of uncensored patients at

the last two visits (2583 patients after 54 months, and 792 patients after 60 months).

However, all analyses are conducted using data of all 60 months (visits ltol4). Ninety five

percent of patients remained in the trial at 24 months, slightly less than 50% at 36 months and

only about 12% at 48 months. Depending on the visit number, between 64% and 85% of

uncensored patients had an observed visit. Visit four (week 18) shows the lowest percentage of

observed visits, with only 64% of uncensored patients assessed at this visit. For the remainder of

this study, all results are reported for the imputed data (with values carried forward for missed

visits as described above) unless noted otherwise.

Blood Pressure

Mean SBP at the baseline visit was 150.9 mm Hg (19.5). After 24 months, the mean SBP

was reduced by 17.2 mm Hg to 133.7 mm Hg (16.8). This reduction occurred mainly early in

the trial with 52%, and 80% of the reduction observed at the six week and 12-week visits,

respectively (Figure 4-2). When only observed visits were evaluated, SBP values at each visit

were on average about 2.5 mm Hg lower than in the imputed dataset. For the majority of the

analyses in this study, SBP was categorized into 7 categories, each spanning 10 mm Hg and

ranging from smaller than 110 mm Hg to greater or equal to 160 mm Hg (Figure 4-3). At

baseline 75% of patients had uncontrolled SBP (>140 mm Hg) and 33% had a SBP of greater or

equal to 160 mm Hg. Forty-four and 31% of patients showed uncontrolled SBP after three and

24 months, respectively, with 15% and 9% of patients in the range of greater than 160 mm Hg.

Figure 4-4 depicts the proportions of patients within each SBP category and at each visit

(starting with visit two) who where not in the same category at the visit before (i.e., had changed

SBP category between visits). The early drop in mean SBP shown in Figure 4-2 is mirrored at









the first data points (six week visit) in Figure 4-4. Between 70% and 85% of patients in the

lowest four SBP categories had not been in the same category at baseline. With the exception of

the highest SBP category that throughout follow-up at each visit included between 25% and 40%

of patients who were in lower SBP categories at the visit before, all other categories show

between 40% and slightly above 60% of patients with changed SBP category at each visit.

Overall, at any given visit, only about half of all patients did not change blood pressure

categories.

Antihypertensive Drugs

At the baseline visit, patients received on average 2.9 antihypertensive drugs, 1.5 of which

were INVEST study drugs (Figure 4-5). After six months of follow-up the number of study drugs

had increased to 1.9 while the total number of drugs had decreased to 2.6. These numbers

remained relatively stable throughout month 30, after which the total number of drugs and the

number of study drugs dropped to about 2 and 1.5, respectively. The proportions of patients

receiving each individual study drug over follow-up are depicted in Figure 4-6. At baseline, the

first line study drugs verapamil and atenolol were utilized by 50% and 45% of patients, with

20% and 33%, respectively, receiving the add-on drugs HCTZ and trandolapril. Over the follow-

up period the percentage of patients on first line study drugs continuously dropped to 40% and

30% of patients on verapamil and atenolol after 24 months, respectively, and 38% and 28% after

48 months. Over the initial six months of follow-up, the proportion of patients on add-on study

drugs increased to 42% and 44% for HCTZ and trandolapril, respectively. Starting at week 12,

trandolapril was the most commonly used study drug within INVEST, with atenolol becoming

the second most commonly used study drug after one year. From 30 months to the end of follow-

up, the proportion of patients on study add-on drugs dropped to about 40% to 45% for HCTZ and

trandolapril, after remaining relatively constant at 47% to 55% from 12 to 30 months.









Proportions of INVEST patients categorized by the number of study and total

antihypertensive drugs are shown in Figures 4-7 and 4-8. At baseline 62% of patients received

one, 28% two, and the remaining 10 percent three study antihypertensive drugs. After the first

six months, the number of patients on one study drug had more than halved to 29%, while 41%

and 25% of patients were placed on two and three study drugs, respectively, and 5% of patients

did not receive any study antihypertensive treatment. Over the following months, the proportion

of patients on one study drug continued to decrease to 19% at month 30, with 20% having no

study antihypertensive drug at this time point. Over the same time period the proportion of

patients on three study drugs increased to 30% while the proportion of patients on two study

drugs dropped to 31%. After 30 months the percentages of patients on study drugs continued to

drop slightly with the proportion of patients without study drugs increasing to 34% by month 48.

Similar trends can be observed when examining the data for all antihypertensive drugs.

From baseline to 24 months most patients (between 33% and 39%) received two

antihypertensive drugs followed by patients on three antihypertensive drugs. From month 30 to

the end of follow-up, patients on three antihypertensive drugs contributed the largest proportion

with 27% to 30%. Starting at month 36 and throughout the remainder of follow-up about one

quarter of patients did not receive any antihypertensive drugs. Throughout the follow-up period a

stable proportion of between 5% and 10% of patients each received five and more than five

antihypertensive drugs.

Compared to the high proportion of patients who experienced changes in their SBP

categories between visits (Figure 4-4), antihypertensive drug use was relatively stable. Figure 4-9

shows by visit and starting at the second visit the proportion of patients who had a change in the

number of prescribed antihypertensive study drugs from the prior visit. After 18 months this









proportion stabilized at around 10% for patients on one to three study drugs, but ranging from

30% to 50% for patients who did not have a prescription for a study drug.

Compared to the changes reported for the number of antihypertensive study drugs (Figure

4-9), changes in the number of total antihypertensive drugs were more pronounced. Figure 4-10

shows by visit and starting at the second visit the proportion of patients who had a change in the

number of prescribed total antihypertensive drugs compared to the prior visit. Patients with no

antihypertensive drugs are most likely to report a change from the visit before (depending on the

visit, 50% to 90% of patients who did not take any antihypertensive drugs were on at least one

antihypertensive drug at the prior visit. After visit two and for those patients who had a

prescription for at least one antihypertensive drug, the proportion who reports changes in the

total number of antihypertensive drugs ranges from 10% to 45% with patients on five total

antihypertensive drugs generally reporting the highest proportion of change.

Primary Outcome Events

Figure 4-11 displays a constant slope for the cumulative number of INVEST primary

outcome events over the initial three years of follow-up, followed by a slightly steeper slope for

the remaining years, indicating that the event rate in INVEST is initially constant with only a

small increase after more than three years of follow-up.

Hazard Ratios

The following section shows plots of hazard ratios (HR) by categories of SBP, obtained by

conventional and time-dependent Cox PH regression. All hazard ratios show the hazard for

primary outcome event in a specific SBP category compared to the hazard for a primary outcome

event in the category of SBP 130-140 mm Hg (reference category). Operationalization of SBP

was varied and included baseline, mean over follow-up, mean over follow-up weighted by time









of follow-up, actual value at prior visit (time-dependent), actual value at the following visit

(time-dependent), and updated mean over follow up (time-dependent).

Baseline SBP Model

Figure 4-12 shows the hazard ratios and 95% confidence intervals for a primary outcome

event by categories of baseline SBP. The relationship between baseline SBP and the hazard for

an outcome event follows a reverse J-shape with a nadir at the reference category of 130 to < 140

mm Hg. The lowest and two highest SBP categories show significantly increased risk, while the

remaining three categories show no difference. The distribution of patients within each SBP

category was as follows: Almost 33% of patients had a baseline SBP of greater than 160 mm Hg

with relatively few patients contributing to categories of 110 and 110 to 120 mm Hg (3%) and

smaller than 110 mm Hg (0.9%). The remaining categories of baseline SBP included between

8% (SBP 120 to <130 mm Hg) and 22% (SBP 140 to <150 mm Hg) of the 22576 INVEST

patients.

Average SBP Model

Calculation of the average SBP over follow up for each subject resulted in 7259 patients

(32%) with an average between 130 mm Hg and 140 mm Hg, followed by 6403 subjects (28%)

with an average follow-up SBP between 120 mm Hg and 130 mm Hg. The two extreme SBP

categories of less than 110 mm Hg and greater than 160 mm Hg, included fewer subjects with

190 (.8%) and 1500 subjects (6.6%), respectively. The relationship between risk for primary

outcome and average SBP categories over follow-up follows a J-curve with the nadir at 120 mm

Hg to 130 mm Hg (Figure 4-13). Patients with an average SBP over follow-up between 120 mm

Hg and 130 mm Hg show no difference in the risk for an outcome event (HR 0.96, 95% CI 0.85-

1.09) compared to the reference category, while all remaining categories show significantly

higher risk. Different from the hazard ratios obtained for baseline SBP the increase in the hazard









is larger for the highest two categories of average SBP (with a maximum increase of 180%, 95%

CI 44%-221%, at SBP greater or equal 160 mm Hg) than for the lowest category (80%, 95% CI

25%-158%). In comparison, the estimates for SBP of greater or equal 160 mm Hg and lower

than 110 mm Hg were a 17% increase (95% CI, 2-33%) and a 64% increase (95% CI, 17-130%)

when the baseline SBP was used.

Average SBP Weighted by Follow-up Time Model

Individual follow-up time in INVEST was used to weight each individual's average

follow-up SBP (Figure 4-14) to avoid over-representation of patients who contributed little

follow-up time due to an early event or loss to follow-up early in the trial. The resulting curve

shows a similar shape as Figure 4-13 but is generally flatter. Its maximum hazard ratio occurs at

an average SBP greater or equal to 160 mm Hg and with 2.11, 95% CI 1.76 2.54, is about one

third lower than the hazard ratio for the un-weighted average at the same SBP category (HR

2.80, 95% CI 2.44-3.21). The risk at the lowest SBP category of less than 110 mm Hg is not

different from the risk at the next higher category and shows a very wide confidence interval due

to the low number of patients with low average SBP.

Time-Dependent SBP Models

Figure 4-15 shows the relationship between the SBP category observed at the last recorded

visit of a given time interval in the Cox model and the risk for a primary outcome event. SBP

categories were continuously updated over the course of follow-up. Figure 4-15 shows a flat V-

shape with its nadir at SBP between 130 mm Hg and 140 mm Hg. All but the category between

120 to 130 mm Hg show a significantly increased risk for a primary outcome event compared to

the reference category. The lowest and the two highest SBP categories show slightly over 50%

increase in risk while the remaining two categories are at about 20%.









In contrast to Figure 4-15, Figure 4-16 shows hazard ratios for the primary outcome by

category of time-dependent SBP from the next observed visit. Here, SBP for each given time

interval is taken from the first observed visit after this time interval. One exception was made:

For the time period immediately preceding an event, the SBP from the last observed visit was

used since there was no observation available after the patient was censored. Figure 4-16 shows a

J-shaped curve with nadir for the hazard ratio at 120 mm Hg to 130 mm Hg, significantly lower

than the reference category (HR 0.73, 95% CI 0.65-0.83). Departing from the curve's J-shape the

two lowest SBP categories show almost identical hazard ratios.

Updated Mean SBP Model

The hazard ratios for Figure 4-17 were derived calculating at each observed visit an

updated mean SBP that was used as a time-dependent covariate in the model. This produced a

nearly symmetric V-shaped curve with its nadir at SBP 130-140 mm Hg. With the exception of

updated mean SBP values between 120 mm Hg and 130 mm Hg (HR 1.09, 95% CI 0.96-1.23),

all remaining SBP categories showed significantly higher hazard ratios than the reference

category. The lowest and highest categories showed the greatest increase in risk with hazard

ratios of 1.61 (95% CI, 1.12-2.32), and 1.80 (95% CI, 1.56 2.06), respectively. Compared to

the analysis using the unweighted average, the highest three categories using the updated mean

showed between 13% (SBP between 140 mm Hg and 150 mm Hg) and 35% (SBP larger than

160 mm Hg) lower risk for a primary outcome event. Compared to the time dependent SBP

model (prior visit) the results of the updated mean model show only small differences ranging

from a 5% lower estimate (SBP between 150 mm Hg and 160 mm Hg) to a 25% overestimation

(SBP between 110 mm Hg and 120 mm Hg) with the lowest and highest SBP category within

3% and 13% respectively.









Incidence

While the previous section presented numerous estimates of the hazard for an outcome

event in a specific SBP category relative to the reference category of 130 to 140 mm Hg,

absolute risks for patients in specific SBP categories have thus far not been presented. The

following section shows both unadjusted and adjusted incidence rates presented as the number of

primary outcome events per 1000 person years spent in the seven respective SBP categories.

Figure 4-18 presents unadjusted incidence rates for the primary outcome events by

category of SBP. Each subject's follow-up period could contribute person time to multiple SBP

categories. Person time was accrued for the last observed SBP category until a change in SBP

category, the occurrence of an event, or censoring. Likewise, events were attributed to the SBP

category observed at the last visit prior to the event. Most person years of follow-up were

accrued in the category of 130-140 mm Hg (16188 person years), while the category of<110

mm Hg contributed the lowest number (1678 person years). The crude incidence of the INVEST

primary outcome by SBP category was V-shaped and consequently highest in the extremely low

and high SBP categories <110 mm Hg (53.6 primary outcome events/1000 person years) and

>160 mm Hg (53.8 primary outcome events/1000 person years). The crude incidence rates in the

categories of 130 to 140 mm Hg, and 120 tol30 mm Hg were more than 40% lower with 30.6

primary outcome events/1000 person years for these SBP categories.

The respective adjusted incidence rates, calculated by Poisson regression for White, US,

female patients without co-morbidities and between the ages of 60 and 70 years, displayed in

Figure 4-19 show a similar V-shape and range from 14.1 primary outcome events/1000 person

years for the SBP category between 130 tol40 mm Hg to 18.8 primary outcome events/1000

patient years for the category greater than 160 mm Hg.









Comparisons

The two previous sections present several approaches to determine relative and absolute

risks to experience an outcome event for patients of the INVEST depending on their SBP

category. The following section compares the results of these approaches and provides a brief

description of the assumptions implied in each of the modeling approaches.

Table 4-2 presents a summary of the results obtained by the modeling approaches of the

previous two sections. For each model, Table 4-2 shows the hazard ratios (relative risks for the

Poisson regression model) for the lowest SBP category (<110 mm Hg), the category with the

lowest risk for an outcome event, and the highest SBP category (>160 mm Hg). Hazard ratios

and relative risks for the lowest and highest SBP category are presented both in comparison to

the reference category (130 tol40 mm Hg) and the SBP category with the lowest risk (in

parenthesis) if that is not the reference category in the respective model. Additionally, Table 4-2

shows the generalized R2 for each model. Compared to the reference category, the hazard

ratios/relative risks for the SBP category of lower than 110 mm Hg range from 1.16 (time-

dependent next) to 1.80 (average over follow up). At the same time hazard ratios/ relative risks

for the highest SBP category (>160 mm Hg) range from 1.17 (baseline) to 2.80 (average).

Notably, the most extreme estimates for both the lowest and highest SBP categories were

obtained from the average SBP model. Generalized R2 values for the presented models were

small, ranging from 0.039 to 0.070, with little difference between models.

Average SBP and Bias

Table 4-3 illustrates in a much simplified scenario that the use of an average of a measure

(e.g., controlled versus uncontrolled SBP averaged over follow-up) can lead to biased estimates

if (1) the duration follow-up time is not fixed but rather determined by the occurrence of an event

and (2) there is a directed change of the measure over the course of follow-up (i.e., mean SBP is









lowered during the course of INVEST, especially early). Of note, conditions (1) and (2) are

typically met in the context of clinical trial data that treat a surrogate over follow-up and have a

primary outcome at which patients are censored, such as the INVEST data. It also applies to

observational studies where a surrogate shows a time-dependent upward or downward trend.

Notably a directed change in a mean over follow-up can also occur as the result of regression to

the mean if inclusion of subjects in the study is dependent on extreme values of the surrogate.

The simplified scenarios (A to F) below make the following assumptions:

* Patients start with either controlled or uncontrolled blood pressure

* Duration of follow-up is three years

* Measures are taken after the first and third years

* The event rate is constant at 10% per year and independent of blood pressure control

* Events occur at the time of measurement

* At the end of follow up the average is calculated as high and low, respectively, for those
patients who remained in their BP category over follow up and for those who changed BP
category after the first year as the value of the second (longer) measurement period.


Scenarios A to F show the effects of varying longitudinal changes in BP (A to D), and

different patient distributions between controlled and uncontrolled BP at baseline (E to F):

* Scenario A: 100 patients each start with controlled and uncontrolled BP respectively.
Patients do not change BP categories throughout follow-up.

* Scenario B: 100 patients each start with controlled and uncontrolled BP respectively. 30%
of patients with uncontrolled blood pressure will be controlled after the first follow-up
year. Patients with controlled BP will continue to have controlled BP.

* Scenario C: 100 patients each start with controlled and uncontrolled BP respectively. 60%
of patients with uncontrolled blood pressure will be controlled after the first follow-up
year. Patients with controlled BP will continue to have controlled BP.









* Scenario D: 100 patients each start with controlled and uncontrolled BP respectively. 60%
of patients with uncontrolled blood pressure will be controlled after the first follow-up
year. 60% of patients with controlled blood pressure will have uncontrolled BP after the
first follow-up year and over the remainder of follow-up.

* Scenario E: Equivalent to scenario D except that 200 patients have uncontrolled BP and
100 patients have controlled BP at baseline.

* Scenario F: Equivalent to scenario D except that 100 patients have uncontrolled BP and
no patients have controlled BP at baseline.


Scenario A (no changes in BP categories over follow-up) results, as expected, in an event

rate of 10 events per 100 patient years. Overall, 28 events occurred, 10 (35.7%) of which

occurred after the first year. The number is slightly higher than one third because only 90 of the

original 100 patients were still at risk for an event in the second, two-year long, follow-up

period. Scenario B, which has 30% of patients switch from uncontrolled to controlled BP after

one year, deviates from the expected event rates. It results in an event rate of 11.6% for patients

with average uncontrolled BP over follow-up and 9.2% for patients with average controlled BP.

The percentage of all events of the categories stemming from patients whose average BP was

based on only the first year of follow-up is about 10 percentage points higher, at 45.5%, as

expected for patients with uncontrolled BP and about 6% lower than expected for those who

average controlled BP (29.4%). Of note, the number of events after one year of follow up is

constant throughout all four scenarios at 10 each for controlled and uncontrolled patients,

respectively. Scenario C, which doubles the percentage of patients who, starting as uncontrolled,

achieve BP control after the one year visit, results in an even larger deviation from the true event

rate. This scenario results in a 16% event rate for those patients averaging uncontrolled BP and

an 8.7% event rate for those averaging controlled BP. Simultaneously, the percentage of all

events per category contributed by patients whose average was only based on the first year of

follow-up diverged further from the expected 35.7%, with 62.5% of all events within patients









whose average BP over follow-up was uncontrolled resulting from patients who had an event at

the end of the first year, and only 25% of all events in patients with an average controlled BP

attributable to patients who had their event after one year. Model D demonstrates, that when

patients switch BP categories evenly, that is when as many patients become uncontrolled after

one year as achieve BP control, calculated event rates-as in scenario A where patients do not

switch between categories at all-match expected event rates. Scenario E demonstrates that not

the proportional change between categories is responsible for the proportion of events that occur

in the first year but rather the absolute number of patients with a change in BP categories. While

the proportions of patients who switch categories in scenario E are identical (60% in each group),

the absolute number of patients who switch from uncontrolled to controlled is double the number

of patients that switch from controlled to uncontrolled since twice as many patients started

follow-up in the uncontrolled group. Overall, model E results in 45.5% of all events within the

uncontrolled group from the first year of follow-up. Lastly, Scenario F, in which all patients start

with uncontrolled BP and thus, change is by definition directed for the first year of follow up,

results in 62.5% of all events within the uncontrolled group resulting from the first visit

compared to 0% of all events in the controlled group from the same time period (since no

patients with uncontrolled BP were at risk during the first year).

To show the consequences of using the average BP control over follow-up as the predictor

of cardiovascular risk, we calculated the relative risks to experience an event comparing patients

with an uncontrolled average over follow-up to patients with a controlled average over follow

up. The relative risks were calculated by dividing the absolute risk (event rate per patient year) of

uncontrolled patients over the absolute risk of patients with controlled SBP over follow-up.

Absolute risk estimates were obtained by dividing the number of events that occurred in each









group by the person years of follow-up in the respective BP category based on the average BP

over follow up (e.g., a patient who was uncontrolled during year one and controlled for the

remaining two years contributes all 3 years of follow-up to the uncontrolled SBP group). Of

note, the true relative risk is 1.0, since the event rates used for the simulation were identical

between groups at 10% per patient per year.

Scenarios A and D, the scenarios that show equal numbers of patients in both average

groups after follow-up (i.e., lack directed change of the measure) accurately show relative risks

of 1.0. In contrast, scenarios B and C, that both simulate a directed change of patients from

uncontrolled to controlled average BP over follow-up as a result of higher rates of change

between groups from uncontrolled to controlled BP, show relative risks of 1.26 and 1.84,

respectively. However, scenario E in which patients change between groups in equal proportions

as in scenario D, but shows a directed net change of subjects resulting from regression to the

mean (since twice as many patients start follow-up in the uncontrolled group with both groups

having equal rates of change), estimates a relative risk of 1.59, similar to scenarios B and C.

Lastly, scenario F, that at baseline only includes patients with uncontrolled BP and thus shows

the strongest possible directed change of patients between groups, estimates the largest relative

risk with 2.39. Scenarios A to F show that even with identical true event rates per year of follow-

up, the mere fact that a directed change in BP control exists, leads to an overestimation of risk in

the categories that lose patients and to an underestimation of risk in those categories that gain

patients.

In contrast, Table 4-4 shows the results of the equivalent six simulations, when the

denominator (person time) of the absolute risk estimates for each BP category is time-dependent.

In these simulations, a patient who started with uncontrolled BP at baseline and achieved blood









pressure control for years two and three, contributes one person year to the total person time in

uncontrolled BP and two person years to the total person time in controlled BP (in the average

calculation the same patient contributes all three years to the total person time in controlled BP

since his average over the entire follow-up is controlled). Notably, when using this updated mean

SBP, the simulations under all scenarios correctly estimate the true relative risk of 1.0.

The results of these simple simulations help explain the observed differences between the

Cox proportional hazards regressions with average SBP over follow-up (Figure 4-15) and

updated mean SBP (Figure 4-19). In the simulation we observe a correlation between the

magnitude of the observed bias in Scenarios B and C and the proportion of total events within

each category that resulted from the patients with only one year of follow-up at their event time.

The higher this proportion, the higher was the observed relative risk (i.e., bias, since the true RR

is 1.0). Figure 4-20 illustrates within INVEST the calculation of bias introduced by the Cox

model using the average SBP, expressed as the percent difference from the hazard ratio obtained

by the time-dependent Cox model using the updated mean SBP. The largest bias exits in the

highest two SBP categories where the Cox model using the average over follow-up

overestimates the hazard ratios by 34% and 56%. Figure 4-21 shows for INVEST within

categories of average blood pressure over follow-up the proportion of total events that were

contributed by patients based on their number of observed visits at the time of the event. Figure

4-21 shows that patients in the highest two and the lowest average SBP categories were

considerably more likely to have their average based on only the baseline visit (i.e., their event

occurred before the second visit).

Figure 4-22 combines data generated by Figures 4-20 and 4-21 and plots the bias of the

Cox model using the average SBP (Figure 4-20) and the proportion of events resulting from









patients with only two observed visits (Figure 4-21) in the same graph by SBP category. As

observed in the simulation, the bias resulting from using an average over follow-up correlates

with the percentage of events after the first follow-up period, strongly suggesting, that the higher

hazard ratios obtained from the Cox model using average SBP over-follow up are indeed

resulting from a bias analogous to the bias simulated in scenarios B, C, E, and F of Table 4-2.

Of note, the time-weighted average is equally affected by this suggested bias. However, the

impact of the bias is likely attenuated since observations who contribute strongest to the bias

(patients who experience events early) receive small weights compared to patients with longer

follow-up times.

Marginal Structural Models

The first part of this section intends to expand on the analyses of the prior sections by

using a marginal structural Cox model to estimate the effect of SBP on the risk for

cardiovascular events controlling for potential time-dependent confounding by antihypertensive

drug use. However, instead of the seven SBP categories used in the previously presented models,

a binary operationalization of SBP (controlled vs. uncontrolled, with controlled defined as SBP<

140 mm Hg) was used to accommodate current limitations in the method. Note that 2038 patients

with extremely low SBP values (< 110 mm Hg at any visit during follow-up) were excluded to

allow the use of a binary SBP variable (required by the marginal structural Cox model) even

though the relationship between SBP and cardiovascular outcomes follows a U shape (Figures 4-

12 to 4-19). Time-dependent use of antihypertensive drugs was operationalized by the number of

total antihypertensive drugs and the number of study antihypertensive drugs (defined as

antihypertensive drugs that were part of the INVEST protocol) at baseline, each follow-up visit,

as well as lagged drug variables that, at each visit other than baseline, represent the values of the

respective prior visit. The second part of the section aims to estimate the effect of









antihypertensive drug use controlling for time-dependent confounding by SBP. Antihypertensive

drug use was operationalized as aggressive (more than two total antihypertensive drugs) versus

standard (two or less total antihypertensive drugs) antihypertensive therapy, with additional

definitions used in a sensitivity analysis. SBP was operationalized as low (lower than 120 mm

Hg); normal (120 mm Hg to lower than 140 mm Hg); and high (equal or higher than 140 mm

Hg).

Effect of Systolic Blood Pressure Control

Table 4-5 shows the result of the inverse probability of treatment weighted Cox model

(marginal structural Cox model) compared to the equivalent standard time-dependent Cox

model. Both models show a significantly reduced hazard for patients with controlled SBP

compared to patients with uncontrolled SBP. The standard model estimates a 46% (95% CI 40%-

52%) reduction in the hazard for a cardiovascular event while the inverse probability of

treatment weighted model estimates an almost identical reduction of 45% (95% CI 39%-50%).

There was no significant difference between the estimates of both models. A significant

difference between the models would support the presence of a time-dependent confounding

effect of antihypertensive treatment (i.e., a non SBP mediated effect of aggressive

antihypertensive treatment as defined).

Effects of Antihypertensive Drugs

Tables 4-6 provides an inverse probability of treatment weighted estimate for the effect of

aggressive (more than two concurrent total antihypertensive drugs) versus standard

antihypertensive treatment (two or less concurrent total antihypertensive drugs), compared with

estimates from the equivalent standard time-dependent Cox model. The standard Cox model

estimated no difference in cardiovascular risk between the treatment with aggressive and

standard antihypertensive therapy (HR 0.96, 95% CI 0.87-1.07). In contrast, the inverse









probability of treatment weighted Cox model estimated a significant 19% (95% CI 8%-29%)

reduction in the hazard of an outcome event for patients treated with aggressive antihypertensive

therapy. However, the two results have overlapping 95% confidence intervals and thus, are not

significantly different from each other. A significant difference between the two estimates would

suggest that time-dependent confounding by SBP control substantially alters the estimate of the

effect of receiving aggressive antihypertensive treatment.

Table 4-6 shows the results of a sensitivity analysis conducted to assess whether and by

how much the results were influenced by the definition of aggressive antihypertensive therapy.

As in the original analysis (Table 4-6), the effect of aggressive versus standard antihypertensive

treatment was assessed by estimating both a standard Cox model and a marginal structural Cox

model. Four additional definitions of aggressive antihypertensive therapy were assessed, (1)

more than one total antihypertensive drug, (2) more than three total antihypertensive drugs, (3)

more than one antihypertensive study drug, and (4) more than two antihypertensive study drugs.

Regardless of the definition used for aggressive antihypertensive treatment, all four comparisons

estimated a larger beneficial effect for aggressive antihypertensive therapy from the marginal

structural Cox model compared to the standard model.

As in the primary analysis, the difference between the models failed to reach significance

in three of the four models. The analyses that define aggressive antihypertensive treatment as the

concomitant use of more than three total antihypertensive drugs found the hazard ratio estimated

from the marginal structural Cox model (HR 0.79, 95% CI 0.71-0.89) to be significantly lower

than the one estimated by the standard model (HR 0.98, 95% CI 0.90-1.07). The analysis

defining aggressive antihypertensive therapy as the concomitant use of more than one study

antihypertensive drug found a borderline significant difference between the models with an HR









estimate of 0.61 (95% CI 0.54-0.68) for the marginal structural Cox model and 0.73 (95% CI

0.67-0.80) for the standard time-dependent Cox model, respectively.



Table 4-1. Composition of the INVEST Cohort at Baseline
Variable N=22576


Demographic
Age, mean (SD), years
Women
Race/Ethnicity
White
Black
Hispanic
Other
Calcium Antagonist Strategy
Condition
Myocardial infarction
Stroke/transient ischemic attack
Congestive Heart Failure
Diabetes
Renal impairment


66.1 (9.8)
11770 (52.1)

10925 (48.4)
3029(13.4)
8045 (35.6)
577 (2.6)
11267 (49.9)

7218(32.0)
1629 (7.2)
1256(5.6)
6400 (28.4)
424(1.9)


Peripheral vascular disease 2699 (12.0)
CABG 6166(27.3)
Smoking (ever) 10454 (46.3)
Abbreviations: SD, Standard deviation; CABG, Coronary artery bypass graft.
Unless indicated otherwise, values express numbers (percentage).





Table 4-2. Comparison of models
Model Hazard Ratio Minimum Hazard
at SBP <110 Ratio (at SBP
mm Hg category)
Baseline 1.64 1.00
(130 to <140 mm Hg)
Average over follow-up 1.80 0.96
(1.88*) (120 to <130 mm Hg)
Time-weighted average 1.41 1.00
(130 to <140 mm Hg)
Time-dependent (prior) 1.57 1.00
(130 to <140 mm Hg)
Time-dependent (next) 1.16 0.73
(1.59*) (120 to <130 mm Hg)
Updated mean 1.61 1.00
(130 to <140 mm Hg)
RR from Poisson 1.50** 1.00**
(130 to <140 mm Hg)
*Compared to the lowest risk category, ** Relative risk


Hazard Ratio
at SBP >160
mm Hg
1.17

2.80
(2.92*)
2.54

1.59

2.26
(3.10*)
1.80

1.57**


Generalized
R2

0.059

0.070

0.039

0.061

0.071

0.062

n/a











Table 4-3. Simulation of six scenarios using average over follow-up


1st Year of Follow-up


2nd & 3rd Years


Average Over Follow-up


N
(baseline)


Events Change
inBP
status


Uncontrolled 100 10 0
Controlled 100 10 0

Uncontrolled 100 10 30
Controlled 100 10 0

Uncontrolled 100 10 60
Controlled 100 10 0

Uncontrolled 100 10 60
Controlled 100 10 60

Uncontrolled 200 20 120
Controlled 100 10 60

Uncontrolled 100 10 60
Controlled 0 0 0
*in average over follow-up controlled vs. uncontrolled


No
change in
Bp status

90
90

60
90

30
90

30
30

60
30

30
0


N
(year 2)


Events


Scenario A
90 1
90 1
Scenario B
60 1
120 2
Scenario C
30
150 3
Scenario D
90 1
90 1
Scenario E
120 2
150 3
Scenario F
30
60 1


Total
Person
Time*


Total Event rate per
Events patient year


280 28
280 28

190 22
370 34

100 16
460 40

280 28
280 28

380 44
460 40


10%
10%

11.6%
9.2%

16%
8.7%

10%
10%

13.8%
8.7%

16%
6.7%


Percentage of
events from 1st
year

35.7
35.7

45.5
29.4

62.5
25

35.7
35.7

45.5
25

62.5
0


BP Status


Relative
Risk


1.0
1.0

1.26
1.0

1.84
1.0

1.0
1.0

1.59
1.0

2.39
1.0











Table 4-4. Simulation of six scenarios using updated mean


1st Year of Follow-up


2nd & 3rd Years


Average Over Follow-up


N
(baseline)


Events Change
inBP
status


Uncontrolled 100 10
Controlled 100 10

Uncontrolled 100 10
Controlled 100 10

Uncontrolled 100 10
Controlled 100 10

Uncontrolled 100 10
Controlled 100 10

Uncontrolled 200 20
Controlled 100 10

Uncontrolled 100 10
Controlled 0 0
* updated mean controlled vs. uncontrolled


No
change in
Bp status

90
90

60
90

30
90

30
30

60
30

30
0


N
(year 2)


Events


Scenario A
90 1
90 1
Scenario B
60 1
120 2
Scenario C
30
150 3
Scenario D
90 1
90 1
Scenario E
120 2
150 3
Scenario F
30
60 1


Total
Person
Time*


Total Event rate per
Events patient year


280 28
280 28

220 22
340 34

160 16
400 40

280 28
280 28

440 44
400 40


10%
10%

11.6%
9.2%

16%
8.7%

10%
10%

13.8%
8.7%

16%
6.7%


Percentage of
events from 1st
year

35.7
35.7

45.5
29.4

62.5
25

35.7
35.7

45.5
25

62.5
0


BP Status


Relative
Risk


1.0
1.0

1.0
1.0

1.0
1.0









Table 4-5. Inverse probability of treatment weighted estimates for the causal effect of controlled
SBP on primary INVEST primary outcome event
Hazard Ratio 95% Confidence Interval
Standard Cox model 0.54 0.48-0.60
Marginal Structural Cox Model 0.55 0.50-0.61
SBP control is defined as SBP < 140 mm Hg; patients who had SBP of<110 mm Hg at any visit
were excluded from the analysis (n=2038)

Table 4-6. Inverse probability of treatment weighted estimates for the effect of receiving more
than two total antihypertensive drugs on primary INVEST primary outcome event
Hazard Ratio 95% Confidence Interval
Standard Cox model 0.96 0.87-1.07
Marginal Structural Cox Model 0.81 0.71-0.92

Table 4-7. Inverse probability of treatment weighted estimates for the causal effect of receiving
various numbers of total antihypertensive drugs on INVEST primary outcome event
Hazard Ratio 95% Confidence Interval
> 1 total antihypertensive drug
Standard Cox model 0.89 0.70-1.13
Marginal structural Cox model 0.83 0.64-1.06
> 3 total antihypertensive drugs
Standard Cox model 0.98 0.90-1.07
Marginal structural Cox model 0.79 0.71-0.89
> 1 study antihypertensive drug
Standard Cox model 0.73 0.67-0.80
Marginal structural Cox model 0.61 0.54-0.68
> 2 study antihypertensive drugs
Standard Cox model 0.78 0.71-0.85
Marginal structural Cox model 0.72 0.64-0.81











25000


20000


15000
N
10000


5000


0


0 6 12 18 24
Time [months]

Figure 4-1. Patients remaining in the study at each visit


30 36 42 48


-*-observed & imputed
-u-observed


0 6 12 18 24 30 36 42
Time [months]

Figure 4-2. Mean systolic blood pressure over follow-up (observed vs. imputed data)


-*-observed & imputed
--w- observed


I











-*-<110 mm Hg -.-110-<120mm Hg -A-120-<130mm Hg
-)- 140-<150 mm Hg -*-150-<160 mm Hg -->160 mm Hg


35%

30%

25%
a,
S20%

S15%

10%

5%

0%


130- <140 mm Hg


0 6 12 18 24 30 36 42 48
Time [months]

Figure 4-3. Percentage of patients within each SBP category over follow-up


-*-<110 mm Hg -u-110 <120mmHg --120 <130mmHg
-)-140-<150mm Hg -*-150-<160mm Hg -i->160mm Hg

90%
80%
70%
60%
50%
40%
30% -
20%
10%
0%


130 -<140 mm Hg


0 6 12 18 24 30 36 42
Time [months]


Figure 4-4. Percentage of patients within each SBP category who were not within the same SBP
category at the prior visit












-*-total antihypertensive drugs
-u-study antihypertensive drugs
3


E 2
z

1


0
0 6 12 18 24 30 36 42 48
Time [months]

Figure 4-5. Number of total antihypertensive drugs and antihypertensive study drugs over
follow-up


-- Atenolol -- HCTZ -x Verapamil Trandolapril


60%

50%

40%
a)

C 30%

I 20%

10%

0%


18 24
Time [months]


30 36 42 48


Figure 4-6. Percentage of patients on each individual study drug over follow-up












-*-0 study drug
-U- 1 study drug
-A- 2 study drugs
3 study drugs


A


18 24
Time [months]


30 36 42 48


Figure 4-7. Number of INVEST study drugs over follow-up


-*-0 antihypertensive drug --1 antihypertensive drug -A-2 antihypertensive drugs
3 antihypertensive drugs -- 4 antihypertensive drugs -*-5 antihypertensive drugs
-->5 antihypertensive drugs

45% -
40% -
35%
S30%
.9 25%
2 20% -------------------/ ^ ^ l ~

10%
15%



0%
0 6 12 18 24 30 36 42 48
Time [months]


Figure 4-8. Number of total antihypertensive drugs over follow-up


70%


60%

50%

40%

8 30%

20%

10%

0%











-s-0 study drug -- 1 study drug -A-2 study drugs


100%
90%
80%
70%
60%
50%
40%
30%
20%
10%
0%


Figure 4-9.


0 6 12 18 24 30 36 42 48
Time [months]

Percentage of patients on a specific number of antihypertensive study drugs who
were not on the same number of antihypertensive drugs at the prior visit


-s-0 antihypertensive drug -.-1 antihypertensive drug -a-2 antihypertensive drugs
3 antihypertensive drugs 4 antihypertensive drugs -*-5 antihypertensive drugs
-i->5 antihypertensive drugs


100%
90%
80%
70%
60%
50%
40%
30%
20%
10%
0%


0 6 12 18 24 30 36 42 48


Time [months]

Figure 4-10. Percentage of patients on a specific number of antihypertensive drugs who were not
on the same number of antihypertensive drugs at the prior visit


3 study drugs
















0_20
o 25






U
C
a 015
U


S0.10
E

0 05



0-00 -
0 250 500 750 1000 1250 1500 1750 2000
Time [days]

Figure 4-11. Cumulative incidence of the primary outcome event over follow-up


2.5 -



o
0

1.5 I
N

1



0.5 -
<110 110to<120 120to<130 130to<140 140to<150 150to<160 160
(n=205) (n=667) (n=1777) (n=3117) (n=4892) (n=4514) (n=7404)
Systolic Blood Pressure Category [mm Hg]


Figure 4-12. Hazard ratios for an INVEST primary outcome event by categories of baseline
systolic blood pressure.














3


0 2.5

2

I 1.5

1

0.5


<110 110to<120 120to<130 130to<140 140to<150 150to<160
(n=190) (n=1500) (n=6403) (n=7259) (n=3983) (n=1761)
Systolic Blood Pressure Category [mm Hg]


Figure 4-13.




2.5 -



2 -
0

-1.5
o




1
1 -



0.5 -


Hazard ratios for an INVEST primary outcome event by categories of average
systolic blood pressure over follow-up.


<110 110to<120 120to<130 130to<140 140to<150 150to<160 160
(n=190) (n=1500) (n=6403) (n=7259) (n=3983) (n=1761) (n=1480)
Systolic Blood Pressure Category [mm Hg]

Figure 4-14. Hazard ratios for an INVEST primary outcome event by categories of average
systolic blood pressure over follow-up, weighted by time of follow-up.


160
(n=1480)



























0.5
<110 110to<120 120to<130 130to<140 140to<150 150to<160 !160
Systolic Blood Pressure Category [mm Hg]

Figure 4-15. Hazard ratios for an INVEST primary outcome event by categories of systolic
blood pressure (updated; carried forward from last observed visit)


2.5
o
2-












.2
re
N


















0.5 -
<110 110to<120 120to<130 130to<140 140to<150 150to<160 160
Systolic Blood Pressure Category [mm Hg]

Figure 4-15. Hazard ratios for an INVEST primary outcome event by categories of systolic
blood pressure (updated; carried forward from lasnext observed visit)
I
1



+

<110 110to<120 120to<130 130to<140 140to<150 150to<160 160
Systolic Blood Pressure Category [mm Hg]

Figure 4-16. Hazard ratios for an INVEST primary outcome event by categories of systolic
blood pressure (updated; from next observed visit)


















2 <
0

1.5
N






0.5
<110 110to<120 120to<130 130to<140 140to<150 150to<160 160
Systolic Blood Pressure Category [mm Hg]


Figure 4-17. Hazard ratios for an INVEST primary outcome event by categories of updated
mean systolic blood pressure (time-dependent; updated at each visit)


60


50 -

40 -


a)
C
S20


U
10 -
10 -
0
<110 110to<120 120to<130 130to<140 140to<1 15150to<160 160
(1678 ptyrs) (7289 ptyrs) (22433 ptyrs) (38621 ptyrs) (48250 ptyrs) (53815 ptyrs) (60939 ptyrs)
Systolic Blood Pressure Category [mm Hg]


Figure 4-18. Crude incidence of primary outcome events by SBP category











30 -

25 -



U)
-

5 20 --
0
o
0
0
S15 --
U
8
-| 10--
C
5 -

0




Figure 4-19.


160%
140%
120%
100%
80%
60%
40%
20%


It


<110 110to<120 120to<130 130to<140 140to<150 150to<160 160
Systolic Blood Pressure Category [mm Hg]

Adjusted incidence of primary outcome events for White, female, US patients
between the ages of 60 to 70 years by SBP category


percent bias average over follow-up updated mean

S- 3

2.5

2 o
'I-
a 56% 1.5

34%
S11% 14%
0% % 0.5


0% -
-3%
-20% -- -11% -- 0
<110 10 llto<120 120to<130 130to<140 140to<150 150to<160 a160
Systolic Blood Pressure Category [mmHg]

Figure 4-20. Bias of outcome event hazard ratios obtained average SBP compared to updated
mean SBP












130 -<140 mm Hg


-*-<110 mm Hg -=-110-<120 mm Hg -&-120-<130 mm Hg
-*-140-<150mm Hg -*- 150-<160mm Hg -->160 mm Hg


50%


40%


30%


20%
a-

10%


0%


1 2 3 4 5 6 7 8 9 10 11 12

Number of Visits


Figure 4-21. Proportion of events within category of average SBP by number of observed visits
at the occurrence of the event


ag Event % -*- Bias %


60


E 50

4-0

> C
0 -
3,0

20


w 10
a.

0
<110 110to<120 120to<130 130to<140 140to<150 150to<160 160

Systolic Blood Pressure Category [mm Hg]


Figure 4-22. Bias and timing of events by category of SBP


LM-
0)>
> M)


0)?
22o
a,




I-a
a>

'I-o



C.,









CHAPTER 5
DISCUSSION

The present study shows that, in the International Verapamil SR/Trandolapril Study

(INVEST), estimates for the effect of SBP on cardiovascular morbidity and mortality vary

significantly depending on the method of SBP operationalization. It further demonstrates that

using the average SBP over follow-up as a predictor of cardiovascular events systematically

overestimates the risk associated with extreme SBP categories. Causal analyses suggest that

time-dependent confounding by SBP may bias estimates of treatment effects, but provides no

evidence of time-dependent confounding by treatment in the estimation of risk associated with

SBP control. However these analyses are considerably restricted by limitations imposed by the

statistical method, which necessitated significant simplifications of the data. Consequently, these

results are only exploratory in nature. Lastly, our study provides detailed longitudinal

descriptions of SBP and antihypertensive treatment patterns over the course of INVEST, which

facilitate better understanding and interpretation of the presented inferential analyses.

Descriptive Analyses: Antihypertensive Treatment and SBP in the INVEST

Several observations from the descriptive analyses deserve note. First, when choosing

specific time points of follow-up to report BP or other variables (e.g., percentage of patients with

BP control at month 24),4 a proportion of patients (those who are uncensored but do not have an

observation at the time-point) is not included in the estimate. Figure 4-1 shows that for the first

24 months of follow-up this proportion is rather significant ranging from about 20% to more than

35% of patients depending on the specific visit chosen to report. As shown in Figure 4-2 there

may be differences between results reported for patients with an observation compared to the

entire uncensored cohort (with imputed values carried forward from the last observation for

patients who do not have an observation at the time-point of interest). A decision between the









two approaches resembles a trade off between a possible selection bias that occurs if the actually

observed patients at a specific point of follow-up differ systematically from the uncensored

patients who lack this observation, and a measurement bias that would occur if the imputed data

for patients who lack the observation of interest is systematically different from the actual,

unmeasured value for the variable of interest (e.g., if there is reduction in mean SBP for the

cohort including those lacking specific observations, then imputation of missing values from the

last observation would systematically overestimate the true SBP value). If feasible, both

approaches should be presented to best reflect the true situation at specific points of follow-up.

Another consideration may involve choosing the descriptive approach that is in line with the

inferential statistical methods to be used. In the present study, all inferential analyses implicitly

or explicitly use imputed data and thus the majority of descriptive information was presented for

these data.

Second, after mean SBP for the INVEST cohort dropped about 15 mm Hg over the first six

months of follow up, it remained rather stable throughout the remaining 42 months, never

diverging more than two to three mm Hg from the value observed at six months (Figure 4-2).

Consequently, the proportion of patients within the respective SBP categories was stable after the

initial six months. However, the proportion of individual patients who experienced a change in

SBP categories between visits was continuously high and remained between 30% and 60%,

depending on SBP category, throughout the entire follow-up. Thus, the rather stable SBP

displayed by the INVEST cohort as a whole after the initial six month of follow-up, was not the

result of equally stable SBP on the individual level but rather the result of a constant undirected

change (steady state) between categories. This observation likely reflects natural variation as

well as measurement error in the assessment of SBP and shows that careful examination of the









data is necessary to distinguish between a stable mean over follow-up that is based on a stable

value on the patient level and significant undirected individual variation as observed in the

INVEST. This distinction has profound consequences for the choice of an appropriate method of

analysis. Standard regression methods using fixed values for SBP may be used when there is

little individual variation or measurement error, while time-dependent methods are likely more

appropriate to capture and incorporate short term individual variation and its potential effects on

outcomes.

Third, descriptive analyses as presented in the first section of Chapter 4 illustrate the

limitation of intend to treat (ITT) analyses in randomized controlled trials. While ITT is

necessary to preserve randomization, it does introduce misclassification (e.g., at the 24 month

visit less than 80% of uncensored patients were still receiving one of the first line study drugs

atenolol or verapamil (Figure 4-6)). The widespread utilization of nonstudy antihypertensive

drugs (more than a quarter of all antihypertensive medication in INVEST were nonstudy drugs)

will likely also result in the attenuation of differences between treatment strategies. Thus, an as

treated analysis as performed in the present study should be considered complementary to the

original ITT analysis, especially when the nature of the results suggesting noninferiority are

considered.

Operationalization of SBP

The present study confirms findings from a prior report which suggested that in the

INVEST both low and high blood pressures are associated with an increase in the risk for the

primary outcome.31 While varying in the magnitude of the risk associated with high and low SBP

categories, all SBP models presented in our study support this observation. The previously

published report, which modeled the average systolic and diastolic BP over follow-up, suggests

that the relationship between BP and the INVEST primary outcome event follows a J-shape with









its nadir for SBP at 120 to 130 mm Hg. However, it is important to note that our study presents

evidence suggesting that the use of average BPs over follow-up may lead to biased estimates of

association. Depending on the SBP model used, our study finds the relationship between SBP

and cardiovascular outcomes varying between a J, V, and a reverse-J-shape with the nadir at

either 120 to 130 mm Hg, or 130 to 140 mm Hg. These findings differ significantly from other

reports that have consistently suggested a log linear increase of cardiovascular risk with

increasing SBP (Figure 2-4). However, the INVEST study population differs significantly from a

general hypertensive population by including only patients with documented CAD. In patients

with CAD low SBP (and more importantly DBP, which was not included in the analyses of our

study) may compromise coronary perfusion and cause cardiac ischemia.31 While it is important

to note that neither the previous INVEST report nor our study, both post hoc observational

analyses, can establish that low blood pressures causes cardiovascular outcomes, they do show

that CAD patients with low SBP are at an increased risk to experience cardiovascular outcomes

and thus suggest caution in lowering SBP in hypertensive patients with CAD.

Modeling Assumptions

The 7 models presented in Table 4-2 make implicit assumptions about the mechanism by

which SBP affects the risk for cardiovascular events. The following section will summarize and

contrast these assumptions of how SBP over time affects cardiovascular outcomes. At one end of

the spectrum is the baseline SBP model. By ignoring any changes in SBP after the beginning of

follow-up, the baseline SBP model assumes that SBP at a single historic point in time (baseline)

acts as a proxy for a patient's cardiovascular risk, while short term changes in SBP after patient

enrollment do not significantly change the cardiovascular risk that has been defined by numerous

years of SBP history. In contrast, the average SBP model assumes that both historic and actual

SBP values affect cardiovascular risk. The respective contributions of historic and actual SBP









values, however, are difficult to quantify since they are dependent on the length of follow-up.

Specifically, the contribution of recent SBP values diminishes as follow up time increases. In

order to adjust for the fact that the average SBP model would apply the same weight to patients

who were followed over multiple years as to patients who were followed for only a short period

of time, the time-weighted average SBP model was introduced by weighing each subject's

observation by its individual follow-up time.

As opposed to the previous models that rely either completely (baseline model) or partially

(both average SBP models) on historic SBP values, the two short term time-dependent models lie

at the other end of the spectrum of possible assumptions. These models assume that there is no

effect of SBP history but rather assume that SBP at each specific point in time determines the

risk for a cardiovascular event at this moment in time. The short term time-dependent SBP

models do not differ in these modeling assumptions but rather in the choice of the best available

SBP measurement at a given point of follow-up. The prior visit model assumes that SBP at each

time point is best approximated by the last measured SBP observation prior to this time point

while the following visit model assumes that the best approximation of SBP for the same time

point is the first observed measurement after this point in time (Figure 3-2). The rationale for the

prior model is straightforward: for each time point it simply uses the last measured SBP value.

The rationale for the next visit model is slightly more complex: since antihypertensive treatment

is potentially changed at each visit (after response to treatment has been assessed by measuring

BP), SBP may change shortly after the visit and thus, true SBP at a given point after this visit

may actually be better reflected by the SBP observed at the next visit. However, this approach is

potentially biased because for patients who experience an event, no SBP values are available

after the event. As a consequence the next visit model treats time periods directly before events









systematically different than all other time periods between visits and therefore may produce a

biased estimate.

The updated average model combines aspects of the previous models in that it incorporates

SBP history by using an average SBP but also allows change over time by calculating a new

(thus time-dependent) average at each observed follow-up time. Last, the Poisson model makes

assumptions that closely resemble those of the time-dependent prior visit model as it assigns

patient time to the last observed SBP category.

The remainder of this section discusses the SBP models presented in Figures 4-14 to 4-19

in more detail. Several comparisons between SBP models are of specific interest.

Baseline SBP Model

Compared to all other models, the baseline SBP model (Figure 4-14) estimates a

substantially smaller risk associated with the two highest SBP categories, while its risk estimates

for low SBP categories are of a similar magnitude as the other models. This observation can be

explained by considering what happened to the average SBP during the INVEST. Since the

INVEST protocol was aimed at controlling patients' SBP, most patients who had high SBP at

baseline experienced a reduction in SBP in the first months follow up as shown in Figures 4-2

and 4-3. Thus, for patients with high SBP at baseline, the baseline SBP value poorly represents

the true SBP over follow-up (which is likely to be lower than baseline) and as a consequence

models that use the baseline value to predict the risk of an outcome event will underestimate the

risk for patients with high baseline SBP. In contrast, this systematic misclassification affects

patients with a low baseline SBP to a much lesser extend since these patients were likely to

remain in a low SBP category. It is therefore not surprising that the baseline SBP model is

comparable in its risk estimates for low SBP categories to the other presented models but it

results in much lower estimates for the highest SBP categories.









Average SBP Models

On the surface, the use of an average of a surrogate over follow-up to predict the risk of an

outcome of interest has many appealing features. Averages over follow-up allow simple

modeling without the need to explicitly incorporate time-dependent changes in the measure.

They incorporate implicitly and to some extend intuitively such time-dependent changes and

create a single value for every subject that allows straightforward incorporation in standard

regression models. As a result, averages over follow-up have been used to estimate the effects of

surrogates on clinical outcomes in various disease states such as diabetes, hyperlipidemia, and

hypertension.31, 34, 35

However, the simulations presented in Chapter 4 demonstrate that the apparent simplicity

of this approach comes at a price. Considerable bias may be introduced when modeling an

outcome with an average over follow-up (Table 4-3). Specifically, for SBP categories that (1)

include a large proportion of patients at baseline and (2) include fewer and fewer patients over

the course of follow up, overestimation of the true risk associated with these SBP categories is

likely. In the INVEST, the above conditions are met for the highest three SBP categories. Table

4-3 shows that these three SBP categories at baseline include the largest proportions of patients

(with SBP >160 mm Hg including the single largest proportion) and include continuously fewer

patients over the subsequent six months of follow-up (with the most significant reduction in

patients observed in the category of SBP >160 mm Hg). As a result, the risk for the highest three

SBP categories is systematically overestimated by the average SBP model. Specifically,

compared to the updated-mean model, the fixed average model overestimates the risk for a

cardiovascular event by 56%, 34%, and 14% for SBP >160 mm Hg, SBP 150 to 160 mm Hg,

and SBP 140 to 150 mm Hg, respectively. The updated mean model is selected as the comparator

because like the average model, it uses an average of SBP to predict cardiovascular outcomes,









but as opposed to the average model does not introduce bias as shown by the second set of

simulations in Chapter 4 (Table 4-4).

The weighted average model (Figure 4-16) estimates results that lie between the average

model and the updated mean model. This is expected since the weighted average model is

subject to the same bias as the average model (it uses the identical averages) but reduces the

impact of the bias by weighting observations according to the length of their follow up time.

Since observations with events in the first follow-up period (and thus rather short follow-up

time) are most responsible for the bias as discussed above, such weighting will, while not

eliminating the bias, reduce its magnitude.

Short Term SBP Models (Time-Dependent)

The two short term time-dependent SBP models differ substantially in their results.

Compared to the model that for each period between visits carries forward the SBP value from

the first visit (updated previous model), the model that utilizes the SBP from the latter visit for

the same interval (updated next model) estimates higher risks associated with SBP categories

above 140 mm Hg and lower risks for SBP categories below 130 mm Hg. Considering that mean

SBP in the INVEST was lowered substantially over follow-up, this pattern is expected. The time-

dependent Cox model used in our analyses compares at each time an event occurs, the SBP of a

patient who experiences this event with all other patients' SBP at the same time. Thus, a shift

from the SBP measured at the visit prior to the event time to the SBP measured at the visit

following the event will on average reduce the SBP of the patients at risk (i.e., those who have

not experienced an event and are uncensored). However, the SBP of patients with events are

unaffected by the shift because (see Figure 3-2) patients are censored at the time of the event and

therefore no post-event SBP measurements exist. Consequently, compared to the updated

previous model, the updated next model compares identical SBP values for patients with events,









to on average lower SBP values for patients without events and therefore overestimates the risk

for high SBP categories and underestimates the risk for low SBP categories.

When comparing the two short term time-dependent models to the updated mean model it

becomes apparent, that the prior model's results are very similar to the updated mean model. The

similarity of results is somewhat surprising considering the significant differences in SBP

operationalization. While the updated prior model incorporates only the most recently observed

SBP values, the updated mean model does incorporate both historic and current SBP values.

Both models would therefore be expected to provide differing results. The similarity of both

approaches in the INVEST may result from the limited follow-up time and the relative stability

of mean SBP after the initial six months of follow-up, but may not generalize to different follow-

up periods or disease states. Even so, in the INVEST it is reassuring that both unbiased time-

dependent models provide similar estimates for the association of SBP with the cardiovascular

risk.

More complex modeling approaches that combine short term time-dependent SBP

measures with one or more lagged historic SBP values (i.e., BP at each time point would be

represented by the most recent SBP as well as SBP measures from fixed time intervals prior to

the most recent visit) are possible, however, such models are more difficult to interpret since

SBP values with different lag times may be associated with different estimates of risk, the and

thus limited in their clinical utility.

Model Selection

The question arising from the presented models is which of the presented modeling

approaches should ultimately be used to estimate the effects of SBP on the risk of cardiovascular

outcomes, or more generally the effects of a surrogate on clinical outcomes? While no single

correct answer to this question exists-any specific decision will always be influenced by a









multitude of factors-a number of points deserve consideration and should guide the selection of

modeling approaches. First and foremost, the assumptions underlying the modeling approach

should be closely aligned with the hypothesized biological mechanism. If the hypothesized

biological mechanism suggests that a surrogate exerts its effect on clinical outcomes in an

immediate fashion, a short term time-dependent model may be preferable. However, the absence

of established biological models as well as limitations in data availability and quality may

complicate this decision. If no established biological models exist, multiple models with varying

assumptions should be produced and compared. If data availability or quality does not allow the

selection of a preferred model, the consequences and limitations of choosing a different model

should be explicitly discussed.

When data availability permits, our study suggests that an updated mean model should be

considered over more extreme (baseline or short term time-dependent) models since it

incorporates both historic and current values of the surrogate. More complex models that use

both current and lagged surrogate values may also be appropriate (especially if overall follow-up

is extremely long and as a consequence recent SBP values would contribute less and less to the

updated mean as time progresses), but results obtained from such models are commonly difficult

to interpret and communicate.

A second general consideration should be the avoidance of models that likely introduce

bias. As discussed above this will generally be the case for baseline models if an intervention or

natural progression of the disease leads to a directed change of the surrogate over follow-up,

which in turn leads to a systematic over- or underestimation of the true value of the surrogate

over follow-up. Even without such directed change, the use of a single measurement at baseline









may introduce an estimate that, due to the effect of measurement error, is biased towards the null

(regression dilution bias).36'37

The use of a fixed average over follow-up will under most conditions introduce bias and

should be generally avoided. If the data allow calculation of an average (i.e., surrogate values are

not limited to baseline), a time-dependent updated mean model should be used instead of a fixed

average model. Lastly, the choice between the two short term time-dependent models is difficult.

While the updated next model may provide more precise approximation of a surrogate than the

updated previous model, especially when changes in drug therapy are common at visits and time-

intervals between visits are long, the differential treatment of time periods before events may

introduce bias. Whether the potential bias introduced in the updated next model through this

differential treatment of time periods preceding events or the potential bias resulting from

systematic measurement error introduced by the updated next model is a greater threat to the

validity of the estimate has to be evaluated in the context of each specific study.

Unfortunately, the comparison of model diagnostics such as generalized R2 (a proxy for

the fit of the model), is not helpful in the process of model selection. Unlike the R2 in linear

regression models, the generalized R2 cannot be interpreted as the proportion of variation in the

dependent variable that is explained by the covariates included in the model but is only

interpretable as a number between 0 and 1 that gets larger when the covariates are associated

more strongly with the outcome.30 More importantly, the generalized R2, as all measures of

model fit, does not distinguish between true associations and associations resulting from bias.

Consequently, a biased model will generally produce a larger generalized R2 than an equivalent

unbiased model. In our study, for instance, the biased average model produces a larger

generalized R2 than the unbiased updated mean model.









These considerations regarding the selection of models to estimate the effect of a surrogate

on a clinical outcome are not mere academic but rather have profound consequences for the

establishment of treatment guidelines and clinical practice.

Time-dependent Confounding

The previous section suggests that the selection of a modeling approach for a surrogate

measure has substantial consequences for the resulting estimates of risk and shows that time-

dependent modeling approaches are preferable under most circumstances. However, the use of a

time-dependent surrogate may introduce time-dependent confounding by any type of treatment

that has nonsurrogate mediated effects on the clinical outcome, affects the surrogate, and whose

initiation is not independent of the surrogate. Such time-dependent confounding by treatment

was not considered in the previously presented modeling approaches. Specifically, the previously

presented time-dependent modeling approaches do not include adjustments for the concurrent

use of antihypertensive medication and thus, may produce biased estimates of the effects of SBP

on cardiovascular outcomes. Time dependent confounding would occur if antihypertensive drug

use has effects on cardiovascular outcomes which are not mediated by SBP control since

initiation and change of antihypertensive treatments is dependent on SBP control. For example,

an increase in the number of antihypertensive drugs will at the same time increase the likelihood

of SBP control and (assuming non-SBP mediated beneficial effects of antihypertensive drugs on

outcome) reduce the patients risk to experience an outcome event. Thus, a model that does not

control for time-dependent confounding by antihypertensive drug use will likely overestimate the

beneficial effects of SBP control by attributing both the effects of SBP control and the beneficial

effects of an increased number of antihypertensive drugs to SBP control. Controlling for time-

dependent confounding by antihypertensive drug use would therefore reduce the estimated

beneficial effect of SBP control compared to the estimate obtained from a standard model.









However, our results do not support the presence of a time-dependent confounding effect

of antihypertensive treatment. Both the standard time-dependent Cox model and the marginal

structural Cox model estimate an almost identical, strong beneficial effect of SBP control with

HRs of 0.54 (95% CI 0.48-0.60) and 0.55 (95% CI 0.50-0.61), respectively. If time-dependent

confounding by treatment (i.e., a non-SBP mediated beneficial or detrimental effect of

antihypertensive drugs) had been present, the HR estimated by the marginal structural model

would have been expected to be closer to 1.0, (i.e., show a weaker association between SBP

control and outcome). In other words, the two complementary analyses suggest that the type of

antihypertensive treatment does not affect cardiovascular outcomes, as long as SBP is adequately

controlled. However, it is important to note, that the drug effect was only operationalized as the

number of antihypertensive total, and study drugs with no regard for drug class or dose, and that

trandolapril, an antihypertensive with demonstrated outcome benefits for patients with specific

comorbidities, was per INVEST protocol prescribed to all patients with an indication. To our

knowledge this is the first time that inverse probability of treatment weighting was used to obtain

an estimate of the effects of a surrogate controlling for time-dependent confounding by

treatment.

Additional marginal structural models were created to estimate the effects of aggressive

versus standard antihypertensive treatment (more than two versus less two or less concurrent

total antihypertensive drugs), controlling for time-dependent confounding by SBP. In this

scenario, the fact that the aggressive treatment is more likely to be initiated in patients with

uncontrolled SBP (confounding by indication), would lead to an underestimation of the

beneficial effect of antihypertensive therapy (or, if the effects of such negative selection

outweigh the beneficial effects of aggressive treatment, in the estimation of a harmful effect of









aggressive treatment) because uncontrolled SBP would at the same time increase the likelihood

of treatment with aggressive antihypertensive therapy and increase the risk for a cardiovascular

event.

The estimate for aggressive antihypertensive treatment obtained from the marginal

structural model is lower than the estimate from the standard Cox model but the 95% CIs of both

estimates overlap (HR 0.81, 95% CI 0.71-0.92 and HR 0.96, 95% CI 0.87-1.07 for marginal

structural and the standard Cox models, respectively). However, while the models are not

significantly different from each other, it is noteworthy that the marginal structural Cox model

shows a significant benefit of aggressive antihypertensive therapy, while the standard Cox model

fails to show such benefit. Sensitivity analyses were conducted to assess the influence of the

definition of aggressive antihypertensive therapy on the results. The marginal structural Cox

models consistently estimate lower point estimates for the HR associated with aggressive

antihypertensive therapy than the standard Cox models for all four additional definitions of

aggressive antihypertensive therapy. Of the four definitions the differences between the two

models were significant for one definition (aggressive antihypertensive therapy defined as more

than three concurrent total antihypertensive drugs), borderline significant for another (aggressive

antihypertensive therapy defined as more than one concurrent study antihypertensive drug) and

not significant for the remaining two definitions.

Although the differences between the standard Cox models and the marginal structural

Cox models did not reach statistical significance in the main analysis and three of the four

additional analyses, the trend for a larger beneficial effect of aggressive antihypertensive

treatment versus standard antihypertensive treatment was consistent across all analyses.

Assuming correct model specification and no violation of the assumptions necessary for the









marginal structural Cox model, the estimate for the beneficial effect of aggressive versus

standard antihypertensive therapy can be interpreted as the effect that would have been observed

in a RCT that compared aggressive to standard antihypertensive treatment over the course of

follow-up. Thus the estimate is causally interpretable and includes all pathways (including SBP

mediated pathways) through which aggressive antihypertensive therapy tends to improve the

clinical outcome, regardless of SBP values preceding the initiation of aggressive

antihypertensive therapy.

These results are in both magnitude and direction comparable to prior studies that have

used inverse probability of treatment weighted estimates to estimate unbiased effects of

treatments in observational studies in the presence of time-dependent confounding. Specifically,

an observational study that assessed the effectiveness of methotrexate in patients with

rheumatoid arthritis estimated a mortality HR of 0.6 (95% CI 0.4-0.8) using a standard time-

dependent Cox model and an mortality HR of 0.4 (95% CI 0.2-0.8) using a marginal structural

Cox model that controlled for time-dependent confounding by several prognostic factors.

Another observational study evaluated the aspirin component of the Physicians' Health Study, a

randomized controlled trial that evaluated the effectiveness of aspirin in the prevention of

cardiovascular disease. While the trial established a strong reduction in first myocardial

infarction in patients treated with aspirin, and was stopped early because of it, it failed to detect a

significant beneficial effect of aspirin on cardiovascular mortality. At the time of the Physicians'

Health Study, the effectiveness of aspirin in the prevention of secondary cardiovascular mortality

already had been established and lead to increased use of aspirin in patients that had experienced

a nonfatal cardiovascular event. The observational study reanalyzed the clinical trial data (similar

to our study) disregarding the original randomization and controlling for time-dependent









confounding by nonfatal cardiovascular events using a marginal structural Cox model. The

standard as treated model controlling for predictors of aspirin exposure at baseline as well as

cardiovascular risk factors estimated a mortality HR of 0.81 (95% CI 0.57-1.15), while the

marginal structural Cox model that additionally controlled for time-dependent confounding by

nonfatal cardiovascular events reduced the estimated HR to 0.74 (95% CI 0.48-1.15). Lastly, a

study that assessed the effectiveness of zidovudine in reducing mortality in patients with HIV

found a significant detrimental effect of zidovudine using standard methods that did not control

for time-dependent confounding by CD4 cell count (HR 2.3, 95% CI 1.9-2.8), but was able to

show a beneficial effect of zidovudine using a marginal structural Cox model (HR 0.7, 95% CI

0.6-1.0). Of these three studies, only the study that investigated the effectiveness of zidovudine

found a statistically significant difference between the HR estimates obtained from a standard

time dependent Cox model and a marginal structural Cox model, but as in our study, all three

studies estimated consistently higher effectiveness of the treatment under study when a using

marginal structural Cox model that controlled for time-dependent confounding by a risk factor

for the clinical outcome that was at the same time a predictor of treatment initiation and

subsequently affected by the treatment.

Limitations

The present study has several noteworthy limitations. All analyses were conducted in a

retrospective, observational design. While our study utilized the dataset of INVEST, a large

international randomized controlled clinical trial, the presented analyses are post hoc and are

independent of the initial randomization. Therefore our analysis of SBP cannot establish a causal

association between SBP and cardiovascular risk. Unmeasured confounding factors may exist

that affect SBP as well as cardiovascular risk. In addition, the generalizability of our study is

limited to elderly hypertensive patients with CAD. Specifically, the increase in risk associated









with lower SBP categories is likely not representative of a healthier population of patients with

uncomplicated hypertension. However, the INVEST population represents a large and important

high risk population that has not been at the center of antihypertensive research efforts and

therefore warrants comprehensive investigation.

Another limitation of our study is the measurement error inherent in the study of

hypertension. Measurement error has been widely reported as a problem in the analysis of

hypertension studies.3840 While the INVEST protocol tried to minimize measurement error by

providing standardized BP measurement instructions following JNC-VI to all providers, a certain

extend of measurement error is unavoidable. However, it is unlikely that the remaining

measurement error is systematic. Random measurement error may affect our results in ways

other than reducing the precision of the provided results. If the absolute magnitude of SBP

variation increases with higher SBP values then the categorization of SBP into 10 mm Hg

categories may affect our results in that the observed variability in the continuous SBP measure

would lead to a larger extend of variation in SBP categories at larger values of SBP.

The use of marginal structural Cox models to adjust for time-dependent confounding

through inverse probability of treatment weighting introduces another set of limitations to the

causal analyses in our study. Inverse probability of treatment weighting as to date established in

statistical theory requires a number of assumptions and a rather simple data structure. First, the

independent variable of interest has to be binary. As clearly shown in Figures 4-12 to 4-19 the

relationship between SBP and clinical outcomes is more complex than our categorization of SBP

into controlled versus uncontrolled. Although we excluded patients with very low SBP to

account for the observed J-shape, our operationalization of SBP is a rather poor representation of

the data. The same applies to the complementary analysis of antihypertensive drug use. Our









study categorized antihypertensive drug use in aggressive versus standard antihypertensive

therapy defined as the use of three or more concurrent total antihypertensive drugs. This

definition does not distinguish between specific drugs and drug classes and does not take dosing

of each specific drug into account. If treatment effects vary between specific drugs and doses,

our model will not show these differences and rather produce an estimate reflective of the

average treatment combinations used in the aggressive and standard antihypertensive therapy

groups. Thus, our results are of limited value in aiding in the selection of specific

antihypertensive drugs. However, we conducted four additional analyses varying the definition

of aggressive antihypertensive therapy to assess how sensitive our results are to the treatment

definition and results were consistent across all analyses. The fact that the marginal structural

Cox model estimates a larger benefit for aggressive antihypertensive therapy than the standard

Cox model regardless of the drug number cutoff used to define aggressive antihypertensive

therapy, shows that more antihypertensive drugs tend to produce more beneficial outcomes than

less antihypertensive drugs, when preceding SBP values that may influence the addition of

antihypertensive drugs to an individual's treatment regimen are controlled for. This beneficial

effect is likely mediated through a more pronounced effect on SBP, since the results presented in

Table 4-5 suggest the absence of non-SBP mediated treatment effects.

Second the method requires the assumption, that once initiated, exposure (in our analyses

either SBP control, or aggressive antihypertensive therapy) is not discontinued until the end of

follow-up or censoring. This assumption is not met in the INVEST (Figures 4-4, 4-9, and 4-10).

We therefore artificially altered the data in order to meet the assumption of the model by keeping

BP controlled after BP control was first achieved or keeping patients on aggressive

antihypertensive therapy once the respective cut-off was reached. This was necessary, because









the marginal structural model, at present, is not able to incorporate complex modeling

approaches that allow reversion of exposure. Lastly, the pooled logistic regression model that

was used to estimate the marginal structural Cox model assumes that observations are equally

spaced, which was not the case in the INVEST where the initial five visits occurred in six week

intervals while the remaining visits occurred in six month intervals. Thus, the pooled logistic

regression model may not be fully equivalent to the Cox model it replaces.

The estimation of a surrogate (SBP control in our study) in the presence of time-dependent

confounding by treatment raises concerns about its interpretability. While controlling for time

dependent confounding by a surrogate is, if all assumptions are fully met and all models are

correctly specified, essentially equivalent to a RCT where treatment initiation is independent of

the surrogate, the same thought experiment does not hold for the analysis of time-dependent

confounding of a surrogate by treatment. Controlling for time-dependent confounding by

treatment in the estimation of the effect of a surrogate on a clinical outcome would-as a thought

experiment-assume that values of the surrogate are randomized to subjects regardless of their

treatment pattern (in our study, SBP control status would be randomly assigned to patients

regardless of the number of antihypertensive drugs they are taking). While this obviously would

not be possible in reality, and the estimate is therefore more difficult to communicate, we do

believe in the validity of the presented approach.

Future Research

The marginal structural models presented in our study demonstrate, in principle, the

importance of considering time-dependent confounding in the analysis of chronic disease drug

studies involving surrogates. However, the limitations described above presently limit the

clinical utility of marginal structural models in the analysis of disease states with complex

treatment patterns such as hypertension. In order to make more clinically useful inferences,









future research will have to extend causal methods such as marginal structural models, to allow a

more realistic representation of the observed data. Specifically, the method should be extended to

allow multi-category independent variables and both initiation as well as discontinuation of

exposure. Another important area of research is the evaluation of dynamic treatment regimens

from observational data. While our analysis compared nondynamic regimens (e.g., aggressive

antihypertensive treatment throughout follow-up versus standard treatment throughout follow-

up), questions involving dynamic treatment regimens (e.g., initiation of antihypertensive therapy

at SBP of greater than 135 mm Hg versus initiation of antihypertensive therapy at 145 mm Hg)

may be equally important for clinical practice. Such analyses require artificial censoring of

patients once they deviate from the defined treatment regimens followed by weighting by the

inverse probability of censoring to adjust for the potential biased introduced by the artificial

41
censoring.

Summary and Conclusions

The complex interplay of surrogate measures, pharmacological treatments, and clinical

outcomes makes the analysis of observational studies of chronic diseases challenging. Our study

shows that the estimation of surrogate effects on a clinical outcome is highly dependent on the

operationalization of the surrogate and that several commonly used approaches may introduce

severe bias to the analysis.

While it is conceptually clear that time-dependent confounding by a surrogate is

problematic for the estimation of treatment effects in observational studies, our study is the first

to empirically support the presence of such time-dependent confounding in the context of

hypertension. Our results suggest that time-dependent confounding by SBP, leads to an

underestimation of the effectiveness of antihypertensive treatment. No evidence for time-

dependent confounding of the effect of SBP control by antihypertensive treatment was found,









suggesting, that antihypertensive treatment as modeled in our analysis does not affect

cardiovascular outcomes in pathways other than SBP. However, limitations in the methods that

were used to allow the inclusion of time-dependent confounders in the analysis required

considerable simplification of the data structure and thus, these methods at present have only

limited practical utility. As such causal methods are further developed, they may become more

useful in the analysis of large observational hypertension studies.









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