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PAGE 1 1 IN VITRO AND IN VIVO METHODS FOR ESTABLISHING BIOEQUIVALENCE FOR ORALLY INHALED DRUG PRODUCTS WITH EMPHASIS ON INHALED CORTICOSTEROIDS By BENJAMIN WEBER 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 2013 PAGE 2 2 2013 Benjamin Weber PAGE 3 3 To my family and friends PAGE 4 4 ACKNOWLEDGMENTS I would like to thank my supervisor, Dr. Guenther Hochhaus, for giving me the opportunity to perform research and pursue a Doctor of Philosophy in this working group I am very thankful for all of his ideas, input, and criticism that have positively affected my scientific development. Additionally, he has always been a great support beyond the scientific environment. I would like to thank all of my other committee members, Dr. Hartmut Derendorf, Dr. Anthony Palmieri III, and Dr. Lawrence Winner, who have all contributed s ignificantly to my personal and professional development over the last years I would like to thank my supervisor at the Food and Drug Administration, Dr. Sau (Larry) Lee, and everybody else at the Office of Generic Drugs who was involved in this project, for giving me the opportunity to perform my research in area of bioequivalence for orally inhaled drug products at the Office of Generic Drugs and for all their contributions to this dissertation. I would like to thank the office staff members in the Dep artment of Pharmaceutics who have always been extremely supportive when I have needed their help with administrative problems. I would like to thank everybody in the Department of Pharmaceutics, the College of Pharmacy, the Department of Statistics, and t he University of Florida that have development in the last four years. In particular, I would like to thank my dear friend, Karin Haug, for her support in all life situations o ver the last years. I am very grateful for the time and moments that we were sharing du ring our time in Gainesville PAGE 5 5 I would like to send s ome special thanks to my fellow lab members, in particular Bhargava Kandala, and to my fellow graduate students, Dr. Daniel Gonzalez, and Dr. Daniela Conrado. Finally, I would like to thank all my family and friends for supporting me in the last years. PAGE 6 6 TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................ ................................ ................................ .. 4 LIST OF TABLES ................................ ................................ ................................ ............ 9 LIST OF FIGURES ................................ ................................ ................................ ........ 10 LIST OF ABBR EVIATIONS ................................ ................................ ........................... 15 ABSTRACT ................................ ................................ ................................ ................... 16 CHAPTER 1 INTRODUCTION ................................ ................................ ................................ .... 18 Background ................................ ................................ ................................ ............. 18 Methods for Establishing Bioequivalence of Systemically Acting Orally Administered Drugs ................................ ................................ ............................. 20 Definition of Bioequivalence ................................ ................................ ............. 20 Interpretation ................................ ................................ ................................ .... 20 Methods ................................ ................................ ................................ ............ 21 Challenges when Establishing Bioequivalence of Locally Acting Orally Inhaled Drug Products ................................ ................................ ................................ ...... 22 FDA Approach Aggregate Weight of Evidence Approach ............................. 22 Device design and formulation similarity ................................ .................... 23 Comparative in vitro tests ................................ ................................ ........... 23 Systemic exposure studies ................................ ................................ ........ 24 Pharmacodynamic or clinical endpoint studies ................................ .......... 24 EMA Approach ................................ ................................ ................................ 24 2 A STABILITY ANALYSIS OF A MODIFIED VERSION OF THE CHI SQUARE RATIO STATISTIC: IMPLICATIONS FOR EQUIVALENCE TESTING OF AERODYNAMIC PARTICLE SIZE DISTRIBUTION ................................ ............... 29 Background ................................ ................................ ................................ ............. 29 Definition of a Modified Version of the CSRS ................................ ......................... 32 Methods ................................ ................................ ................................ .................. 33 Results ................................ ................................ ................................ .................... 36 mCSRS ................................ ................................ ................................ ............ 36 CSRS ................................ ................................ ................................ ............... 37 Discussion ................................ ................................ ................................ .............. 37 Summary ................................ ................................ ................................ ................ 42 PAGE 7 7 3 A SENSITIVITY ANALYSIS OF THE MODIFIED CHI SQUARE RATIO STATISTIC FOR EQUIVALENCE TESTING OF AERODYNAMIC PARTICLE SIZE DISTRIBUTION ................................ ................................ .............................. 51 Background ................................ ................................ ................................ ............. 51 Methods ................................ ................................ ................................ .................. 52 Evaluation of the Behavior of the MmCSRS when T and R CI Profiles Differ From Each Other on a Single Deposition Site ................................ ............... 54 Single site mean difference T and R CI profiles with identical variability ................................ ................................ ................................ 55 Single site mean difference T and R CI profiles with different variability ................................ ................................ ................................ 55 Evaluation o f the Behavior of the MmCSRS when T and R CI Profiles Differ From Each Other on Multiple Deposition Sites ................................ .............. 57 Results ................................ ................................ ................................ .................... 60 Evaluation of the Behavior of the MmCSRS when T and R CI Profiles differ from each other on a Single Site ................................ ................................ ... 60 Single site mean difference T and R CI profiles with identical variability ................................ ................................ ................................ 60 Single site mean difference T and R CI profiles with different variability ................................ ................................ ................................ 60 Evaluation of the Behavior of the MmCSRS when T and R CI Profiles Differ From Each Other on Multiple Deposition Sites ................................ .............. 61 Discussion ................................ ................................ ................................ .............. 62 Single Site Differences ................................ ................................ ..................... 63 Multiple Site Differences ................................ ................................ ................... 66 Summary ................................ ................................ ................................ ................ 72 4 AN AERODYNAMIC PARTICLE SIZE DISTRIBUTION EQUIVALENCE TESTING METHOD BASED UPON THE MEDIAN OF THE MODIFIED CHI SQUARE RATIO STATISTIC ................................ ................................ ............... 104 Introduction ................................ ................................ ................................ ........... 104 CI Profile Simulation ................................ ................................ ............................. 105 APSD Equivalence Test ................................ ................................ ........................ 106 Construction of a Cut Off Value for an MmCSRS based Profile Comparison Test ................................ ................................ ................................ .................... 107 Definition ................................ ................................ ................................ ........ 107 Principles ................................ ................................ ................................ ........ 107 Methods ................................ ................................ ................................ .......... 109 Results and Interpretation ................................ ................................ .............. 111 A Method for Estimating a Single Metric for Reference Variance Scali ng ............ 111 A Method for Constructing a Confidence Interval for the MmCSRS ..................... 112 Evaluation of the APSD Equivalence Test Classification of 55 PQRI Scenarios 113 Methods ................................ ................................ ................................ .......... 113 Results ................................ ................................ ................................ ........... 114 Discussion ................................ ................................ ................................ ...... 115 PAGE 8 8 Scenarios for wh ich classification did not match (PQRI: Pass, APSD: Fail) ................................ ................................ ................................ ....... 115 Scenarios for which classification did not match (PQRI: Fail, APSD: Pass) ................................ ................................ ................................ .... 116 Discussion ................................ ................................ ................................ ............ 117 Conclusions ................................ ................................ ................................ .......... 120 5 A PHARMACOKINE TIC SIMULATION TOOL FOR INHALED CORTICOSTEROIDS ................................ ................................ ........................... 146 Background ................................ ................................ ................................ ........... 146 Compartment Model ................................ ................................ ............................. 149 Plasma Concentration Time Profile Closed Form Expression ............................ 150 Random Structure of PK Model Between and Within Subject Variability ........... 152 Drug Specific Modules Literature Based Parameter Estimates ......................... 152 Performance Check of the Drug Specific Modules of PK Trial Simulation Tool .... 153 Methods ................................ ................................ ................................ .......... 153 Results ................................ ................................ ................................ ........... 154 Discussion ................................ ................................ ................................ ............ 154 Summary ................................ ................................ ................................ .............. 163 Additional Equations ................................ ................................ ............................. 163 ICSpkTS R Extension Package Hands on Examples ................................ ........ 165 Hands on Example 1: ICS ................................ ................................ .............. 166 Hands on Example 2: FP ................................ ................................ ............... 169 6 FI NAL DIS C U SSION AND CONCLUSIONS ................................ ......................... 182 A Critical Evaluation of the Current EMA and FDA Approaches for Establishment of Bioequivalence of Locally Acting Orally Inhaled Drug Products ................................ ................................ ................................ ............ 182 Impact of the Modified Chi Square Ratio Statistic, the Aerodynamic Particle Size Distribution Equivalence Test, and Pharmacokinetic Trial Simulation Software on the Current EMA and FDA Guidelines ................................ ........... 185 LIST OF REFERENCES ................................ ................................ ............................. 187 BIOGRAPHICAL SKETCH ................................ ................................ .......................... 194 PAGE 9 9 LIST OF TABLES Table page 2 1 ................................ ................................ ................................ 44 2 2 Distribution of mCSRS across the .. 44 2 3 .... 45 2 4 Distribution .... 45 2 5 ) ..... 46 2 6 ...... 46 2 7 ) ....... 47 3 1 Illustration of multiple site change procedure for CI profiles M1 M10. ............. 73 3 2 Results of the analysis of the effect of multiple site changes on the MmCSRS .. 74 3 3 Covariance matrix of the CI profile that was used for evaluation of the effect of singe site changes on the MmCSRS ................................ .............................. 76 4 1 Illustration of construction of test and referen ce CI profiles for deriving a cut off value for the MmCSRS ................................ ................................ ................ 122 4 2 Estimated intercept and slope parameters and coefficients of d etermination when regressing the MmCSRS against the squared inverse of the coefficients of variation ................................ ................................ ..................... 1 22 4 3 Results of application of APSD equivalence test to 55 PQRI scenarios ........... 123 4 4 Classification of 55 PQRI scenarios based upon PQRI WG and APSD equivalence test results ................................ ................................ .................... 125 5 1 Typical value parameters for the BUD, FLU, FP, and TA modules of the PK trial simulation tool ................................ ................................ ............................ 173 5 2 .... 174 5 3 ....... 175 5 4 package ................................ ................................ ................................ ............ 176 PAGE 10 10 LIST OF FIGURES Figure page 1 1 Market approval of innovator and generic products ................................ ............ 25 1 2 Bioequivalence approach for systemically acting orally administered drug products ................................ ................................ ................................ .............. 26 1 3 Bioequivalence approach for locally acting orally inhaled drug products ............ 26 1 4 Aggregate weight of evidence approach for establishment of bioequivalence of orally inhaled drug products ................................ ................................ ............ 27 1 5 EMA approach for establishment of bioequivalence of orally inhaled drug products ................................ ................................ ................................ .............. 28 2 1 .......... 48 2 2 ........... 48 2 3 Comparison of distribution of the 900 mCSRSs and F distribution with 7 1 4 and 8 deposition sites ................................ ................................ ......................... 49 2 4 Comparison of distribution of the 900 mCSRSs and F distribution with 7 8 and 8 dep osition sites ................................ ................................ ......................... 50 3 1 Reference CI profile that was used for the evaluation of the impact of differences between T and R CI profil e on a single deposition site on the MmCSRS ................................ ................................ ................................ ............ 77 3 2 Population mean depos ition (mcg) of the CI profiles M1 M10 ......................... 78 3 3 Analysis of the behavior of the MmCSRS when T and R CI profiles differed from each other on a single stage in their mean deposition ............................... 79 3 4 Analysis of behavior of MmCSRS for single site difference between T and R CI profiles with identical variability ................................ ................................ ...... 80 3 5 Analysis of the behavior of the MmCSRS when T and R CI profiles differed from each other in their mean deposition on a single site b y 30% and in their variability on all sites ................................ ................................ ........................... 81 3 6 Behavior of the MmCSRS when T and R CI profiles differ from each other on mult iple sites in their mean deposition and variability for CI profile M2 without inter site correlation ................................ ................................ ............................ 82 PAGE 11 11 3 7 Behavior of the MmCSRSwhen T and R CI profiles differ from each other on multiple sites in their mean deposition and variability for CI profile M5 with inter site correlation ................................ ................................ ............................ 83 3 8 Analysis of effect of differences between T and R CI profiles in mean deposition and/or variability on multiple sites for the scenarios where T and R CI profile had the same variability ................................ ................................ ....... 84 3 9 Analysis of the behavior of the MmCSRS when T and R CI profiles differed from each other in their mean deposi tion on a single site by 1 0% and in their varia bility on all sites ................................ ................................ ........................... 85 3 10 Behavior of the MmCSRS when T and R CI profiles differ from each other on multiple sites in their mean deposition and variability for CI profile M1 without inter site correlation ................................ ................................ ............................ 86 3 11 Behavior of the MmCSRS when T and R CI pr ofiles differ from each other on multiple sites in their mean deposition and variability for CI profile M3 without inter site correlation ................................ ................................ ............................ 87 3 12 Behavior of the MmCSRS when T and R CI profiles differ from each other on multiple sites in their mean deposition and variability for CI profile M4 without inter site correlation ................................ ................................ ............................ 88 3 13 Behavior of the MmCSRS when T and R CI profiles differ from each other on multiple sites in their mean deposition and variability for CI profile M5 without inter s ite correlation ................................ ................................ ............................ 89 3 14 Behavior of the MmCSRS when T and R CI profiles differ from each other on multiple sites in their mean deposition and variability for CI profile M6 without inter site correlation ................................ ................................ ............................ 90 3 15 Behavior of the MmCSRS when T and R CI profil es differ from each other on multiple sites in their mean deposition and variability for CI profile M7 without inter site correlation ................................ ................................ ............................ 91 3 16 Behavior of the MmCSRS when T and R CI profiles differ from each other on multiple sites in their mean deposition and variability for CI profile M8 without inter site correlation ................................ ................................ ............................ 92 3 17 Behavior of the MmCSRS when T and R CI profiles differ from each other on multiple sites in their mean deposition and variability for CI profile M9 without inter site correlation ................................ ................................ ............................ 93 3 18 Behavior of the MmCSRS when T and R CI profiles differ from each other on multiple sites in their mean deposition and variability for CI profile M10 with out inter site correlation ................................ ................................ ................ 94 PAGE 12 12 3 19 Behavior of the MmCSRS when T and R CI profiles differ from each other on multiple sites in the ir mean deposition and variability for CI profile M1 with inter site correlation ................................ ................................ ............................ 95 3 20 Behavior of the MmCSRS when T and R CI pr ofiles differ from each other on multiple sites in their mean deposition and variability for CI profile M2 with inter site correlation ................................ ................................ ............................ 96 3 21 Behavior of the MmCSRS when T and R CI profiles differ from each other on multiple sites in their mean deposition and variability for CI profile M3 with inter site correlation ................................ ................................ ............................ 97 3 22 Behavior of the MmCSRS when T and R CI profiles differ from each other on multiple sites in their mean deposition and variability for CI profile M4 with inter site correlation ................................ ................................ ............................ 98 3 23 Behavior of the MmCSRS when T and R CI profiles differ from each other on multiple sites in their m ean deposition and variability for CI profile M6 with inter site correlation ................................ ................................ ............................ 99 3 24 Behavior of the MmCSRS when T and R CI prof iles differ from each other on multiple sites in their mean deposition and variability for CI profile M7 with inter site correlation ................................ ................................ .......................... 100 3 25 Behavior of the MmCSRS when T and R CI profiles differ from each other on multiple sites in their mean deposition and variability for CI profile M8 with inter site correlation ................................ ................................ .......................... 101 3 26 Behavior of the MmCSRS when T and R CI profiles differ from each other on multiple sites in their mean deposition and variability for CI profile M9 with inter site correlation ................................ ................................ .......................... 102 3 27 Behavior of the MmCSRS when T and R CI profiles differ from each other on multiple sites in their mean deposition and variability for CI profile M10 with inter site correlation ................................ ................................ .......................... 103 4 1 Proposed APSD equivalence test ................................ ................................ ..... 126 4 2 Real CI profiles ................................ ................................ ................................ 127 4 3 Average and reference CI profiles for constructing cut off value for MmCSRS based CI profile comparison tes ................................ ................................ ....... 128 4 4 Cut off value plot and example confidence interval for the MmCSRS .............. 129 4 5 Categorization of 55 PQRI scenarios based upon proposed APSD equivalence test ................................ ................................ ................................ 130 PAGE 13 13 4 6 Average ISM ratio (T/R) and normalized mean ISM profiles for PQRI scenarios 1 4 ................................ ................................ ................................ .... 131 4 7 Average ISM ratio (T/R) and normalized mean ISM profiles for PQRI scenarios 5 8 ................................ ................................ ................................ .... 132 4 8 Average ISM ratio (T/R) and normalized mean ISM profiles for PQRI scenarios 9 12 ................................ ................................ ................................ .. 133 4 9 Average ISM ratio (T/R) and normalized mean ISM profiles for PQRI scenarios 13 16 ................................ ................................ ................................ 134 4 10 Average ISM ratio (T/R) and normalized mean ISM profiles for PQRI scenarios 17 20 ................................ ................................ ................................ 135 4 11 Average ISM ratio (T/R) and normalized mean ISM profiles for PQRI scenarios 21 24 ................................ ................................ ................................ 136 4 12 Average ISM ratio (T/R) and normalized mean ISM profiles for PQRI scenarios 25 28 ................................ ................................ ................................ 137 4 13 Average ISM ratio (T/R) and normalized mean ISM profiles for PQRI scenarios 29 32 ................................ ................................ ................................ 138 4 14 Average ISM ratio (T/R) and normalized mean ISM profiles for PQRI scenarios 33 36 ................................ ................................ ................................ 139 4 15 Average ISM ratio (T/R) and normalized mean ISM profiles for PQRI scenarios 37 40 ................................ ................................ ................................ 140 4 16 Average ISM ratio (T/R) and normalized mean ISM profiles for PQRI scenarios 41 44 ................................ ................................ ................................ 141 4 17 Average ISM ratio (T/R) and normalized mean ISM profiles for PQRI scenarios 45 48 ................................ ................................ ................................ 142 4 18 Ave rage ISM ratio (T/R) and normalized mean ISM profiles for PQRI scenarios 49 51 ................................ ................................ ................................ 143 4 19 Average ISM ratio (T/R) and normalized me an ISM profiles for PQRI scenarios 52 55; eight ISM sites ................................ ................................ ....... 144 4 20 Average ISM ratio (T/R) and normalized mean ISM profiles for PQRI scenarios 52 55; seven ISM sites ................................ ................................ ..... 145 5 1 Compartment model for characterization of plasma concentration after administration of ICS ................................ ................................ ........................ 177 5 2 ................... 178 PAGE 14 14 5 3 ...................... 179 5 4 Hand ................................ ................................ .... 180 5 5 Hand ................................ ................................ ..... 181 PAGE 15 15 LIST OF ABBREVIATIONS ACI Andersen Cascade Impactor APSD Aerodynamic particle size distribution BE Bioequivalence BUD Budesonide CI Cascade impactor COPD Chronic obstructive pulmonary disease CSRS Chi square ratio statistic EMA European Medicines Agency FDA Food and Drug Administration FLU Flunisolide FP Fluticasone propionate ICS Inhaled corticosteroids mCSRS Modified chi square ratio statistic MmCSRS Median of the distribution of all modified chi square ratio statistics NGI Next Generation Impactor OIDP s Orally inhaled drug products PD Pharmacodynamic PK Pharmacokinetic T Test R Reference TA Triamcinolone acetonide PAGE 16 16 Abstract of Dissertation Presented to the Gra duate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy I N VITRO AND IN VIVO METHODS FOR ESTABLISHING BIOEQUIVALENCE FOR ORALLY INHALED DRUG PRODUCTS WITH EMPHASIS ON INHALED CORTICOSTEROIDS By Benjamin Weber May 2013 Chair: Guenther Hochhaus Major: Pharmaceutical Sciences Background: Demonstrating bioequivalence (BE) of locally acting orally inhaled drug products (OIDPs) remains challenging. Both the European Medicines Agency and the Food and Drug Administration have proposed approaches for establishing BE of OIDPs. Both ap proaches comprise in vitro (e.g., determination of aerodynamic particle size distribution via cascade impactor (CI) studies) and in vivo methods (e.g., pharmacokinetic (PK) and pharmacodynamic studies) that should ensure an equivalent safety and efficacy p rofile of both products (i.e., test (T) and reference (R)). However, a scientific consensus about the appropriateness and/or necessity of those methods has not been reached. Two of the major problems that have not been resolved yet are (1) the lack of a st atistical test for testing APSD equivalence and (2) the sensitivity of plasma concentration data to differences in pulmonary behavior. Objectives: (1) To develop and characterize a metric (i.e., modified chi square ratio statistic; mCSRS) and a statistical method for APSD equivalence testing and (2) to develop a software tool for PK trial simulation of inhaled corticosteroids, which could be applied to elucidate the sensitivity of plasma concentration data to differences in pulmonary behavior. Methods: PAGE 17 17 (1) The mCSRS was applied to CI profiles for situation in which T and R products were identical (robustness analysis) or differed from each other (sensitivity analysis). CI profiles were simulated based upon hypothetical or modified actual data. (2) A compartm ent model that describes the fate of ICS and incorporates physiological and patient aspects of inhalation therapy was developed and a closed form expression for the plasma concentration time profile derived. Results: The median of the distribution of mCSRS s (MmCSRS) was one regardless of the shape and number of sites of the CI profile. The MmCSRS is more sensitive to differences that occur on high deposition sites and requires reference variance scaling for consistent APSD equivalence decision making. 55 ty pical CI scenarios were classified according to expert opinion. The PK trial simulation tool was successfully developed and validated. Conclusions: A statistical test for APSD equivalence testing and a software tool published that could be applied for eval uating the sensitivity of the PK approach to pulmonary differences were developed. PAGE 18 18 CHAPTER 1 INTRODUCTION Background Asthma and chroni c obstructive pulmonary disease (COPD) are the most common chronic inflammatory lung diseases worldwide ( 1 2 ) An estimated 300 million people are worldwide affected by asthma. The prevalence of asthma varies globally between 1 18% in different countries (United States: approximately 11%). Annual worldwide deaths of asthma are estimated at 250,000 ( 1 ) The prevalence of COPD is reported as 6% but is estimated to be higher. COPD will become the third leading cause of death worldwide by 2020. In the European Union, COPD accounts for annual costs of 38.6 billion Euros. In the United States the estimated direct costs of COPD are $29.5 billion and th e indirect costs $20.4 billion ( 2 ) The social and e conomic burden of both diseases is immense. Ab sence from school or work is reported as substantial social and economic consequences of asthma and COPD in various countries ( 1 2 ) Orally inhaled drugs products (OIDPs) comprising inhaled corticosteroids (ICS), beta 2 agonists, and anticholinergic drugs play an important role in the treatment of asthma and COPD ( 1 2 ) The availability of OIDPs has improved the treatment quality (i.e., desired effect to side effects ratio) by delivering the drugs directly to the lung ( 1 4 ) In particular when considering the economic impact of both diseases, the development of generic alternatives to the commercially available innovator products is of great importance ( 5 6 ) Whereas obtaining market approval for an innovator product requires demonstration of safety and efficacy, which is a very time and cost intensive process, market approval for generics can be obtained by simply dem onstrating bioequivalence (BE; see below) between the generic and the innovator product, which is usually less PAGE 19 19 time and cost intensive ( Figure 1 1 ). Hence, generic dr ugs are usually much cheaper than the respective innovator products. However, even though guidelines and methods for demonstrating BE of OIDPs have been published by the European and United States (US) drug regulating agencies, there is no scientific cons ensus which methods are most appropriate and necessary for demonstrating BE of OIDPs, in particular for ICS. This dissertation is structured as follows. In Chapter 1 the principles of the methods that are used for demonstrating BE of systemically acting orally administered drug are briefly reviewed, the challenges that are involved in demonstrating BE of locally acting OIDPs are described, the guidelines and methods for demonstrating BE that have been published by the European Medicines Agency (EMA) and the Food and Drug Administration (FDA) are reviewed, and the current needs for research in this area addressed. In Chapter 2, a metric (i.e., modified chi square ratio statistic; mCSRS) for testing equivalence in aerodynamic particle size distribution (APS D), an important in vitro characteristic in both EMA and FDA guidelines, is introduced and its behavior when two OIDPs a re identical characterized. In C hapter 3, the behavior of the mCSRS when two OIDPs differ from each other in their APSD is analyzed. In C hapter 4, a method for testing equivalence in APSD based upon the mCSRS is proposed and evaluated. In C hapter 5, a semi mechanistic pharmacokinetic (PK) model that describes the fate of an ICS after administration and that can be used for trial simulation is developed and its features characterized. In C hapter 6, the current EMA and FDA guidelines and methods for demonstrating BE of OIDPs/ICS are critically analyzed and PAGE 20 20 the impact of the results of this dissertation of the EMA and FDA guidelines and BE tes ting of OIDPs/ICS is debated. Methods for Establishing Bioequivalence of Systemically Acting Orally Administered Drugs Definition of Bioequivalence 21 Code of Fed eral Regulations 320.1 (e): Bioequivalence means the absence of a significant difference in the rate and extent to which the active ingredient or active moiety in pharmaceutical equivalents or pharmaceutical alternatives becomes available at the site of drug action when administered at the same molar dose under similar conditions in an appropriat ely designed study. Where there is an intentional difference in rate (e.g., in certain extended release dosage forms), certain pharmaceutical equivalents or alternatives may be considered bioequivalent if there is no significant difference in the extent to which the active ingredient or moiety from each product becomes available at the site of drug action. This applies only if the difference in the rate at which the active ingredient or moiety becomes available at the site of drug action is intentional and is reflected in the proposed labeling, is not essential to the attainment of effective body drug concentrations on chronic use, and is considered medically insignificant for the drug Interpretation It is important to recognize that the generic product nee ds to demonstrate the absence of a significant difference (in rate and extent) at the site of drug action compared with the innovator product. However, it is often not feasible to determine drug concentrations at the site of action (e.g., heart, kidney, br ain). Hence, demonstrating BE of systemically acting orally administered drugs is based upon the principle that for PAGE 21 21 those formulations, the drug reaches the site of action via the systemic circulation (i.e., blood). Thus, BE can be establish by showing the absence of a significant difference (in rate and extent) at which the drug becomes available in the systemic circulation and the scientifically justified assumption that an absence of a significant difference in the systemic circulation results in an abse nce of a significant difference at the site of action ( Figure 1 2 ). Methods Demonstration of BE for systemically acting orally administered drug products is based upo n showing an absence in the rate and extent at which the drug becomes available in the blood (see above). For instance, if the generic and the innovator formulation show the same or a similar plasma concentration time profile after administration, they wou ld certainly be bioequivalent as an absence in rate and extent at which the drug becomes available would be clearly established. However, demonstrating an identical or equivalent plasma concentration time profile is, first, not necessary as bioequivalence refers only to the extent and rate at which the drug becomes available and, second, very challenging from a statistical perspective as it would require multiple comparisons at each time point at which a plasma sample was taken. Thus, demonstration of BE is based upon showing an absence in a significant difference in the maximum plasma concentration (C max ) and the area under the plasma concentration time curve (AUC) as surrogates for rate and extent at which the drug becomes available in the systemic circulation. In particular, C max is a metric for the rate and extent at which the drug becomes available wh ereas AUC is a metric for the extent at which the drug becomes available. PAGE 22 22 Based upon a crossover design (i.e., each subjects receives both the generic and the innovator product), BE is then demonstrated by showing that a 90% confidence interval for the te st to reference (i.e., generic to innovator) ratio for AUC and C max is and can be interpreted that the customers can be 90% confident that the two products do not differ by mor e than 20% in the rate and extent at which drug becomes available at the systemic circulation and, hence, the at the site of action. I would like to remark here that the skewed acceptance range of 80 125% is solely a consequence of the logarithmic transf ormation of the data that is required prior to analysis Furthermore, those BE studies are usually conducted in healthy subjects. Challenges when Establishing Bioequivalence of Locally Acting Orally Inhaled Drug Products The approach for establishing BE o f systemically acting orally administered drug based upon C max and AUC (see above) cannot generally be applied to locally acting OIDPs for the following two reasons. First, the drug reaches the site of action (lung) before it reaches the systemic circulati on and, second, the plasma concentrations may reflect both drug that has been absorbed through the lung and the gastrointestinal (GI) tract ( Figure 1 3 ). Hence, a diff erent methodology may be required to establish BE of locally acting OIDPs. Interestingly, the EMA and FDA have proposed very different approaches for the establishment of BE of locally acting OIDPs. Those two approaches are briefly summarized below. FDA Ap proach Aggregate Weight of Evidence Approach The FDA proposed the so establishment of BE of OIDPs ( 7 ) This approach comprises four principles (i.e., device PAGE 23 23 design and formulation similarity, comparative in vitro tests, systemic exposure studies, and pharmacodynamic and clinical en dpoint studies) all of which need to be passed in order to demonstrate BE between a generic and an innovator inhaler ( Figure 1 4 ). Device design and formulation simi larity The FDA requires that the generic and innovator products have a similar device the generic inhaler. Moreover, the FDA recommends that the formulation of the gener ic product is qualitatively (Q1) and quantitatively (Q2) with respect to the inactive ingredients similar (+/ 5%) to that of the innovator product. However, the FDA is aware that e.g., certain differences in the internal geometry of the devices require di fferences in formulation (e.g., different excipients or different amounts of the same excipients) for delivering an equivalent lung dose or maintaining a similar device resistance. Hence, the Q1 and Q2 sameness is a recommendation but not a formal requirem ent. Comparative in vitro tests The FDA requires the demonstration of equivalence in four comparative in vitro tests (i.e., device resistance, flow rates, single inhalation/actuation content, and particle size distribution) for demonstration of BE of two d ry powder inhalers (DPIs). These comparative in vitro tests are required in addition to the pharmacokinetic (PK) and pharmacodynamics PD studies (PD), which are intended to show an equivalent systemic safety profile and equivalent pulmonary efficacy (see b elow), respectively, as it is generally assumed that in vitro tests are more sensitive to possible difference between two products. PAGE 24 24 Systemic exposure studies The FDA requires comparative systemic exposure studies for demonstration of an equivalent systemi c safety profile between a generic and an innovator product. A classical crossover design PK study using C max and AUC as metrics, which is used for demonstrating BE of systemically acting orally administered drugs and described above, is recommended. It should be remarked that drug plasma concentration represent drug that is absorbed via the GI tract and the lung for OIDPs with a relevant oral bioavailability. Pharmacodynamic or clinical endpoint studies The FDA requires comparative pharmcodynamic and clinical endpoint studies for demonstration of an equivalent pulmonary efficacy profile between a generic and the innovator product. However, a sensitive and robust metric for testing equivalence in pulmonary efficacy has not been established up to date. EMA A pproach A schematic of the EMA approach for establishing BE of OIDPs is shown in Figure 1 5 In principle, the EMA allows the generic company to choose which method (in vitro study, PK study, or PD study) to use for establishing both an equivalent systemic safety profile and an equivalent pulmonary efficacy profile. Furthermore, in case one of the selected methods fails to show BE, the EMA gives the optio n of using a different method. PAGE 25 25 Figure 1 1 Market approval of innovator and generic products PAGE 26 26 Figure 1 2 Bioequivalence approach for systemically acting orally administered drug products Figure 1 3 Bioequivalence approach for locally acting orally inhaled drug products PAGE 27 27 Figure 1 4 Aggregate weight of evidence approach for establishment of bioequivalence (BE) of orally inhaled drug products (OIDPs), adapted from reference ( 7 ) PAGE 28 28 Figure 1 5 EMA approach for establishment of bioequivalence (BE) of orally inhaled drug products (OIDPs) PAGE 29 29 CHAPTER 2 A STABILITY ANALYSIS OF A MODIFIED VERSION OF THE CHI SQU ARE RATIO STATISTIC: IMPLICATIONS FOR EQUIVALENCE TESTING OF AERODYNAMIC PARTICLE SIZE DISTRIBUTION 1 Background drug products (OIDPs) is based upon the aggregate weight of scientific evidence. In this approach, demonstration of equivalence in aerodynamic particle size distribution (APS D) constitutes one of key in vitro tests for supporting BE between test (T) and reference (R) OIDPs ( 7 ) APSD is assessed through multistage cascade impaction a method evaluating the size distribution of the emitted dose on the basis of size dependent particle inertia with an Andersen Cascade Impactor (ACI) or Next Generation Impactor (NGI). This test provides an important in vitro performance attribute, as APSD is believed to affect the total and regional deposition of drug(s) in the lung and therefore influence the safety and efficacy of OIDPs. For comparing c ascade impactor (CI) profiles of T and R products, an accurate, sensitive and robust statistical method comparing APSD profiles across the relevant deposition sites is desirable. Besides other proposed methods ( 8 9 ) a chi square ratio statistic (CSRS) was proposed by the FDA for equivalence testing of CI profiles in the June 1999 Draft Guidance for Industry: Bioavailability and Bioequivalence Studies for N asal Aerosols and Nasal Sprays for Local A ction ( 10 ) and discussed by Cheng and Shao ( 11 ) that allowed univariate 1 Chapter 2 was originally published in the AAPS Journal Weber B, Hochhaus G, Adams W, Lionberger R, Li B, Tsong Y, Lee SL. A stability analysis of a modified version of the chi square ratio statistic: implications for equivalence testing of aerodynamic particle size distribution. AAPS J 2013 ; 15(1): 1 9 PAGE 30 30 cumulative assessment of the entire multivariate CI profiles. The computational form of the 1999 CSRS is given in Eq. 2 1 2 (2 1) where p represents the number of deposition sites of the CI profile, T ij represents the normalized deposition (i.e., by dividing the absolute deposition on each individual site by the total deposition on all sites under consideration (%)) on the i th p) of the j th CI profile T ) of the T sample, R ik and R im represent the normalized deposition on the i th site of the k th and m th CI profile (k R ) of the R sample, respectively. n T and n R represent the number of CI profile samples that were obtained from the T and R product, respectively. The k th and m th CI profile are two different samples obtained from the same R product (e.g., different units from the same batch or different batches of the R product). The Product Quality Research Institute (PQRI) (WG) evaluated the suitability of the CSRS to discriminate between equivalent and inequivalent APSD profiles by applying the CSRS on all individual deposition sites (e.g., amount of drug deposited within the MDI actuator, on mouthpiece adaptor and within the throat, and on CI stages including filter) and a constant critical value (i.e., a cut off value for equivalen ce testing). The PQRI WG concluded that the CSRS could not consistently discriminate between equivalent and inequivalent CI profiles ( 12 13 ) However, no alternative approach was proposed at that time. 2 The notation of the CSRS was adjusted from the original version to be able to directly compare it to the mCSRS PAGE 31 31 In particular, the PQRI WG demonstr ated that the behavior of the CSRS was dependent on the shape and the number of deposition sites of the CI profile ( 12 ) Since the increased, the PQRI WG concluded that the CSRS could not be applied to a reduced number of deposition sites of the CI profile (e.g., deposition sites that may be more related to lung deposition) ( 12 13 ) This non applicability to a reduced number of deposition sites was one of the major limitations of the CSRS since the CSRS was demonstrated to be more sensitive to changes in high deposition sites (e.g., throat or pre separator), which may not be relevant for the performance of an OIDP wi th respect to lung deposition. The objective of this study was to develop a robust and sensitive methodology for assessing equivalence of APSD profiles of T and R OIDPs. We proposed a modified version of the CSRS (mCSRS, Eq. 2 2 ) and evaluated systematically its behavior when T and R CI profiles were identical or diff ered from each other on single or multiple deposition site(s). The results of this evaluation are published as a series of three articles. In this article (Part I), the computational form of the mCSRS is introduced and the behavior of the mCSRS, when T and R CI profiles are identical, is characterized and hypothesized to be robust. 3 Subsequent publications will continue to characterize the behavior of the mCSRS. In the second article (Part II), the behavior of the mCSRS when T and R CI profiles differ from each other on a single or multiple deposition site(s) will be characterized. In the third article (Part III), a stepwise APSD equivalence testing procedure is proposed that uses the mCSRS within a series of statistical tests. The 3 The sub optimal behavior of the CSRS within this task was one of the reasons for the PQRI WG to conclu de that the CSRS was not robust PAGE 32 32 sensitivity and robustness of this overall procedure is evaluated by categorizing 55 ( 13 15 ) which were judged by the PQRI WG members as equivalent or inequivalent Definition of a Modified Version of the CSRS The computational form of the mCSRS is given in Eq. 2 2 (2 2) where p was defined above, T ij and R ik represent the normalized deposition on the i th site of the j th CI profile T ) of the T sample and on the i th site of the k th CI R ) of the R sample, respectively, n T and n R are defined above, and represents the sample mean on the i th stage of all R CI profiles. Similar to the CSRS ( Eq 2 1 ), the numerator and denominator of the mCSRS represent a measure of the T to R and R to R distance, respectively. By design, for a constant denominator, the numerator of the mCSRS increases with increasing difference in mean deposition between T and R CI profiles and with increasing variability of the T product, and decreases with decreasing variability of the T product. Hence, the mCSRS rewards or penalizes the T product for havin g a lower or higher variability than the R product, respectively. Unlike for the computation of the CSRS, where a triplet of CI profiles (i.e., one T and two distinct R CI profiles) is required, the mCSRS only requires sampling of a pair of CI profiles (i. e., one T an d one R profile). square statistic for goodness of fit tests ( 16 ) ( Eq. 2 3 square statistic and both the numerato r and denominator of the mCSRS. PAGE 33 33 (2 3) where q represents the number of cells (translates into the number of deposition site s in a CI profile). O r represents the observed cell count (translates into percentage of drug on i th deposition site of T or R CI profiles) in the r th r represents the expected cell count in the r th cell (translates to true percenta ge of drug on the i th square statistic compares observations to expectations (true values), both the numerator and denominator of the mCSRS compare individual CI profiles (T and R, respectively) t o the average CI profile of the R product. In the context of BE, however, ( Eq. 2 2 ) can be viewed as an estimator for the expected (true) deposition on the i th site of both the T and R product. Hence, both numerator and denominator of the mCSRS compar e, in some sense, observations (i.e., two individual CI profiles (T and R)) to expectations The similarity of both the numerator and the denominator of the mCSRS ( Eq. 2 2 square statistic ( Eq. 2 3 ) was expected to result in a favorable distributional behavior of the mCSRS, namely that of an approximate F distribution ( 17 ) when certain criteria are met ( see Discussion ). 4 Methods The behavior of the mCSRS was evaluated and compared to that of the CSRS with respect to the capability to conclude equivalence when T and R CI profiles are identical ( i.e., the same set of CI profiles is used for both T and R) under a wide range of possible situations (i.e., CI profiles differ in the shape of the overall profiles and 4 Before any evaluation of the behavior of the mCSRS was performed it was thought that it was beneficial when the mCSRS followed a known distribution PAGE 34 34 variability on the sites). This was done, as a robust test statistic mCSRS should be in dependent of the shape and number of deposition sites when T and R CI profiles are identical. All evaluations were based upon simulated CI profiles ( see below ). This allowed evaluating the performance of the mCSRS in all theoretically conceivable CI profi le scenarios. CI profile simulations and all computations were performed in the statistical ( 18 ) high performance scientific computer provided by the FDA/CDRH/OSEL Scientific core diskle ss compute nodes each containing eight Intel(R) Xeon(R) CPUs @ 2.67GHz 2.10.1. The simulated CI profiles used for this evaluation were constructed based on a so their initial evaluation of the CSRS when T and R CI profiles were identical ( 12 ) Details about this CI profile simulation approach were described by the PQRI WG ( 12 ) Briefly, rank ordered CI profiles (i.e., deposition sites were ordered according to their decreasing magnitude of normalized drug deposition (% of drug on an individual deposition site relative to total amount of drug on the entire CI profile; see Figure 2 1 and Supplemental Materials)) were modeled by controlling three parameters, the shape of the profile (uniform to maximally skewed), the standard deviation on the first deposition site (low to high), and the linear change of the coefficient of variation (CV) across sites (no change to maximum change). Furthermore, normally distributed PAGE 35 35 deposition on each site 5 and no inter site correlation were assumed in this appro ach. Table 2 1 Figure 2 1 and Figure 2 2 ) could therefore be modeled by systematically changing each of the three parameters (shape, standard deviation of first site, and change in CV). In addition, these eight scenarios were applied for CI profiles comprising 13, 8, and 4 deposition sites to cover a wide range of CI setups. Thus, a total number of 24 CI profile scenarios were evaluated. CI profiles were simulated in units of mass deposition and, subsequently, normalized by dividing the mass on individual sites by the total mass of all deposition sites. For each of the 24 scenarios, a set of 30 CI profiles was generated based upon the respective mean and standard deviation of the rank ordered ( see above ) CI profiles. If a negative deposition on a site was simulat ed, its value was set to 0.001 mcg. This value was selected as it could possibly represent a reasonable lower limit of quantification on a deposition site ( see Discussion ). The set of 30 CI profiles was then used as both T and R CI profiles. The number of T and R CI profiles was in accordance with the recommendations in the June 1999 Draft Guidance for Industry: Bioavailability and Bioequivalence Studies for Nasal Aerosols and Nasal Sprays for Local Action and the analysis of the PQRI working group ( 10 12 13 ) The mCSRS ( Eq. 2 2 ) was then applied to all 900 possible pairs (30 T 30 R) comprising one T and one R CI profile and, consequently, the distribution of the 900 mCSRSs was obtained. Six metrics, the 5 th 10 th 50 th (median), 90 th 95 th perc entiles and the mean of the distribution of the 900 mCSRSs, were then calculated. These six metrics were potential candidates for a test statistic for the mCSRS and should provide some information about the distributional 5 Checking normality assumptions of real CI profiles showed that the assumption of a normally distributed depositions on sites is reasonable PAGE 36 36 behavior of the mCSRS. This proced ure was replicated 20,000 times and the averages (of the 20,000 replicates) of each of the six metrics were determined for each of the 24 scenarios. Furthermore, the averages of the six metrics of the distribution of the 900 mCSRSs were compared to their t heoretical equivalents of an F distribution ( 17 ) This comparison was performed since it was expec ted that the distribution of the 900 mCSRSs is approximately an F distribution when certain criteria are met ( see Discussion ). The same analysis was performed for the CSRS. However, the CSRS ( Eq. 2 1 ) was applied to all 13050 (30 T 0.5*(30 29) R) possi ble triplets comprising one T and two distinct R profiles. It should be noted that this evaluation of the CSRS differed slightly ( see Discussion ) from the algorithm that was originally proposed ( 15 ) This alteration was needed in order to directly compare the performance of the mCSRS with that of the CSRS. Results mCSRS For each of the 24 scenarios (8 profile shapes for 13, 8, and 4 deposition sites), the averages (n = 20,000) of each of the six metrics ( see above ) and their theoretical equivalents of the respective F distribution are presented in Table 2 2 Table 2 3 and Table 2 4 All six metrics were viable candidates for a robust and sensitive metric for comparing T and R CI profil es. The median of the distribution of 900 mCSRSs (MmCSRS) was equal to one regardless of the shape and the number of stages of the CI profiles. All other metrics varied across CI profiles with a different shape and number of deposition sites. Numerical com parison of the empirical percentiles/means ( Table 2 2 Table 2 3 and Table 2 4 ) and visual comparison of the histograms (examples shown PAGE 37 37 for eight deposition stages, Figure 2 3 and Figure 2 4 ) of the distributions of the 900 mCSRSs to those of the respective F distribution show a certain agreement for the uniforml y shaped beta scenarios (i.e. #1, 2, 5, and 6, Figure 2 1 and Figure 2 2 ). For those scenarios, the similarity between the empirical percentiles/mean of the distributi on of the 900 mCSRSs and those of the respective F distribution was confirmed by a Kolmogorov Smirnov test ( 18 ) (results not shown). CSRS For each of the 24 scenarios, the averages (n = 20,000) of each of the six metrics of the distribution of 13050 CSRSs and their theoretical equivalents of the respective F d istribution are presented in Table 2 5 Table 2 6 and Table 2 7 None of the metrics (5 th 10 th 50 th 90 th 95 th percentiles and the mean) returned th e same value (in average) across the 24 beta scenarios. The median of the distribution of 13050 original CSRS was close to 0.7 (in average) and varied the least across the 24 scenarios when compared with the other metrics. Numerical comparison of the empir ical percentiles/mean of the distribution of 13050 CSRSs to those of the respective F distribution did not show any similarities ( Table 2 5 Table 2 6 and Table 2 7 ), which was confirmed by a Kolmogorov Smirnov test (results not shown). Discuss ion Comparison of the mCSRS ( Eq. 2 2 square statistic for goodness of fit tests ( Eq. 2 3 square statistic for goodness of fit tests and both the numerator and denominator of the mCSRS ( see above ). If the population mean depositions (true values) on all sites of the R CI profile (E[R i ]) and T CI profile (E[T i ]) were known and under the assumption of PAGE 38 38 identical T and R CI profiles (i.e. E[R i ] = E[T i ]), the mCSRS ( Eq. 2 2 ) could be expressed as (2 4) In this case, both the numerator and the denominator of Eq. 2 4 have the same square statistic for goodness of fit tests ( Eq. 2 3 ) and are expected to follow approx imately a chi square distribution (with degrees of freedom equal to the number of sites (p) minus one) when only a few low deposition sites are present 6 ( 16 19 ) Furthermore, numerator and denominator are independent of each other ( 20 ) and have the same degrees of freedom. Thus, under the assumption of identical T and R CI profiles, Eq. 2 4 is expected to follow an approximate F distribution (with numerator and denominator degrees of freedom equal to the number of stages minus one) ( 17 21 ) Since Eq. 2 4 and the mCSRS measure the same quantity under the assumption of identical T and R CI profiles, the distribution of the mCSRS is expected to be related to an F distribution under this assumptio n. The behavior of the mCSRS when T and R CI profiles were identical was evaluated using CI profiles that were generated by simulation. These simulations assumed that drug deposition on a site is normally distributed. This assumption was based upon analys is of actual CI data that suggested normal distribution. Furthermore, it allowed comparison of the results with those of the PQRI working group that also assumed normal distribution during data generation ( 12 ) However, this procedure 6 One of the assumptions for Eq. 2 4 to follow approximately a chi square distribution is that there are no (or only a few) low cell counts (deposition sites) present PAGE 39 39 resulted in simulation of negative depositions. Those negative values were, subsequently, converted to 0.001 mcg ( see Methods ). Analysis of actual CI da ta suggested that an amount of 0.001 mcg could represent a reasonable lower limit of quantification on a deposition site on a CI profile. Setting the negative values to zero would have been an alternative option that is not expected to have affected the re sults ( see below ). However, it might be a worthwhile discussion on how to deal with CI data that contain a lot of zero (below lower limit of quantification) deposition sites. The number of negative amounts was dependent on the total number of deposition si tes (4, 8, or 13) (data not shown). If the drug was deposited on a total of 4 sites, negative simulation data averaged 1.1% (0 5.93%) while deposition of the same dose on 13 sites resulted in average in 13% (0 31%) negative data. It is unlikely that this p rocedure (simulations assuming normal distribution and using 0.001 mcg as default value for negative data) would affect the conclusions drawn from these simulations. First, we assumed that T and R CI profiles were identical and, thus, potential interferenc es should cancel out. Second, the numerical value of the selected test statistic (MmCSRS) was one regardless of the shape and the number of deposition sites of the CI profiles ( Table 2 2 Table 2 3 and Table 2 4 ), both of which affected the percentage of negative results. Hence, the method of data generation does not invalida te the conclusions of this work. It must be also noted that all CI profiles were generated by assuming that the deposition between two sites is not correlated. Furthermore, all evaluations were performed for a sample size of 30 T and 30 R CI profiles, which is in accordance with the recommendations in the June 1999 Draft Guidance for Industry: Bioavailability and PAGE 40 40 Bioequivalence Studies for Nasal Aerosols and Nasal Sprays for Local Action and the analysis of the PQRI working group ( 10 12 13 ) Since T and R CI profiles were identical throughout this analysis of the mCSRS, it is not expected that these assumptions would affe ct the conclusion regarding the behavior of the mCSRS in this case. However, the influence of varying both factors will be a subject of the forthcoming articles when T and R profi les differ in their properties. One limitation of the CSRS was its non applic ability to a reduced number of deposition sites (e.g., deposition sites that may be more related to lung deposition) was related to the mean of the distribution of CSRSs ( 15 ) was dep endent of the number of depositions sites of the CI profiles ( 12 13 ) ( see Introduction ). The current analysis of the behavior of the CSRS when the set of T and R CI profiles were identical confirmed the dependency of the mean of the distribution of 13050 CSRSs on the number of deposition sites and shape of the CI profile ( Table 2 5 Table 2 6 and Table 2 7 ). Since the algorithm of the original CSRS specified obtaining a bootstrap estimate of the mean of a distribution of 500 randomly sampled triplets ( 15 ) rather than obtaining metrics from the distribution of all possible 13050 triplets, direct nume rical comparison of the results in this article to those of the original algorithm might differ slightly. However, the different algorithms did not affect the conclusions. Interestingly, it appeared that the median of the distribution of 13050 CSRSs, which was close to 0.7, is the most robust metric across the 24 scenarios ( Table 2 5 Table 2 6 and Table 2 7 ). On the other hand, the MmCSRS was equal to one in all 24 scenarios ( Table 2 2 Table 2 3 and Table 2 4 ). Hence, the MmCSRS is independent of the shape and PAGE 41 41 number of deposition sites of the CI profile when the sets of T and R CI profiles are identical and, thus, is applicable to CI profiles with a reduced number of deposition s ites. Furthermore, the MmCSRS returns a for ratios correct value of one when sets of T and R CI profiles are identical. All other metrics (e.g., P95 or P99) varied across the 24 scenarios and, thus, were not considered as potential test statistics for APSD equivalence testing. It must be noted that those percentiles (e.g., P95 or P99) were not evaluated as potential metrics for constructing confidence intervals for APSD equivalence testing based on the mCSRS. A method for constructing confidence intervals f or the MmCSRS will be introduced and discussed in a forthcoming publication (Part III). It is desirable for a new statistical metric to follow a known distribution. If certain criteria are met, the distribution of the 900 mCSRSs is expected to follow an ap proximate F distribution ( see above ). Indeed for CI profiles with only a few or no low deposition sites (beta scenarios 1, 2, 5, and 6, Figure 2 1 and Supplemental Ma terials), the similarity between the distribution of 900 mCSRSs and the F distribution was empirically confirmed by numerical comparison of the six metrics (see above) of the distribution of the 900 mCSRSs to their theoretical equivalents of the respective F distribution ( Table 2 2 Table 2 3 and Table 2 4 ) and by visual inspection of the histograms of the distributions of the 900 mCSRSs ( Figure 2 3 and Figure 2 4 ). Comparison of those metrics for more skewed CI profiles (i.e. more low deposition sites are present) indicated that the agreement between the distribution of 900 mCSRS and the F distribution is worsening ( Table 2 2 Table 2 3 and Table 2 4 ). However, the MmCSRS remains stable. PAGE 42 42 Even though the characteristic, that the distribution of the 900 mCSRS seems to be approximately F distributed when T and R CI profiles are identical and only a few low deposition sites are present, seems to be a desirable feature, it might not be of any practical relevance as realistic CI profiles are very likely to show several low deposition sites. Nonetheless, the MmCSRS is not affected by these distributional considerations and is equal to one for all 24 scenarios regardless of the number of deposition sites and shape of the CI profiles. On the other hand, numerical comparison of the six metrics of the distribution of 13050 CSRSs to their theoretical equivalents of the respective F distribution ( Table 2 5 Table 2 6 and Table 2 7 ) shows that the CSRS does not follow an approximate F distribution in any of the cases under consideration. These results support findings of a more detailed analysis of the CSRS, its relationship to the F distribution, and a discussion on independence of its numerator and denominator ( 22 ) Since the 24 scenar ios covered in this evaluation are expected to cover all possible CI profiles, the robustness of the MmCSRS was demonstrated in cases when the T and R CI profiles are identical. Thus, this result suggests that the MmCSRS is a potential test statistic for A PSD equivalence testing. Summary The current analysis suggests that MmCSRS is independent of the shape and number of deposition sites of a CI profile and is equal to one when T and R CI profiles are identical. Hence, the MmCSRS is a robust metric and, thus is potentially useful as test statistic for APSD equivalence testing. Moreover, the MmCSRS could be applied to CI profiles comprising a reduced number of deposition sites (e.g., sites that may be more relevant for lung deposition). The behavior of the Mm CSRS when T and R CI PAGE 43 43 profiles differ from each other on a single or multiple deposition site(s) will be evaluated in a forthcoming article (Part II) in order to better understand the suitability of the MmCSRS for APSD equivalence testing. PAGE 44 44 Table 2 1 Beta Scenario Profile Shape SD First Stage Change in CV 1 Uniform Low Low 2 Uniform High Low 3 Skewed Low Low 4 Skewed High Low 5 Uniform Low High 6 Uniform High High 7 Skewed Low High 8 Skewed High High Profile Shape: shape of the rank ordered CI profile (for uniform and skewed profiles the beta parameter of the beta distribution was set to 1 and 4 respectively) SD First Stage: standard deviation of the first stage of the rank ordered CI profile (low: 1, high 10), Change in CV: magnitude of increase in coefficient of variation from the first to the last stage of the rank ordered CI profile (low: 0, high: 15). Detailed information on the parameters values is available elsewhere (7). Table 2 2 Distribution (percentiles and mean) of mCSRS (900 pairs) across the eight profiles) Beta Scenario P5 P10 P50 P90 P95 Mean 1 0.38 0.47 1.00 2.16 2.70 1.20 2 0.36 0.45 1.00 2.23 2.81 1.22 3 0.24 0.32 1.00 3.17 4.44 1.50 4 0.21 0.29 1.00 3.56 5.12 1.62 5 0.36 0.46 1.00 2.22 2.81 1.22 6 0.36 0.45 1.00 2.26 2.86 1.22 7 0.31 0.40 1.00 2.55 3.36 1.31 8 0.27 0.36 1.00 2.85 3.86 1.40 F(12,12) 0.37 0.47 1.00 2.15 2.69 1.20 Results are represented as averages (n = 20,000), F(12,12): theoretical percentiles and expected value of the F distribution with 12 numerator and 12 denominator degrees of freedom, P5: 5 th percentile, P10: 10 th percentile, P50: Median, P90 : 90 th percentile, P95: 95 th percentile PAGE 45 45 Table 2 3 Distribution (percentiles and mean) of mCSRS (900 pairs) across the eight profiles) Beta Scenario P5 P10 P50 P90 P95 Mean 1 0.27 0.37 1.00 2.79 3.81 1.39 2 0.26 0.35 1.00 2.95 4.11 1.45 3 0.14 0.22 1.00 4.77 7.58 2.12 4 0.13 0.21 1.00 5.07 8.18 2.25 5 0.24 0.34 1.00 3.07 4.38 1.49 6 0.27 0.36 1.00 2.83 3.88 1.41 7 0.20 0.28 1.00 3.63 5.35 1.68 8 0.18 0.26 1.00 3.95 5.96 1.80 F(7,7) 0.26 0.36 1.00 2.78 3.79 1.40 Results are represented as averages (n = 20,000), F(7,7): theoretical percentiles and expected value of the F distribution with 7 numerator and 7 denominator degrees of freedom, P5: 5 th percentile, P10: 10 th percentile, P50: Median, P90: 90 th percentile, P95: 95 th percentile Table 2 4 Distribution (percentiles and mean) of mCSRS (900 pairs) across the eight of 30 T and 30 R CI profiles) Beta Scenario P5 P10 P50 P90 P95 Mean 1 0.12 0.20 1.00 5.51 9.94 2.94 2 0.10 0.17 1.00 6.32 11.62 3.40 3 0.04 0.08 1.00 13.98 34.43 22.41 4 0.04 0.08 1.00 14.28 35.22 26.49 5 0.08 0.14 1.00 7.72 14.60 4.30 6 0.10 0.17 1.00 6.21 11.49 3.34 7 0.06 0.12 1.00 9.83 23.76 11.56 8 0.05 0.10 1.00 11.07 26.54 11.59 F(3,3) 0.11 0.19 1.00 5.39 9.28 3.00 Results are represented as averages (n = 20,000), F(3,3): theoretical percentiles and expected value of the F distribution with 3 numerator and 3 denominator degrees of freedom, P5: 5 th percentile, P10: 10 th percentile, P50: Median, P90: 90 th percentile, P95: 95 th percentile PAGE 46 46 Table 2 5 Distribution (percentiles and mean) of CSRS (13500 triplets) a cross the eight profiles ) Beta Scenario P5 P10 P50 P90 P95 Mean 1 0.25 0.26 0.71 1.58 1.99 0.86 2 0.30 0.35 0.76 1.47 1.78 0.86 3 0.17 0.24 0.69 2.31 3.25 1.08 4 0.17 0.22 0.68 2.43 3.50 1.12 5 0.28 0.33 0.75 1.60 2.02 0.90 6 0.31 0.36 0.79 1.49 1.80 0.89 7 0.22 0.27 0.70 1.91 2.55 0.96 8 0.23 0.27 0.71 1.91 2.53 0.96 F(12,12) 0.37 0.47 1.00 2.15 2.69 1.20 Results are represented as averages (n = 20,000), F(12,12): theoretical percentiles and expected value of the F distribution with 12 numerator and 12 denominator degrees of freedom, P5: 5 th percentile, P10: 10 th percentile, P50: Median, P90: 90 th percentile, P95: 95 th percentile Table 2 6 Distribution (percentiles and mean) of CSRS (13500 triplets) across the eight profiles) Beta Scenario P5 P10 P50 P90 P95 Mean 1 0.20 0.25 0.70 2.03 2.77 1.00 2 0.22 0.27 0.71 1.87 2.50 0.96 3 0.11 0.17 0.67 3.41 5.42 1.53 4 0.10 0.16 0.67 3.49 5.60 1.57 5 0.18 0.24 0.70 2.28 3.28 1.11 6 0.25 0.30 0.74 1.84 2.43 0.98 7 0.14 0.20 0.67 2.69 4.01 1.23 8 0.14 0.20 0.68 2.70 4.04 1.24 F(7,7) 0.26 0.36 1.00 2.78 3.79 1.40 Results are represented as averages (n = 20,000), F(7,7): theoretical percentiles and expected value of the F distribution with 7 numerator and 7 denominator degrees of freedom, P5: 5 th percentile, P10: 10 th percentile, P50: Median, P90: 90 th percentile, P 95: 95 th percentile PAGE 47 47 Table 2 7 Distribution (percentiles and mean) of CSRS (13500 triplets) across the eight profiles) represented as the average (n = 20,000) Beta Scenario P5 P10 P50 P90 P95 Mean 1 0.09 0.15 0.67 3.83 6.64 2.11 2 0.08 0.14 0.65 4.01 7.05 2.26 3 0.03 0.06 0.63 9.22 20.78 24.01 4 0.03 0.06 0.63 9.28 21.02 18.07 5 0.06 0.11 0.62 5.63 10.80 3.46 6 0.08 0.14 0.65 3.95 7.04 3.04 7 0.04 0.09 0.64 6.60 14.19 11.08 8 0.04 0.08 0.63 7.14 15.57 14.69 F(3,3) 0.11 0.19 1.00 5.39 9.28 3.00 Results are represented as averages (n = 20,000), F(3,3): theoretical percentiles and expected value of the F distribution with 3 numerator and 3 denominator degrees of freedom, P5: 5 th percentile, P10: 10 th percentile, P50: Median, P90: 90 th percentile, P95: 95 th percentile PAGE 48 48 Figure 2 1 Representative CI profile plots (rank 8 for 13 deposition sites Figure 2 2 Representative CI profile plots (rank ordered, see Methods 8 for 8 deposition sites PAGE 49 49 Figure 2 3 Comparison of distribution of the 900 mCSRSs (histogram) and F distribution with 7 numerator and 7 denominator degrees of freedom (solid 4 and 8 deposition sites, representative examples are displayed PAGE 50 50 Figure 2 4 Comparison of distribut ion of the 900 mCSRSs (histogram) and F distribution with 7 numerator and 7 denominator degrees of freedom (solid 8 and 8 deposition sites, representative examples are displayed PAGE 51 51 CHAPTER 3 A SENSITIVITY ANALYSIS OF THE MODIFIED CHI SQUARE RATIO STATISTIC FOR EQUIVALENCE TESTING OF AERODYNAMIC PARTICLE SIZE DISTRIBUTION 1 Background Demonstration of equivalence in aerodynamic particle size distribution (APSD) is one of several key components in the aggregate weight of scientific evidence approach that the FDA proposed for establishing bioequivalence (BE) of orally inhaled drug products (OIDPs) ( 7 ) APSD equivalence between a test (T) and reference (R) OIDP can be assessed by comparative analysis of multi stage cascade impactor (CI) (e.g., Andersen Cascade Impactor (ACI) or Next Generation Impacto r (NGI)) data. A modified ch i square ratio statistic (mCSRS, Eq. 3 1 ) was introduced as a potential metric for equivalence testing of APSD in the first part of this series of three articles ( 23 ) (3 1) where p represents the number of deposition sites of the CI profile, T ij and R ik represent the normalized deposition (i.e., by the dividing the absolute deposition on the i th site by the total deposition on all sites under consideration) on the i th site of the j th CI T ) of the T sample and on the i th site of the k th R ) of the R sample, respectively. n T and n R represent the number of CI profile samples that were obtained from the T and R product, respectively, and represents the sample mean on the i th site of all R CI profiles. 1 Chapter 3 was originally published in the AAPS Journal Weber B, Lee SL, Lionberger R, Li BV, Tsong Y, Hochhaus G A Sensitivity Analysis of the Modified Chi square Ratio Statistic for Equivalence Testi ng of Aerodyn amic Particle Size Distribution AAPS J Jan 24. [Epub ahead of print] PAGE 52 52 The mCSRS is a modified version of the CSRS tha t was proposed as a statistical method for equivalence testing of CI profiles in the June 1999 Draft Guidance for Industry: Bioavailability and Bioequivalence Studies for Nasal Aerosols and Nasal Sprays for Local A ction ( 10 ) The previous study ( 23 ) evaluated the behavi or of the distribution of the 900 mCSRSs of 30 T and 30 R CI profiles when the two products were identical (i.e., all 60 CI profiles originate from the same product). The key finding of this study was that the median of the distribution of 900 mCSRSs (MmCS RS) consistently yields one when T and R CI profiles are identical regardless of the shape and number of deposition sites of a CI profile. Hence, the MmCSRS is a potential test statistic for APSD equivalence testing and can be applied to deposition sites t hat may be considered more relevant to lung deposition. In contrast, it was reported that the with the number of CI deposition sites, and thus this metric could not be applied to a CI profile with a reduced number of deposition sites ( 12 13 ) However, the application of the MmCSRS for the APSD equivalence testin g warrants adequate understanding of the behavior of this metric when T and R CI profiles differ from each other. In this article, the behavior of the MmCSRS when T and R CI profiles differed were systemically evaluated in a serious of simulations that var ied in complexity with respect to both differences in mean deposition (single site vs. multiple site differences) and variability (variability of the T product is identical or differs from that of the R product). Methods Monte Carlo simulations were used t o generate CI profiles that were, subsequently, used for evaluating the behavior of the MmCSRS. Within these PAGE 53 53 simulations, CI profiles with defined mean depositions and variability were generated from a p dimensional random vector X with p dimensional popul p*p deposition sites of the CI profile. The i th observed deposition and the population mean deposition on the i th site of the CI profile, respectively. The i th th site of the CI profile. The off covariance between two sites of the CI profile. Fur thermore, it was assumed that X follows a multivariate normal distribution ( 24 25 ) ( 26 ) was used for random sample generation from the multivariate normal distribution. In the case that a negative deposition on a site was simulated, its value was set to 0.001 mcg. A discussion on the selection of this value and the assumption of normally dist ributed CI data is given in the first paper of the series of three publications ( 23 ) In their respective population mean vectors and their respective population covariance matrices. Differences in mean deposition on a single or multiple site(s) between two CI adjustment (i.e. when two CI profiles differed in their variability) without affecting the inter site correlation (i.e., the correlation between the deposition on different sites) was achiev (3 2) where D 1/2 is a matrix whose i th diagonal element represents the population standard deviation of the i th site of the CI profile and R is the population (inter site) PAGE 54 54 correlation matrix. Thus, the variability of the i th site was modified by changing the i th diag onal entry in D 1/2 CI profiles were simulated in units of mass deposition and, subsequently, normalized by dividing the mass on individual sites by the total mass of all deposition sites. It should be emphasized here that differences between T and R CI pr ofiles always apply to absolute depositions (i.e., mcg scale) and that the mCSRS is always applied to normalized CI profiles throughout this articles. In the case of the single site differences, a difference in absolute deposition resulted in difference on all deposition sites after normalization (see below). In the case of multiple site differences, differences in absolute deposition were constructed such that the mass balance was maintained even prio r to normalization (see below). Evaluation of the Behavi or of the MmCSRS when T and R CI Profiles Differ From Each Other on a Single Deposition Site For scenarios where the T and R CI profiles differed from each other in their mean deposition on a single site, the behavior of the MmCSRS was characterized for T and R CI profiles with the same variability as well as for T CI profiles that were more modified version of actual CI data, which comprised 11 deposition sites. Speci fically, the R CI profile was supposed to represent a typical CI profile of OIDPs, such as nebulizers, and allowed evaluation of the effect of the location (e.g., low vs. high deposition sites) of single site changes on the MmCSRS. The mean depositions and standard deviations of all deposition sites are displayed in Figure 3 1 The inter site correlation structure is provided as supplemental material (Table 3 3 ). PAGE 55 55 Single site mean difference T and R CI profiles with identical variability T and R CI profiles differed from each other on a single site in their mean deposition by 90%, 80%, instance, if the deposition on site 1 of the R CI profile is 5 mcg and a 60% mean difference was studied, then the deposition on site 1 of the T CI profile is changed to 1.6*5 = 8 mcg. Subsequent ly, the deposition on all sites is normalized to % of the total deposition (see above) and, as a consequence, there will be a mean difference between T and R on all deposition sites (in % scale but not in mcg scale). The above differences were applied to a ll of the 11 deposition sites, one site at a time. T and R CI profiles had the same variability. Thus, a total number of 209 (19*11) scenarios were generated in this part of the study. Single site mean difference T and R CI profiles with different v aria bility T and R CI profiles differed from each other on a single site in their mean deposition by 10% or 30% 2 These differences were applied to the deposition sites 1, 7, 3, and 11 ( Figure 3 1 ) that represent high (approximately 53% of total deposition (i.e., 194.51 mg of 366.55 mg), medium (11.7%), low (4.7%) and very low (0.36%) deposition sites, respectively. The effects of these differences on the M mCSRS were evaluated for R products with a high variability (variances increased by a factor of five compared to Table 3 3 ), medium variability (variances identical to Table 3 3 ), and low variabilty (variances decreased by a factor of five compared to Tabl e 3 3 ). Furthermore, the variability of the T CI profiles was adjusted such that the T/R variability ratio was 0.1, 0.2, 0.5, 2, 5, or 10 on all sites. The T/R variability ratio was assumed to be the same on 2 These two numbers were arbitrarily chosen but could possibly represent accepted differences for equivalence testing of CI profiles PAGE 56 56 all deposition sites to keep the complexity of t he results and their interpretation at a manageable level. However, the inter site correlation structure (Table 3 3 ) was maintained. A total number of 168 (2*4*3*7) scenarios were generated in this part of the study. For each of these 377 scenarios (209 wi th identical + 168 with different variability), 20,000 sets of 30 T and 30 R CI profiles were simulated and the MmCSRS was recorded for all of the 20,000 sets. The average of the 20,000 MmCSRS was then used for evaluating the effect of single site differen ces between T and R CI profiles on the behavior of the MmCSRS. Since the T and R CI profiles were constructed by modification of the absolute deposition but the mCSRS is applied to normalized CI profiles ( see above ), the normalized squared difference refe rence scaled (NSDRS, Eq. 3 3 )) was designed to correlate (i.e., regression analysis) the observed differences in MmCSRS and the differences between T and R CI profiles (after normalization) between the 209 scenarios for which T and R CI profiles had the sa me variability. (3 3) where p is defined above and and represent the i th element of the normalized population mean vectors of the T and R CI profiles, respectively. The NSDRS is introduced here to provide a numerical description for the expected behavior of the MmCSRS when T and R CI profiles differ from each other on a single site (i.e., a difference on a single site in absolute deposition will results in a difference on all sites after normalization; see above and Discussion). PAGE 57 57 Evaluation of the Behavior of the M mCSRS when T and R CI Profiles Differ From Each O ther on Multiple Deposition Sites Since the value of the MmCSRS, according to its computational form, is independent of the ordering of the deposition sites it was sufficient to systematically study rank ordered CI profiles (i.e., deposition sites were ordered according to their decreasing magnitude of normalized drug deposition). The CI profiles M1 M10 ( Figure 3 2 presented as rank ordered CI profile of different shapes) were used for assessment of the impact of changes on multiple deposition sites on the behavior of the MmCSRS. All of the ten CI profiles M1 M10 consisted of 8 deposition sites that could, for instance, represent the sites that are comprised in th e definition of the impactor sized mass (ISM) 3 for the Andersen CI ( see Discussion ). The mean vectors of CI profiles M1 10 were constructed as follows to cover a wide range of theoretically possible CI profiles (i.e., from a uniform to extremely skewed dis tribution) and to facilitate the understanding of the complex analysis related to multiple site changes. The deposition on all eight restrictions were made in order to m differences on multiple deposition sites between T and R CI profiles were introduced. First, for the R CI profiles, the deposition on one site was equal to that of at least one other site. Second, the T CI profiles were constructed by letting the deposition on four sites be higher than those of the R CI profile and the deposition on the other four sites be lower than those of the R CI profile, while pairing two sites with identical depositions. Table 3 1 gives the mean vectors of two specific T and R CI profiles for better 3 ISM is defined as the sum of the drug mass on all CI stages plus the filter, but excluding the initial stage because of its lack of a specified upper cutoff size limit (3). PAGE 58 58 illustration of this procedure. In order to facilitate interpretation of the result s, the variances of the CI profiles M1 M10 were constructed such that all eight CI sites had identical coefficients of variation (CVs). The effect of different inter site correlation structures on the behavior of the MmCSRS was studied by generating the CI profiles M1 M10 with (i.e., deposition on different sites are correlated with each other) and without (i.e., deposition on different sites are independent of each other) inter site correlation. In detail, the following procedure was applied to the CI profiles M1 M10 for constructing T and R CI profiles that differed from each other on multiple sites in their mean depositions and/or variability. First, the inter site correlation structure was selected between two possibilities. In particular, there was either no inter site correlation or the inter site correlation was based upon the covariance matrix (sites 4 11) that was used for the evaluation of the effect of single site changes on the MmCSRS (Table 3 3 ) 4 The same inter stage correlation struct ure was then applied to both T and R CI profiles. Second, the CVs were set on each of the eight deposition sites of the R CI profile to the same value of 10, 15, 20, 25, 30, 35, 40, 45, or 50%. These values were chosen as they could possibly cover a range of realistically observed CVs for CI profiles. It should be noted that the assumption of identical CVs on all deposition sites is not expected for real CI profiles but was mainly used here for systematic evaluation and understanding of the MmCSRS behavior ( see Discussion ). Third, the difference between the T and R CI profiles in their mean depositions was set to 5, 10, 15, 20, 25, or 30% on all eight sites 4 It must be noted that the purpose of this was rather to create some correlation between the deposition sites than to m odel realistic inter site correlation. PAGE 59 59 ( see above and Table 3 1 ). These values were chosen to cover a certain range of differences between CI profiles that could possibly be considered as equivalent. Fourth, t he standard deviations on the depositions site s of the T CI profile were adjusted such that their CVs were half as large, the same as, or double as large as those of the R CI profile. Hence, a total number of 3240 (10 2 9 6 3) scenarios were evaluated. For each of the 3240 scenarios, 20,000 s ets of 30 T and 30 R CI profiles were simulated and the average of the MmCSRS across the 20,000 sets was recorded. The scenarios were then grouped according to their inter stage correlation structure, the shape of the R profiles (i.e., M1 M10), and the d ifference in mean deposition between T and R CI profiles. For the 1080 scenarios for which T and R CI profiles had the same variability, the averages of the MmCSRS were then regressed against the respective squared inverse of the CV (SqInCV) separately for each of the groups ( see above ) to relate the change in MmCSRS to the variability of the R product. Subsequently, the estimated slopes and intercepts of the this regression analysis were numerically compared to the normalized squared difference (NSD, Eq. 3 4 ) between T and R CI profiles to explore the influence of the inter site correlation structure, the different shape of the CI profiles, and the difference in mean deposition on the MmCSRS. (3 4) PAGE 60 60 Results Evaluat ion of the Behavior of the MmCSRS when T and R CI Profiles differ from each other on a Single Site Single site mean difference T and R CI profiles with identical v ariability The behavior of the MmCSRS when T and R CI profiles differed from each other in their mean deposition on only a single site while both T and R CI profiles had the same variability is displayed in Figure 3 3 for all of 209 scenario s under consideration. Linear regression of the averages of the 20,000 MmCSRS against the NSDRS ( Eq. 3 3 ), as a measure of differences between two CI profiles after normalization ( see Introduction ), displayed a perfect linear relationship (coefficient of determination (R 2 ) > 0.999) between the MmCSRS and the NSDRS ( Figure 3 4 ). This relationship was expected from the computational form of the mCSRS giv en that the mCSRS is applied to normalized CI profiles. A more detailed explanation of this relationship is given in the Discussion. Single site mean difference T and R CI profiles with different v ariability The behavior of the MmCSRS when T and R CI pro files differed from each other in their mean deposition on a single site by 30% and had a different variability on all sites is shown in Figure 3 5 Th e results for a 10% difference in mean deposition between T and R CI profiles are provided as supplemental material (Figure 3 9 ). For all scenarios, the MmCSRS increased as the T/R variability ratio increased. However, for a constant T/R variability ratio, the MmCSRS was increased and decreased for a highly variable and less variable R product, respectively. Furthermore, a partial linear PAGE 61 61 relationship 5 between the MmCSRS and the T/R variability ratio was observed for a T/R variability ratio between 1/10 and 10. Evaluation of the Behavior of the MmCSRS when T and R CI Profiles Differ From Each O ther on Multiple Deposition Sites The behavior of the MmCSRS when T and R CI profiles differ from each on multiple sites in their mean deposition and/or variability is displayed in Figure 3 6 and Figure 3 7 for the CI profiles M2 (no inter site correlation) and M5 (with inter site correlation), respectively Plots for all ten CI profiles M1 M10 (with and without inter site correlation), which show similar behavior, are provided as supplemental material (Figure 3 10 Figure 3 27 ). For the scenarios where T and R CI profiles had the same variability, line ar regression of the average of the 20,000 MmCSRSs against the SqInCV separately for each group (grouping was based upon the inter site correlation structure, the shape of the R profiles (i.e., M1 M10), and the difference between T and R CI profiles; see above ) yielded a perfect linear relationship (R 2 > 0.999) ( Table 3 2 ). The estimated slope and intercept parameters from the simple linear regression analysis are given in Table 3 2 All estimated intercept parameters were between 0.8 and 1.3 and negatively correlated with the NSD ( Table 3 2 ; Figure 3 8 : top left panel; Pearson product moment correlation coefficient (r) = 0. 566). Furthermore, the estimated intercept parameters seem to be independent of the inter site correlation structure ( Figure 3 8 : top left and bottom left panel). The estimated slope parameters increased with increasing NSD 5 Further evaluation of the behavior of the MmCSRS for larger T/R variance ratios than 10 was performed and showed that the MmCSRS increased disproportionally with increasing T/R variance ratio. Specifically, the M mCSRS seemed to approach a certain maximum. However, since cases for which the variability of the T CI profile are more than 10 fold larger than that of the R CI profile are very unrealistic and, thus, were not considered in this article. PAGE 62 62 ( Table 3 2 ; Figure 3 8 : top right panel) while the two metrics were highly correlated with each other (r = 0.941). The estimated slope parameters of the scenarios with and without inter site correlation are linear functions of each other (R 2 = 0.97; Figure 3 8 : top right panel) Discussion In a previous publication ( 23 ) we introduced the MmCSRS and characterized its behavior when T and R profiles did not differ from each other. Under these conditions, the MmCSRS was found to be one, regardless of the shape and the number of deposition sites of the CI prof iles. This behavior was promising and indicated that the MmCSRS is a robust metric for APSD equivalence testing and potentially useful for determining whether T and R CI profiles are equivalent. As a next step, it was of interest to characterize the behavi or of the MmCSRS (e.g., the expected increase of the MmCSRS) under conditions where T and R CI profiles are not identical. This paper evaluated the behavior of the MmCSRS under such conditions using a systematic approach of increasing complexity. First, si mulations evaluated the behavior of MmCSRS when T and R CI profiles differed only on a single site, while the variability was identical; followed by simulations that also allowed differences in variability between T and R products. Subsequently, T and R CI profiles differed on multiple deposition sites from each other. However, the overall deposited mass on all sites under consideration was maintained constant (see above), as this would be the prerequisite for a T product before performing an APSD equivalen ce test based upon the MmCSRS. Such a prerequisite will be further discussed in a forthcoming article (Part III). Maintaining mass balance between T and R CI profiles was not possible for single site difference (see above). For the multiple site difference s PAGE 63 63 scenarios, T and R CI profiles either had the same or a different variability. Knowing the behavior of MmCSRS under such conditions was important, especially when the variability of the R product would affect MmCSRS. Under such conditions, a reference va riance scaling approach might have to be employed for establishing critical values for determining APSD equivalence of the T to R OIDP. Single Site Differences In this part of the study, a total number of 11 deposition sites (8 of which may be thought to be more relevant for pulmonary deposition, e.g., definition of ISM for Andersen CI) were incorporated to study the behavior of the MmCSRS over wider range of sites with a distinct difference in drug deposition across the investigated sites (deposition on n on ISM sites (e.g., pre separator) is generally higher). When T and R CI profiles differed from each other in their mean deposition on a single site, while variability associated with both profiles was identical, the MmCSRS increased as the difference betw een T and R CI profiles increased ( Figure 3 3 ). This was true for all sites, independent on what site showed the difference. However, this increase wa s not symmetric around 1 as, for example, a 70% increase or a 70% decrease in a specific site deposition resulted in different MmCSRS values. The extent of change in MmCSRS was also dependent on how much drug was deposited on a given site (Figure 3 3). As an example, a difference in mean deposition of 50% between T and R CI profiles would result in an MmCSRS of more than 15 for the high deposition site 1, compared to an MmCSRS of 1 if T and R were identical (Figure 3 3). If a 50% difference is observed for one of the low deposition stages (e.g., site 11; Figure 3 3), MmCSRS hardly ch anges at all (very close to 1). PAGE 64 64 Thus, the increase in MmCSRS is more pronounced when sites are involved that capture a larger amount of drug while changes on low deposition affe ct the MmCSRS less. This behavior, suggested from Figure 3 3, is more quantitatively expressed in Figure 3 4, which depicts a linear relationship between the MmCSRS and the NSDRS ( Eq. 3 3 a measure for differences in mean deposition between two CI profiles after normalization). This behavior is expected from Eq. 3 1 and was similarly observed for the originally proposed CSRS ( 12 ) It is generally believed that such a behavior is desirable for APSD equivalence testing as the smaller effect of low deposition sites (often related to non product factors, such as challen ges of the analytical procedure to quantify potential differences in the ng range) on the overall MmCSRS are expected to be much less relevant for BE of the T and R OIDPs. Contrary to univariate approaches such as the mCSRS, procedures employing a site by site analysis of cascade impactor data using standard BE test methodology for a given stage (e.g., proposed by EMA ( 9 27 ) ) do not possess this characteristic as they will even fail different batches of the same R OIDP, in part, due to the high variability (in terms o f CV%) associated with the low deposition sites. Furthermore, such methods face statistical challenges because of necessity of perform multiple comparisons. Overall, an equivalence test based upon the MmCSRS might have the potential to be more robust, as a bove factors have a smaller effect on MmCSRS (differences of low deposition stages) or are not applicable (challenges because of multiple comparisons). To further evaluate the behavior of the MmCSRS, differences in the mean deposition between the T and CI profiles were still limited to one site. However, T and R CI profiles were also allowed to differ in their variability. Therefore, the variability was PAGE 65 65 modulated on all deposition sites, which was believed as being more realistic than changing the variabili ty of a single site only. As expected from the simulations where T and R CI profiles had the same variability (Figure 3 3), the MmCSRS increased with increasing difference in mean deposition (compare Figure 5 for 30% difference with those observed for a 10 % difference in the supplemental material Figure 3 9 for the same deposition site). More importantly, MmCSRS was also sensitive to changes in the variability of the T product, as a higher T variability (i.e., an increased T/R ratio) resulted in an increase in MmCSRS (Figure 5). This increase was almost linear and seen for all deposition sites under consideration (site 1, 3, 7, and 11; see Figure 3 1 for shape of CI profile) ( Figure 3 5 ). These observed behaviors were expected from the computational form of the mCSRS ( Eq. 3 1 ), as the value of the cumulative numerator expression is driven by the overall difference in mean T and R deposition (the larger this difference, the larger the expression, (3 5) t he larger the MmCSRS; Figure 3 3). This expression is also affected by the degree of T variability (the larger T variability, the l arger the numerator expression, (3 6) the larger the MmCSRS). For both cases, the denominat or is not affected. Even though only differences between T and R CI profiles of 10% and 30% were evaluated, it seems reasonable to extrapolate these results to any difference between T and R CI profiles that is relevant in the context of equivalence testin g. Overall, the fact that PAGE 66 66 MmCSRS increases with increasing T/R variability ratio is desired as it penalizes and rewards the T product for having an increased and decreased variability, respectively. Figure 5 also indicates that MmCSRS depends on the variab ility of the R product (not only on the T/R ratio), as MmCSRS for a constant T/R ratio differs depending on 3 5). Whereas in previous simulations (differences in mean deposition and differences in T variability), MmCSRS behavior was driven by differences in the numerator, Eq. 3 1 readily suggests that the sensitivity of MmCSRS to differences in R variability is driven solely by the denominator expression, (3 7) This cumulative denominator expression is only capturing variability of in the R product (per definition there cannot be a difference in mean deposition between R products). The cumulative denominator term will increase with increasing R variabi lity and as consequence the MmCSRS will decrease. Reduced R variability will result in an increase in MmCSRS. Hence, the observed increase in MmCSRS with decreasing variability of the R product while the difference between T and R CI profiles and the T/R v ariability ratio were kept constant is a consequence of the computational form of the mCSRS. The implications of this behavior for equivalence testing of CI profiles are d iscussed below. Multiple Site Differences The analysis of the effect of differences b etween T and R CI profiles on multiple sites on the MmCSRS was restricted to eight sites because of the following reasons. The eight sites could possibly represent the sites that are comprised in the definition of PAGE 67 67 the ISM of an Andersen CI ( 13 ) A CI profile comparison test for establishing equivalence between T and R OIDPs would most likely be applied to those sites only since differences o n non ISM sites, which the MmCSRS would be sensitive to, are not very relevant for lung deposition, and could be detected by other means, for example, by testing the equivalence of the single actuation content and ISM before a MmCSRS based profile comparis on test is applied. In addition, we showed in the previous publication, that the MmCSRS behavior was not dependent on the number of stages included in the analysis of identical T and R profiles ( 23 ) We assumed within these simulations that the deposited mass on the eight deposition sites (ISM sites) was constant, a likely pre condition asked for within future APSD tests. It should be emphasized that only such conditions, insured th rough preliminary statistical tests, would allow truly testing for differences between two CI profiles in mean deposition and/or variance of sites that are considered more relevant for lung deposition. The effects of multiple site differences on the behav ior of the MmCSRS under these conditions were assessed for a variety of CI profiles (M1 M10, Figure 3 1 ) by changing mean deposition and variability without changing total cumulative deposition (i.e., T and R CI profiles had an identical total deposition on all eight sites; see above), as shown for two scenarios in Table 3 1 As expected, the MmCSRS increased with increasing differences in mean deposition ( Figure 3 6 and Figure 3 7 comparison of MmCSRS for a constant CV% across panels). This confirmed the results obtained for single site mean differences between two CI profiles ( see above ), but without the influence of differences in PAGE 68 68 cumulative deposition. Similarly, it could be seen from these simulations that for a given difference in mean deposition MmCSRS increases again with increasing variability of the T product ( see above ). These relationships were not surprising, but validated the expected behavior of the MmCSRS. In these simulations, we included situations that incorporated an inter site correlation (the characteristic of one site affecting the behavior of another site), as this impactor studies, and the behavior of the MmCSRS under those conditions warranted further evaluations. For any of the CI profiles M1 M10 and regardless of the inter site correlation structure, the MmCSRS increased as the variability (in terms of CV) of the R CI profiles decreased even for the situation where the T/R variability ratio was kept constant ( Figure 3 6 and Figure 3 7 ). This behavior of the MmCSRS for multiple site differences is similar to that for single site changes where the MmCSRS was increased for less variable R products in spite of a constant T/R variability rat io and was explained above. However, this dependency of the MmCSRS on the variability of the R product for a constant T/R variability ratio and a constant difference in mean deposition between T and R CI profiles, even for the situation where the cumulativ e deposited drug amount was constant, have the following significant implication. A rigid cut off value for an APSD equivalence test based upon a fixed MmCSRS is not feasible, and needs to be scaled by the variability of the R CI profile, in order to be ab le to consistently discriminate equivalent and inequivalent CI profiles (i.e., a certain difference (e.g., 20%) between T and R CI profiles on all of the deposition sites under consideration yields a different MmCSRS dependent on the variability of the R p roduct). PAGE 69 69 The relationship between MmCSRS and variability of the R product could be identified as straight line when plotting the MmCSRS against the SqInCV when T and R CI profiles had the same variability or the T product was less variable ( Figure 3 6 and Figure 3 7 ). However, this lin ear relationship could not be observed when the T product was more variable and the variability of both products became high ( Figure 3 6 and Figure 3 7 ). Since for construction of a APSD equivalence test the understanding of the behavior of the MmCSRS where T and R CI profiles have the same variabili ty is considered as most important, simple linear regression of the average of the 20,000 MmCSRSs against SqInCV separately for each CI profile M1 M10 and each difference between T and R CI profile in their mean depositions was performed only for those s cenarios, and yielded a perfect linear relationship (R 2 > 0.999) ( Table 3 2 ). The estimated intercept parameters seemed to be independent of the inter stage correlation structure and were close to one regardless of the NSD ( Eq. 3 4 a measure for the difference betw een T and R CI profiles in mean deposition) and the shape of the CI profiles (i.e., M1 M10) ( Table 3 2 and Figure 3 8 top left and bottom left panel). The estimated slope parameters increased as the NSD increased and were highly correlated (R 2 = 0.89) ( Figure 3 8 top right panel). Therefore, the estimated slope parameters represent a good measure for quantification of the differences between T and R CI profiles in their mean site depositions. Moreover, after scaling the slope parameters on their respective NSD, the scaled metrics (slope/NSD) were similar within a certain CI profile ( Table 3 2 ). On the other hand, there were still some differences in the scaled metrics between the 10 CI profiles PAGE 70 70 M1 M10 ( Table 3 2 ). These differences in the scaled metrics are a consequence of the fact that a certain difference in mean deposition does not result in the same NSD for different profiles (e.g., a 30% difference in mean deposition yielded an NSD of 112.5 and 153 for the CI profiles M1 and M10, respectively, Table 3 2 ) and result in a larger weighting of sites with an increased depositions. The positive implications of this characteristic for APSD equivalence testing were disc ussed above. In spite of being highly correlated (R 2 = 0.97), the estimated slope parameters were smaller for the cases without any inter site correlation compared to those with inter site correlation ( Table 3 2 and Figure 3 8 bottom left panel). Specifically, for a specific SqInCV of the R CI profile, the MmCSRS was decreased in average by 8.76 + 0.86 SqInCV for the zero inter site correlation case compared to that with inter site correlation. The implications and practical relevance of this for APSD equivalence testing need to be further eva luated by simulatio n studies. In summary, for multiple site differences, the observed differences in MmCSRS were dependent on the difference in mean deposition between T and R CI profiles, the T/R variability ratio, the variability of the R product, and the inter stage corre lation structure. For the 1080 scenarios where T and R CI profiles had the same variability, the differences in MmCSRS is a function of the NSD (as a measure for difference in mean deposition) and the SqInCV (as a measure of the variability of the R produc t) of the R CI profile. Since the value of the MmCSRS is perfectly correlated with the SqInCV of the R CI profile for any of the ten CI profiles M1 M10, the SqInCV of the R CI profiles appears to be a good choice as a metric for reference variance scalin g. A more PAGE 71 71 detailed analysis of the reference variance scaling approach will be given in a forthcoming article (Part III). It should be noted that all CI profiles were constructed such that the CV was the same on all deposition sites. However, the assumptio n of identical CVs on all deposition sites is not expected for real CI profiles. In fact, the variability (expressed as CV) is expected to be increased on low deposition sites compared to that for high deposition sites. However, setting the CVs to be equal on all eight deposition sites was necessary for being able to systematically evaluate and understand the behavior of the MmCSRS when T and R CI profiles differ from each other on multiple deposition sites while maintaining a manageable level of complexity The behavior of MmCSRS in situations where the CI profiles have an increased variability on low deposition sites warrants further analysis. Furthermore, simulation analysis is required to evaluate which metric is the best measure for the variability when the CI profiles have different CVs on the deposition sites. These will be addressed in the forthcoming article (Part III). All results are based upon the assumption that a sample of 30 T and R CI profiles is obtained, which is in accordance with the Jun e 1999 Draft Guidance for Industry: Bioavailability and Bioequivalence Studies for Nasal Aerosols and Nasal Sprays for Local A ction ( 10 ) It should be noted that the behavior of the MmCSRS has not been studied when a different sample size is obtained. However, since the expected s not expected that a different sample size would affect the conclusions here. The sample size will, of course, influence the width of confidence intervals for the MmCSRS and will be discussed in a f orthcoming article (Part III). PAGE 72 72 It should also be remarked that the application of the MmCSRS is not limited to the comparison of CI profiles and may potentially be applied to other multivariat e equivalence testing problems. Summary When T and R CI profiles differ from each other on a single or multiple depositio n sites, the MmCSRS increases as the magnitude of deposition on the site(s) on which the difference(s) occur(s) becomes larger. Thus, the MmCSRS gives a larger weight to differences on sites with increased deposition. This characteristic was considered as beneficial for APSD equivalence/profile comparison testing, as it should decrease the likelihood of failing identical products due to increased variability on low deposition sites (e.g., constructing univariate confidence intervals on each deposition site ( 9 27 ) ). Mos t importantly, it was demonstrated that a cut off (critical) value for APSD equivalence testing based on the MmCSRS needs to be scaled on variability of the R product for consistently being able to discriminate equivalent from inequivalent CI profiles. PAGE 73 73 Table 3 1 Illustration of multiple site change procedure for CI profiles M1 M10 as an example shown for the profiles M1 and M10 ( Figure 3 2 ). Profile/Stage 1 2 3 4 5 6 7 8 M1 R 12.5 12.5 12.5 12.5 12.5 12.5 12.5 12.5 M1 T 13.75 11.25 13.75 11.25 13.75 11.25 13.75 11.25 Difference 10% 10% 10% 10% 10% 10% 10% 10% M10 R 20 20 15 15 10 10 5 5 M10 T 24 16 18 12 12 8 6 4 Difference 20% 20% 20% 20% 20% 20% 20% 20% Entries for the reference (R) and test (T) product are the site depositions in mcg PAGE 74 74 Table 3 2 Results of the analysis of the effect of multiple site changes on the MmCSRS for the CI profiles M1 M10 ( Figure 3 2 ) No Inter Stage Corrleation Inter Stage Corre lation P Diff R 2 0 1 NSD 1 / NSD R 2 0 1 NSD 1 / NSD M1 5 0.9998 1.08 30.3 3.1 9.7 0.9999 1.09 42.5 3.125 13.6 M1 10 1 1.08 126.1 12.5 10.09 1 1.1 170.3 12.5 13.6 M1 15 0.9999 1.08 289.7 28.1 10.3 1 1.12 380.4 28.125 13.5 M1 20 1 1.09 519.5 50.0 10.39 1 1.14 673.3 50 13.5 M1 25 1 1.09 815.0 78.1 10.43 1 1.17 1046.1 78.125 13.4 M1 30 1 1.1 1177.1 112.5 10.46 1 1.22 1503.7 112.5 13.4 M2 5 0.9998 1.08 30.6 3.3 9.42 0.9999 1.09 42.4 3.25 13.1 M2 10 0.9999 1.08 127.7 13.0 9.82 1 1.1 169.5 13 13.0 M2 15 0.9999 1.08 291.8 29.3 9.98 1 1.11 378.4 29.25 12.9 M2 20 0.9999 1.08 524.4 52.0 10.08 0.9999 1.14 667.1 52 12.8 M2 25 1 1.09 824.8 81.3 10.15 1 1.17 1044 81.25 12.9 M2 30 1 1.1 1190.0 117.0 10.17 1 1.21 1496.9 117 12.8 M3 5 0.9995 1.09 32.2 4.3 7.58 0.9998 1.09 46 4.25 10.8 M3 10 0.9997 1.09 135.6 17.0 7.98 1 1.1 183.5 17 10.8 M3 15 0.9998 1.08 315.3 38.3 8.24 1 1.11 411.5 38.25 10.8 M3 20 0.9999 1.07 569.3 68.0 8.37 1 1.13 731.2 68 10.8 M3 25 0.9999 1.07 899.2 106.3 8.46 1 1.16 1141.7 106.25 10.8 M3 30 0.9999 1.07 1304.5 153.0 8.53 1 1.2 1642.5 153 10.7 M4 5 0.9991 1.1 37.8 8.5 4.43 0.9996 1.11 40.6 8.54 4.8 M4 10 0.9983 1.09 175.9 34.2 5.15 0.9993 1.09 182.1 34.16 5.3 M4 15 0.9984 1.04 436.2 76.9 5.68 0.9991 1.04 446.8 76.86 5.8 M4 20 0.9987 0.97 818.5 136.6 5.99 0.9994 0.99 827.3 136.64 6.1 M4 25 0.9992 0.91 1317.6 213.5 6.17 0.9996 0.95 1328.2 213.5 6.2 M4 30 0.9995 0.85 1935.3 307.4 6.29 0.9998 0.9 1944.9 307.44 6.3 M5 5 0.9988 1.09 32.4 4.6 7.1 0.9999 1.09 42.2 4.5625 9.3 M5 10 0.9996 1.08 138.5 18.3 7.59 1 1.09 171.6 18.25 9.4 M5 15 0.9998 1.08 321.5 41.1 7.83 1 1.1 387.8 41.0625 9.4 M5 20 0.9999 1.07 582.5 73.0 7.98 1 1.11 692.5 73 9.5 M5 25 0.9999 1.06 918.8 114.1 8.06 1 1.14 1081.7 114.0625 9.5 M5 30 0.9999 1.06 1331.2 164.3 8.1 1 1.17 1558.2 164.25 9.5 M6 5 0.9996 1.1 36.0 5.8 6.24 0.9999 1.1 58.4 5.77 10.1 M6 10 0.9996 1.09 154.7 23.1 6.7 1 1.11 236.3 23.08 10.2 M6 15 0.9996 1.07 361.9 51.9 6.97 1 1.11 537 51.93 10.3 M6 20 0.9998 1.05 661.4 92.3 7.16 1 1.12 957.7 92.32 10.4 M6 25 0.9999 1.02 1046.2 144.3 7.25 1 1.13 1496 144.25 10.4 M6 30 0.9999 1 1516.7 207.7 7.3 1 1.16 2156.8 207.72 10.4 PAGE 75 75 Table 3 2. Continued No Inter Stage Corrleation Inter Stage Correlation P Diff R 2 0 1 NSD 1 / NSD R 2 0 1 NSD 1 / NSD M7 5 0.9989 1.09 33.1 5.3 6.3 0.9997 1.1 39.8 5.25 7.6 M7 10 0.9995 1.09 141.9 21.0 6.76 0.9999 1.09 166.1 21 7.9 M7 15 0.9996 1.07 334.5 47.3 7.08 1 1.09 383.4 47.25 8.1 M7 20 0.9998 1.06 607.2 84.0 7.23 1 1.08 693.8 84 8.3 M7 25 0.9998 1.05 963.5 131.3 7.34 1 1.09 1089.7 131.25 8.3 M7 30 0.9999 1.04 1398.4 189.0 7.4 1 1.1 1579.5 189 8.4 M8 5 0.9994 1.1 35.1 6.7 5.23 0.9995 1.1 42.3 6.71 6.3 M8 10 0.9993 1.09 157.0 26.8 5.85 0.9998 1.09 181 26.84 6.7 M8 15 0.9994 1.06 374.2 60.4 6.2 0.9998 1.08 425.1 60.39 7.0 M8 20 0.9995 1.03 691.2 107.4 6.44 0.9998 1.06 775.1 107.36 7.2 M8 25 0.9997 1 1098.9 167.8 6.55 0.9999 1.05 1224.2 167.75 7.3 M8 30 0.9998 0.98 1603.8 241.6 6.64 1 1.05 1775.7 241.56 7.4 M9 5 0.9988 1.1 37.8 8.2 4.62 0.9997 1.11 40.8 8.19 5.0 M9 10 0.9987 1.09 171.6 32.8 5.24 0.9994 1.09 183.4 32.76 5.6 M9 15 0.9985 1.04 421.6 73.7 5.72 0.9993 1.05 442.8 73.71 6.0 M9 20 0.9991 0.99 786.0 131.0 6 0.9994 1.01 824 131.04 6.3 M9 25 0.9994 0.93 1267.1 204.8 6.19 0.9996 0.97 1314.8 204.75 6.4 M9 30 0.9996 0.88 1857.6 294.8 6.3 0.9998 0.93 1928.2 294.84 6.5 M10 5 0.9997 1.09 31.4 3.8 8.37 0.9999 1.09 42 3.75 11.2 M10 10 0.9999 1.09 131.1 15.0 8.74 1 1.1 166.4 15 11.1 M10 15 0.9999 1.08 302.3 33.8 8.96 1 1.11 374.3 33.75 11.1 M10 20 0.9999 1.08 545.4 60.0 9.09 1 1.13 664 60 11.1 M10 25 1 1.08 860.1 93.8 9.17 1 1.16 1035.6 93.75 11.1 M10 30 1 1.08 1243.7 135.0 9.21 1 1.19 1486.3 135 11.0 Scenarios with and without inter site correaltion are displayed for the 1080 cases for which T and R CI profiles had the same variability, the averages of the MmCSRS were regressed against the squared inverse of the coefficient of variation of the R product separately for each of the groups (defined by the CI profile M 1 M10 and the difference in mean deposition between T and R CI profiles) P: profile, Diff: percentage difference between test and reference CI profile on all stages, R 2 : coefficient of determination, 0 1 : estimated slop e parameter, NSD: normalized squared difference between test and reference CI profiles PAGE 76 76 Table 3 3 Covariance matrix of the CI profile that was used for evaluation of the effect of singe site changes on the MmCSRS (Figure 3 1 ) Site 1 2 3 4 5 6 7 8 9 10 11 1 21.01 1.60 7.11 4.47 0.43 7.47 7.47 2.01 0.46 0.40 0.48 2 1.60 29.17 4.04 5.80 1.24 14.83 8.30 1.79 0.23 0.13 0.12 3 7.11 4.04 9.09 6.54 0.54 1.51 4.08 2.80 0.47 0.27 0.36 4 4.47 5.80 6.54 5.68 0.36 1.30 1.50 2.28 0.29 0.15 0.21 5 0.43 1.24 0.54 0.36 0.98 2.23 2.31 0.27 0.03 0.03 0.08 6 7.47 14.83 1.51 1.30 2.23 47.32 37.86 1.72 0.24 0.17 0.05 7 7.47 8.30 4.08 1.50 2.31 37.86 38.21 2.05 0.30 0.13 0.01 8 2.01 1.79 2.80 2.28 0.27 1.72 2.05 2.50 0.23 0.17 0.18 9 0.46 0.23 0.47 0.29 0.03 0.24 0.30 0.23 0.10 0.05 0.06 10 0.40 0.13 0.27 0.15 0.03 0.17 0.13 0.17 0.05 0.07 0.05 11 0.48 0.12 0.36 0.21 0.08 0.05 0.01 0.18 0.06 0.05 0.09 Units are in mcg 2 PAGE 77 77 Figure 3 1 Reference CI profile that was used for the evaluation of the impact of differences between T and R CI profile on a single deposition site on the MmCSRS. For each of the 11 sites the mean and standard deviation (mg) of the deposition is displayed in the leg end. Total deposition across all stages is 366.55 mg PAGE 78 78 Figure 3 2 as rank ordered CI profiles profile (i.e., deposition sites were ordered according to their decreasing magnitude of normalized drug deposition) PAGE 79 79 Figure 3 3 Analysis of the behavior of the MmCSRS. T and R CI profiles differed from each other on a single stage in their mean deposition by a certain percentage (x axis). T and R CI profiles had identical covariance matrices. The effect of single site dif ference was evaluated on all eleven stages of the CI profile that is displayed in Figure 3 1 ; right panel is a magnification of the left panel PAGE 80 80 Figure 3 4 Analysis of behavior of MmCSRS for single site difference between T and R CI profiles with identical variability. Simple linear regression of average of MmCSRS (n = 20,000) vs. NSDRS was used for quantification of the difference betw een T and R CI profiles after normalization. RSQ: coefficient of determination PAGE 81 81 Figure 3 5 Analysis of the behavior of the MmCSRS (y axis: average of 20,000 replicates) when T and R CI profiles differed from each other in t heir mean deposition on a single site by 30% and in their variability on all sites by a factor of 0.1 through 10 (x axis); Site 1: high deposition site, Site 3: low deposition site, Site 7: medium deposition site, Site 11: very low deposition site, : high ly variable R product (variances increased by a factor of 5 compared to Table 3 3 ), : normally variable R product (variances identical to Table 3 3 ), +: less variable R product (variances decreased by a factor of 5 compared to Table 3 3 ) PAGE 82 82 Figure 3 6 Behavior of the MmCSRS (displayed as average of the 20,000 samples (y axis)) when T and R CI profiles differ from each other on multiple sites in their mean deposition and variability for CI profile M2 ( Figure 3 2 ) without inter site correlation, x axis: variability of the R CI profiles (displayed as the squared inverse of the coefficient of variation (CV%)), T and R CI profiles differed from each other by +/ 5, 10, 15, 20, 25, or 30% on all deposition sites such that the sites of T CI profiles was half of that of the R CI profiles, (+): the variability on the sites of T CI profiles was twice as large as that of the R CI profiles PAGE 83 83 Figure 3 7 Behavior of the MmCSRS (displayed as average of the 20,00 0 samples (y axis)) when T and R CI profiles differ from each other on multiple sites in their mean deposition and variability for CI profile M5 ( Figure 3 2 ) with int er site correlation, x axis: variability of the R CI profiles (displayed as the squared inverse of the coefficient of variation (CV%)), T and R CI profiles differed from each other by +/ 5, 10, 15, 20, 25, or 30% on all deposition sites such that the cumu the sites of T CI profiles was half of that of the R CI profiles, (+): the variability on the sites of T CI profiles was twice as large as that of the R CI profiles PAGE 84 84 Figure 3 8 Analysis of effect of differences between T and R CI profiles in mean deposition and/or variability on multiple sites for the scenarios where T and R CI profile had the same variability, top left panel: Estimated intercepts from simple linear regression o f MmCSRS against SqInCV on all deposition sites (y axis) plotted against the NSD between T and R CI profiles (x axis), top right panel: Estimated slopes from simple linear regression of MmCSRS against SqInCV on all deposition sites (y axis) plotted against the NSD between T and R CI profiles (x axis), bottom left panel: Estimated intercepts from simple linear regression of MmCSRS against SqInCV on all deposition sites for scenarios without inter site correlation (y axis) plotted against estimated intercepts from simple linear regression of MmCSRS against SqInCV on all deposition sites for scenarios with inter site correlation (x axis), bottom right panel: Estimated slopes from simple linear regression of MmCSRS against SqInCV on all deposition sites for scen arios without inter site correlation (y axis) plotted against estimated slopes from simple linear regression of MmCSRS against SqInCV on all deposition sites for scenarios with inter site correlation (x axis), r: correlation coefficient, b0: intercept, b1 : slope, RSQ: coefficient of determination PAGE 85 85 Figure 3 9 Analysis of the behavior of the MmCSRS (y axis: average of 20,000 replicates) when T and R CI profiles differed from each other in their mean deposition on a single site by 1 0% and in their variability on all sites by a factor of 0.1 through 10 (x axis); Site 1: high deposition site, Site 3: low deposition site, Site 7: medium deposition site, Site 11: very low deposition site, : highly variable R product (variances increased by a factor of 5 compared to Table 3 3 ), : normally variable R product (variances identical to Table 3 3 ), +: less variable R product (variances decreased by a factor of 5 compared to Table 3 3 ) PAGE 86 86 Figure 3 10 Beha vior of the MmCSRS (displayed as average of the 20,000 samples (y axis)) when T and R CI profiles differ from each other on multiple sites in their mean deposition a nd variability for CI profile M1 (Figure 3 2 ) without inter site correlation, x axis: varia bility of the R CI profiles (displayed as the squared inverse of the coefficient of variation (CV%)), T and R CI profiles differed from each other by +/ 5, 10, 15, 20, 25, or 30% on all deposition sites such that the cumulative total mass of all depositio the sites of T CI profiles was half of that of the R CI profiles, (+): the variability on the sites of T CI profiles was twice as larg e as that of the R CI profiles PAGE 87 87 Figure 3 11 Behavior of the MmCSRS (displayed as average of the 20,000 samples (y axis)) when T and R CI profiles differ from each other on multiple sites in their mean deposition a nd variability for CI profile M3 (Figure 3 2 ) without inter site correlation, x axis: variability of the R CI profiles (displayed as the squared inverse of the coefficient of variation (CV%)), T and R CI profiles differed from each other by +/ 5, 10, 15, 20, 25, or 30% on all deposition sites such that the sites of T CI profiles was half of that of the R CI profiles, (+): the variability on the sites of T CI profiles was twice as large as that of the R CI profiles PAGE 88 88 Figure 3 12 Behavior of the MmCSRS (displayed as average of the 20,000 samples (y axis)) when T and R CI profiles differ from each other on multiple sites in their mean deposition a nd variability for CI profile M4 (Figure 3 2 ) without inter site correlation, x axis: variability of the R CI profiles (displayed as the squared inverse of the coefficient of va riation (CV%)), T and R CI profiles differed from each other by +/ 5, 10, 15, 20, 25, or 30% on all deposition sites such that profiles had the same variability on all deposi the sites of T CI profiles was half of that of the R CI profiles, (+): the variability on the sites of T CI profiles was twice as large as that of the R CI profiles PAGE 89 89 Figure 3 13 Behavior of the MmCSRS (displayed as average of the 20,000 samples (y axis)) when T and R CI profiles differ from each other on multiple sites in their mean deposition a nd variability for CI profile M5 (Figure 3 2 ) without inter site correlation, x axis: variabili ty of the R CI profiles (displayed as the squared inverse of the coefficient of variation (CV%)), T and R CI profiles differed from each other by +/ 5, 10, 15, 20, 25, or 30% on all deposition sites such that the cumulative total mass of all deposition si the sites of T CI profiles was half of that of the R CI profiles, (+): the variability on the sites of T CI profiles was twice as large as that of the R CI profiles PAGE 90 90 Figure 3 14 Behavior of the MmCSRS (displayed as average of the 20,000 samples (y axis)) when T and R CI profiles differ from each other on multiple sites in their mean deposition a nd variability for CI profile M6 (Figure 3 2 ) without inter site correlation, x axis: variability of the R CI profiles (displayed as the squared inverse of the coefficient of variation (CV%)), T and R CI profiles differed from each other by +/ 5, 10, 15, 20, 25, or 30% on all deposition sites such that the sites of T CI profiles was half of that of the R CI profiles, (+): the variability on the sites of T CI profiles was twice as large as that of the R CI profiles PAGE 91 91 Figure 3 15 Behavior of the MmCSRS (displayed as average of the 20,000 samples (y axis)) when T and R CI profiles differ from each other on multiple sites in their mean deposition a nd variability for CI profile M7 (Figure 3 2 ) without inter site correlation, x axis: variability of the R CI profiles (displayed as the squared inverse of the coefficient of variation (CV%)), T and R CI profiles differed from each other by +/ 5, 10, 15, 20, 25, or 30% on all deposition sites such that the cumulative total mass of all deposition sites was identi the sites of T CI profiles was half of that of the R CI profiles, (+): the variability on the sites of T CI profiles was twice as large as that of the R CI profiles PAGE 92 92 Figure 3 16 Behavior of the MmCSRS (displayed as average of the 20,000 samples (y axis)) when T and R CI profiles differ from each other on multiple sites in their mean deposition a nd variability for CI profi le M8 (Figure 3 2 ) without inter site correlation, x axis: variability of the R CI profiles (displayed as the squared inverse of the coefficient of variation (CV%)), T and R CI profiles differed from each other by +/ 5, 10, 15, 20, 25, or 30% on all depos ition sites such that the sites of T CI profiles was half of that of the R CI profiles, (+): the variability on the sites of T CI profiles was twice as large as that of the R CI profiles PAGE 93 93 Figure 3 1 7 Behavior of the MmCSRS (displayed as average of the 20,000 samples (y axis)) when T and R CI profiles differ from each other on multiple sites in their mean deposition a nd variability for CI profile M9 (Figure 3 2 ) without inter site correlation, x axis: variability of the R CI profiles (displayed as the squared inverse of the coefficient of variation (CV%)), T and R CI profiles differed from each other by +/ 5, 10, 15, 20, 25, or 30% on all deposition sites such that the sites of T CI profiles was half of that of the R CI profiles, (+): the variability on the sites of T CI profiles was twice as large as that of the R CI profiles PAGE 94 94 Figure 3 18 Behavior of the MmCSRS (displayed as average of the 20,000 samples (y axis)) when T and R CI profiles differ from each other on mul tiple sites in their mean deposition a nd variability for CI profile M10 (Figure 3 2 ) without inter site correlation, x axis: variability of the R CI profiles (displayed as the squared inverse of the coefficient of variation (CV%)), T and R CI profiles diff ered from each other by +/ 5, 10, 15, 20, 25, or 30% on all deposition sites variability on the sites of T CI profiles was half of that of the R CI profiles, (+): the variability on the sites of T CI profiles was twice as large as that of the R CI profiles PAGE 95 95 Figure 3 19 Behavior of the MmCSRS (displayed as average of the 20,000 samples (y axis)) when T and R CI profiles differ from each other on multiple sites in their mean deposition and variability for CI profile M1 (Figure 3 2 ) with inter site correlation, x axis: variability of the R CI profiles (displayed as the s quared inverse of the coefficient of variation (CV%)), T and R CI profiles differed from each other by +/ 5, 10, 15, 20, 25, or 30% on all deposition sites such that profiles the sites of T CI profiles was half of that of the R CI profiles, (+): the variability on the sites of T CI profiles was twice as large as that of the R CI profiles PAGE 96 96 Figure 3 20 Behavior of the MmCSRS (displayed as average of the 20,000 samples (y axis)) when T and R CI profiles differ from each other on multiple sites in their mean deposition a nd variability for CI profile M2 (Figure 3 2 ) with inter site correlation, x axis: variability of the R CI profiles (displayed as the squared inverse of the coefficient of variation (CV%)), T and R CI profiles differed from each other by +/ 5, 10, 15, 20, 25, or 30% on all deposition sites such that the cumula the sites of T CI profiles was half of that of the R CI profiles, (+): the variability on the sites of T CI profiles was twice as large as that of the R CI profiles PAGE 97 97 Figure 3 21 Behavior of the MmCSRS (displayed as average of the 20,000 samples (y axis)) when T and R CI profiles differ from each other on multiple sites in their mean deposition a nd variability for CI profile M3 (Figure 3 2 ) with inter site correlation, x axis: variability of the R CI profiles (displayed as the squared inverse of the coefficient of variation (CV%)), T and R CI profiles differed from each other by +/ 5, 10, 15, 20, 25, or 30% on all deposition sites such that the cumulative total mass of all deposition sites was identic the sites of T CI profiles was half of that of the R CI profiles, (+): the variability on the sites of T CI profiles was twice as large as that of the R CI profiles PAGE 98 98 Figure 3 22 Behavior of the MmCSRS (displayed as average of the 20,000 samples (y axis)) when T and R CI profiles differ from each other on multiple sites in their mean deposition a nd variability for CI profil e M4 (Figure 3 2 ) with inter site correlation, x axis: variability of the R CI profiles (displayed as the squared inverse of the coefficient of variation (CV%)), T and R CI profiles differed from each other by +/ 5, 10, 15, 20, 25, or 30% on all depositio n sites such that the sites of T CI profiles was half of that of the R CI profiles, (+): the variability on the sites of T CI profiles was twice as large as that of the R CI profiles PAGE 99 99 Figure 3 23 Behavior of the MmCSRS (displayed as average of the 20,000 samples (y axis)) when T and R CI profiles differ from each other on multiple sites in their mean deposition a nd variability for CI profile M6 (Figure 3 2 ) with inter site correlation, x axis: variability of the R CI profiles (displayed as the squared inverse of the coefficient of variation (CV%)), T and R CI prof iles differed from each other by +/ 5, 10, 15, 20, 25, or 30% on all deposition sites such that y on the sites of T CI profiles was half of that of the R CI profiles, (+): the variability on the sites of T CI profiles was twice as large as that of the R CI profiles PAGE 100 100 Figure 3 24 Behavior of the MmCSRS (displayed as av erage of the 20,000 samples (y axis)) when T and R CI profiles differ from each other on multiple sites in their mean deposition a nd variability for CI profile M7 (Figure 3 2 ) with inter site correlation, x axis: variability of the R CI profiles (displayed as the squared inverse of the coefficient of variation (CV%)), T and R CI profiles differed from each other by +/ 5, 10, 15, 20, 25, or 30% on all deposition sites such that the sites of T CI profiles was half of that of the R CI profiles, (+): the variability on the sites of T CI profiles was twice as large as that of the R CI profiles PAGE 101 101 F igure 3 25 Behavior of the MmCSRS (displayed as average of the 20,000 samples (y axis)) when T and R CI profiles differ from each other on multiple sites in their mean deposition a nd variability for CI profile M8 (Figure 3 2 ) with inter site correlation, x axis: variability of the R CI profiles (displayed as the squared inverse of the coefficient of variation (CV%)), T and R CI profiles differed from each other by +/ 5, 10, 15, 20, 25, or 30% on all deposition sites such that the sites of T CI profiles was half of that of the R CI profiles, (+): the variability on th e sites of T CI profiles was twice as large as that of the R CI profiles PAGE 102 102 Figure 3 26 Behavior of the MmCSRS (displayed as average of the 20,000 samples (y axis)) when T and R CI profiles differ from each other on multiple sites in their mean deposition a nd variability for CI profile M9 (Figure 3 2 ) with inter site correlation, x axis: variability of the R CI profiles (displayed as the squared inverse of the coefficient of variation (CV%)), T and R CI profiles differed from each other by +/ 5, 10, 15, 20, 25, or 30% on all deposition sites such that the sites of T CI profiles was half of that of the R CI profiles, (+): the variability on the sites of T CI profiles was twice as large as that of the R CI profiles PAGE 103 103 Figure 3 27 Behavior of the MmCSRS (displayed as average of the 20,000 samples (y axis)) when T and R CI profiles differ from each other on multiple sites in their mean deposition a nd variability for CI profile M10 (Figure 3 2 ) with inter site correlation, x axis: variability of the R CI p rofiles (displayed as the squared inverse of the coefficient of variation (CV%)), T and R CI profiles differed from each other by +/ 5, 10, 15, 20, 25, or 30% on all deposition sites such that the cumulative total mass of all deposition sites was identica the sites of T CI profiles was half of that of the R CI profiles, (+): the variability on the sites of T CI profiles was twice as large as that of the R CI profiles PAGE 104 104 CHAPTER 4 AN AERODYNAMIC PARTICLE SIZE DISTRIBUTION EQUIVALENCE TESTING METHOD BASED UPON THE MEDIAN OF THE MODIFIED CHI SQUARE RATIO STATISTIC Introduction Demonstration of equivalence in aerodynamic particle size distribution (APSD) plays an important role for establishing bioequivalence (BE) of orally inhaled drug products (OIDPs) in both the US and Europe ( 7 9 ) E quivalence in APSD between a test (T) and reference (R) OIDP can be assessed by comparative analysis of multi stage cascade impactor (CI) (e.g., Andersen Cascad e Impactor (ACI) or Next Generation Impactor (NGI)) data. The modified chi square ratio statistic (mCSRS, Eq. 4 1) was introduced as a metric for APSD equivalence testing in the first part of this series of three articles ( 23 ) (4 1) where p represents the number of deposition sites, T ij and R ik represent the normalized deposition (i.e., by the dividing the absolut e deposition on the i th site by the total deposition on all sites under consideration) on the i th site of the j th n T ) of the T sample and on the i th site of the k th R ) of the R sample, respectively. n T and n R represent the number of samples that were obtained from the T and R product, respectively, and represents the sample mean on the i th site of all R profiles. Furthermore, the median of the distribution of 900 mCSRSs (MmCSRS; assuming a sa mple size of 30 T and 30 R products) was demonstrated to be equal to PAGE 105 105 one regardless of the shape and the number of deposition sites of the profiles when T and R products were identical. In the second part of this series, the behavior of the MmCSRS when T and R profiles differ from each other on a single or multiple deposition site(s) was characterized ( 28 ) The two major finding of this analysis were, first, that the MmCSRS is more sensitive to differences between T and R profiles that occur on high deposition sites and, second, that a cut off value for equivalence testing requires scaling on the variabil ity of the R product for consistently discriminating equivalent and inequivalent CI profiles. In this third part of the series, we propose an APSD equivalence test based upon the MmCSRS, develop an approach for constructing a cut off value for an MmCSRS b ased profile comparison test, propose a method for estimating a metric for reference variance scaling (RVS) for the MmCSRS, describe a method for constructing confidence intervals for the MmCSRS, and classify 55 CI profile scenarios, which were published a nd evaluated by an expert panel ( 13 15 ) as equivalent or inequivalent based upon the proposed APSD equivalence test. CI Profile Simulation Throughout this project, CI profiles were generated based upon Monte C arlo simulations assuming a multivariate normal distribution. Details about profile simulation and distributional considerations were provided in the second part of this series of publications ( 28 ) A ll computations were perform ed in the statistical software R ( 18 ) normal distribution ( 26 ) PAGE 106 106 APSD Equivalence Test A flowchart describing the proposed APSD equivalence test is displayed in Figure 4 1 The unde rlying principle of the test is the following. First, a CI profile comparison test (e.g., application of the MmCSRS) should be applied to deposition sites that are relevant for lung deposition (e.g., deposition sites that are comprised in the definitions o f the impactor sized mass 1 (ISM) 2 Second, other statistical tests can ensure the equivalence of particle fractions that are deposited in other impactor parts (e.g., particles that are predominantly deposited in parts that correspond to deposition in the o ropharynx). In detail, two OIDPs that do not emit an equivalent dose (i.e., single actuation content) should not be considered as equivalent and, hence, comparative CI profile testing is not necessary (first step) 3 Two OIDPs that emit an equivalent dose b ut do not deposit an equivalent dose in the lung should not be considered as equivalent and, thus, comparative CI profile testing is again not necessary (second step). Finally, for two OIDPs that emit an equivalent dose and deposit an equivalent dose in th e lung, a CI profile comparison test (e.g., MmCSRS) could be applied to deposition sites that are relevant for lung deposition (see above; third step). In summary, this stepwise APSD equivalence test ensures that two OIDPs only pass if they emit an equival ent dose, deposit an equivalent dose in the lung (thus deposit an equivalent dose in the oropharynx), and have an equivalent CI profile with respect to their lung deposition. A population BE test ( 29 ) may be the preferred statistica l method for steps one and two. 1 ISM is defined as the sum of the drug mass on all CI stages plus the filter, but excluding the initial stage because of its lack of a specified upper cutoff size limit 2 Deposition sites are comprised in the definition of the fine particle mass could be used alternatively 3 The first step may be omitted for products with negligible oral bioavailability PAGE 107 10 7 Construction of a Cut Off Value for an MmCSRS based Profile Comparison Test Definition A cut off value for an MmCSRS based profile comparison test translates a difference between T and R profiles (e.g., a +/ 20% difference on all ISM sites) that is considered as tolerable for being equivalent into a numerical value for the MmCSRS Thus, two OIDPs are considered as equivalent when a confidence interval constructed based upon a sample of T and R products is smaller than the cut off value. It should be remarked that a tolerable difference for equivalence of CI pro files has yet to be determined. Principles The following construction of a cut off value is based upon eight deposition sites, which would represent the ISM sites of the ACI setup. This is in accordance with the proposed APSD equivalence test that specifies application of a p rofile comparison to sites that are relevant for lung deposition (see above). It should be remarked that the ISM comprises seven sites for the NGI setup. Implications of this reduced number of deposition sites are debated below (see Discussion). The follow ing characteristics of the MmCSRS require consideration when constructing a cut off value for an MmCSRS based profile comparison test. First, the MmCSRS puts a larger weight on differences between T and R that occur on high deposition sites ( 28 ) Thus, a certain difference between T and R profiles (e.g., +/ 20% on all deposition sites) would result in a smaller MmCSRS for a uniform R profile (i.e., depositions are equal on all sites) than the same difference for a skewed R profile. This characteristic could theoretically be addressed by three approaches; constructing a cut off value (a) based upon a unifo rm R profile that would result in PAGE 108 108 criteria that are most difficult to pass, (b) based upon the actual shape of the respective R profile, or (c) based upon a R profile that represents a typical CI profile. Since visual analysis of real CI profiles from diff erent inhalation products (dry powder inhalers, metered dose inhalers, and inhalation suspensions) after ordering them by decreasing magnitude of their normalized deposition on the ISM sites displays a certain similarity across the products ( Figure 4 2 ), approach (c) was selected for defining a cut off value for the MmCSRS (see below). Second, T and R profiles should have an equivalent, ideally identical, ISM (second s tep of APSD equivalence test; Figure 4 1 ). Hence, T and R profiles that are employed for defining a cut off value for the MmCSRS should have an identical ISM. Third, since the MmCSRS rewards and punishes the T product for having a decreased and increased variability, respectively, a cut off value for the MmCSRS needs to be defined for T and R profiles with the same variability. Fourth, it was previously demonst rated that for a certain difference between T and R profiles the MmCSRS is inversely proportional to the squared coefficient of variation (CV) of the R product ( 28 ) Thus, a cut off value for the MmCSRS requires scaling on the variability of the R product. Fifth, even though CI profiles are very likely to have different CVs on all deposition sites, RVS s hould be based upon a single metric for maintaining a reasonable level of complexity. Thus, a cut off value for the MmCSRS will be based on CI profiles with identical CVs on all sites and a method for estimating a single metric for RVS is presented below. PAGE 109 109 Sixth, it was previously shown that the inter site correlation structure (i.e., deposition on a site is affected by the deposition on another site) influences the behavior of the MmCSRS when T and R profiles differ from each other ( 28 ) However, there was evidence that the MmCSRS tends to be smaller when no inter site correlation structure (i.e., depositi on on a site is not affected by the deposition on another site) is present ( 28 ) Hence, a cut off val ue based upon T and R profiles without inter site correlation would result in a criterion that is most difficult to pass. Seventh, a cut off value for the MmCSRS needs to be defined for several differences between T and R CI profiles as it has not been de cided which difference between T and R profiles would still be considered as equivalent and different criteria might be proposed by different drug regulation agencies. The relevance of a potential impact of these seven characteristics on the consistency o f APSD equivalence testing is discussed below (see Discussion). Methods A typical CI profile (after ordering the sites by decreasing magnitude of their normalized deposition) was constructed by averaging the normalized deposition (separately for each site) for all CI profiles that are displayed in Figure 4 2 This typical CI profile is shown in Figure 4 3 constructing an R CI profile for deriving a cut off value for the MmCSRS. This R profile was designed such that T and R profiles that differ from each other by a certain percentage on each site (e.g., +/ 20%) and have the same ISM could be easily ( Figure 4 3 ) were paired and their depositions averaged. The CI profile that resulted from this procedure is displayed in Figure 4 3 e PAGE 110 110 was then used as mean vector for simulating R profiles. The mean vectors for the T profiles were constructed by letting the deposition on four sites be higher than those of the R profile and the deposition on the other four sites be lower than those of t he R profile, while pairing the two sites of the R profile with identical depositions. F or better illustration of this procedure, Table 4 1 gives the mean vectors of the T and R profiles that were used for evaluating 10% differences. The behavior of the Mm CSRS for T and R profiles that differed from each other in their mean deposition by 10, 15, 20, 25, or 30% were investigated. These values were chosen to cover a certain range of differences between CI profiles that could possibly be considered as equivale nt. The variability of the R CI profiles was assigned by setting the CV of all sites to 2.5, 5, 10, 1 5, 20, 25, 30, 35, 40, or 45 %. It should be remarked that the selection of the numbers is not relevant for setting up a cut off as it was previously shown that the MmCSRS is perfectly correlated to the squared inverse of the CV (SqInCV) ( 28 ) The variability of the T profiles was assigned by adjusting the standard deviations on the depositions sites such that their CVs were the same as those of the R profile s. For both T and R profiles, no inter site correlation was assumed (see above). Hence, a total number of 50 (5*10) scenarios were evaluated for defining a cut off value for an MmCSRS based profile comparison test. For each scenario, 20,000 sets of 30 T and 30 R profiles were simulated and, subsequently, the MmCSRS calculated. For each of the five studied differences between T and R profiles, the averages of the 20,000 MmCSRSs were then regressed against the respective SqInCVs. PAGE 111 111 Resul ts and Interpretation The estimated intercept and slope parameters and the coefficients of determinations when regressing the averages of the 20,000 MmCSRSs against the respective SqInCVs separately for each of the five studied differences between T and R CI profiles are shown in Table 4 2 As expected from previous evaluations ( 28 ) a perfect linear relationship (R 2 > 0.999), an estimated intercept close to one, and an increasing slope with increasing difference between T and R CI profile was observed ( Table 4 2 ). Those intercept and slope parameters were then used to create the so off value for an MmCSRS based profil e comparison test ( Figure 4 4 ). Figure 4 4 contains a hypothetical confidence interval for the MmCSRS of a sample of T and R profiles for illustration of how to use the cut off value plot. Figure 4 4 shows that RVS was determined to be 7.5 (CV%; see below for details) and that a 90% confidence interval for the MmCSRS (see below for details) yielded lower and upper bounds of 3 and 12, respectively. If a 10% or 15% criterion was applied, the two produc ts would fail to show BE as the respective cut off values of 4.11 or 8.00 (calculated using the slope and intercept parameters from Table 4 2 and 7.5 2 for RVS), are s maller than the upper bound of the confidence interval (i.e., 12). On the other hand, if a 20, 25, or 30% criterion were applied, the two products would show BE as the respective cut off values of 13.4, 20.5, or 29.1 would be larger than the upper bound of the confidence interval. A Method for Estimating a Single Metric for Reference Variance Scaling The method for the determining a cut off value for an MmCSRS based profile comparison test (i.e., cut off value plot; Figure 4 4 ) was based upon the assumption that the variability in terms of CV is identical on all deposition sites. However, this PAGE 112 112 assumption is not realistic for real CI profiles. Hence, it is necessary to find a metric that can reduce the variability information on all ISM deposition sites of the R product and estimate the variability of the R product as a single metric. We propose the following approach for estimating a single metric for RVS. Determine th e four ISM sites with the highest deposition (after normalization) and calculate their CVs. Then, calculate the average across the four CVs and use this metric for RVS. This approach is based on the observation that the CV is often higher for low depositio n sites and we, thus, believe that variability estimation should be based on sites with a larger deposition. It is apparent that this approach comprising reduction of variability on multiple sites into a single metric and not considering low deposition sit es leaves some room for interpretation. However, it will be demonstrated below that 55 CI profile scenarios can be classified according to the opinion of the expert panel, when using this RVS metric. Furthermore, possible shortcomings of this RVS metric wi ll be discussed below (see Discussion). A Method for Constructing a Confidence Interval for the MmCSRS Even though it was demonstrated that the mCSRS follows approximately an F distribution when certain criteria are met and T and R CI profiles are identic al ( 23 ) the distributional behavior of the MmCSRS is unknown. Hence, it seems reasonable to use a non parametric method for constructing confidence intervals for the MmCSRS. We prop ose here to construct two sided non parametric confidence intervals using the bias corrected and accelerated (BCA) bootstrapping method ( 29 ) A brief discussion on the suitability of two sided confidence intervals vs. one sided confi dence intervals is given below. PAGE 113 113 Evaluation of the APSD Equivalence Test C lassification of 55 PQRI Scenarios rticle Size Distribution published 55 scenarios, comprising 30 T and 30 R CI profiles, and classified them as equivalent or inequivalent ( 13 15 ) The PQRI WG used those 55 scenarios for evaluating the original CSRS ( 10 15 ) As a result, the PQRI WG concluded that the original CSRS could not consistently discriminate between equivalent and inequivalent CI profiles ( 12 13 ) We applied the proposed APSD equivalence test (see above; Figure 4 1 ) to those 55 scenarios to assess whether the test could classify the scenarios according to the opinion of the PQRI WG. Methods The means and the standard deviations of the depositi on (in mcg) on all sites of both the T and R products were publicly available for the 55 scenarios ( 14 15 ) Those means and standard deviations were used as population means and population stand ard deviations for profile simulation, respectively. Since information on the inter site correlation was not readily available, profile simulation was performed under the assumption of no inter site correlation. The implications of this assumption are di sc ussed below (see Discussion). For each of the 55 scenarios, 20,000 independent sets of 30 T and 30 R profiles were simulated and, subsequently, the proposed APSD equivalence test method ( Figure 4 1 ; see above) applied. A population bioequivalence (PBE) ( 29 ) test was performed at the first and second steps of the APSD equivalence test. The total mass on all deposition sites was used as a surrogate for single actuation content at the first step of the APSD test. The deposition sites 6 13, 4 11, and 3 10 were de fined as ISM PAGE 114 114 sites for scenarios 1 44, 45 51, and 52 55, respectively. This selection corresponds to the definition of the ISM for an ACI setup. For scenarios 52 55, the APSD equivalence test was also applied when defining deposition sites 4 10 as ISM, whi ch corresponds to the ISM definition for an NGI setup. A two sided 90% BCA confidence interval for the MmCSRS (see above and Appendix) was constructed at step 3. The results of the APSD equivalence test (i.e., fail/pass at steps 1 and 2, the upper and lowe r bounds of the confidence intervals and the RVS metric (see above) at step 3) were recorded and compared to the classification of the PQRI WG ( 13 ) For evaluating the performance of the APSD test, the results were simplified as follows. A pass for the PQRI WG was assigned when >50% of the members classified a scenario as equivalent. A pass for the first and seconds step s of the APSD equivalence test was assigned when in >50% of 20,000 simulations the total mass PBE test and ISM PBE test resulted in a pass, respectively. A pass for the third step of the APSD equivalence test was assigned when the upper bound of the 90% BC A bootstrap confidence intervals was below a cut off value. It should be remarked that the results of the third step were evaluated for different cut off criteria since a cut off criterion for the MmCSRS has not been determined (see above). In order to pro vide a method for classifying the PQRI scenarios as objectively as possible and to evaluate a possible discrepancy between in the PQRI WG and APSD equivalence test classifications, the average ISM ratio (T/R) and the normalized mean ISM profiles (T and R) were obtained ( Figure 4 6 for scenarios 1 4; scenarios 5 55 are prov ided as supplemental material). Results The results of the classification of the 55 PQRI scenarios based upon the proposed APSD equivalence test are summarized in Table 4 3 and visually displayed in PAGE 115 115 Figure 4 5 63.3, 72.7, 67.3, 69.1, and 69.1% of the 55 PQRI scenarios were classified according to the opinion of the PQRI WG for cut off values of 10, 15, 20, 25, and 30%, respectively ( Table 4 3 and Table 4 4 ). For a 15% cut off value, Table 4 4 compares the results (pass or fail) of the APSD equivalence test to those of the PQRI WG classification. The scenarios for which the classification of the APSD equivalen ce test did not match that of t he PQRI WG are discussed below. Discussion When a cut off value of 15% for CI profile comparison testing is applied, the APSD equivalence test (see above; Figure 4 1 ) matched 40 of the 55 PQRI scenarios (72.7%) according to the PQRI WG evaluation ( Table 4 4 ). The classification of the low variability scenarios 39, 40, and 42 44 ( Table 4 3 ) as equivalent despite their increased MmCSRS shows nicely the importance of the RVS ( Figure 4 5 right panel). RVS was not performed when the PQRI WG evaluated the original CSRS. In fact, a constant cut off value was applied ( 13 ) For the 15 scenarios where the APSD equivalence test and PQRI WG classifications did not match ( Table 4 4 ), a detailed analysis of this discrepancy is given below using the normalized mean ISM profiles (see above; Figure 4 6 ; supplemental material). In summary, one of three possible reasons (i.e., misclassification by PQRI WG, negative characteristics of PBE test, borderline cases for which the classifications depends on the cut off value that is applied for comparative CI prof ile comparison testing) could be ident ified for all those scenarios. Scenarios for which classification did not match (PQRI: Pass, APSD: Fail) Scenarios 1, 2, 14, 25, 45, 46, and 55 were classified as equivalent by >50% of the PQRI WG despite having an ISM difference of >10% ( Table 4 3 ; Figure 4 6 ; Supplemental Material). For all of those scenarios, the second step of the APSD PAGE 116 116 equivalence test (PBE test for equivalent ISM) was passed in <50% of the cases ( Table 4 3 ). Thus, the APSD equivalence test resulted correctly in a fail for those scenarios as T and R products differ in their ISM by >10%. Scenarios 10, 13, and 17 were classified as equivalent by >50% of the PQRI WG but were classified as inequivalent by the third step (MmCSRS) of the APSD test (for a 15% cut off value). Visual assessment of the normalized mean ISM profiles (Supplemental Material) for those scenarios suggests a certain difference between the two products that was categorized by the MmCSRS (point estimate) as a 25% difference for scenarios 10 and 13 ( Table 4 3 ; Figure 4 5 ) and a 30% difference for scenario 17 ( Table 4 3 ; Figure 4 5 ). Those three scenarios are likely border line cases for which the classification (i.e., equivalent or inequivalent) is dependent on the difference criterion that is applied for comparative CI profile comparison testing. Scenarios 5, 20, and 21 were classified as equivalent by >50% of the PQRI WG ( Table 4 3 ). This classification is supported by visual assessment of normalized mean ISM profiles (Supplemental Material). Those scenarios were classified as inequiv alent by the third step (MmCSRS) of the APSD test (for a 15% cut off value; Table 4 3 ; Figure 4 5 ). For all three scenarios, the point estimates for the MmCSRS suggest a 15% difference between the two products ( Table 4 3 ; Figure 4 5 ). Those scenarios would pass the APSD equivalent test ( Table 4 3 ; Figure 4 5 ) for a 25% cut off value. The discrepancy in the classification between PQRI WG and APSD equivalence test may indicate that a 15% cut off value would be too conservative or that a larger sample size, which would results in narrower conf idence intervals, is required. Scenarios for which classification did not match (PQRI: Fail, APSD: Pass) Scenario 26 was classified by < =50% of the PQRI WG as equivalent but received a pass based upon the APSD equivalence test. Visual assessment of the normalized PAGE 117 117 ISM profiles (mean deposition) indicates only small differences in mean deposition. The MmCSRS characterizes the difference betw een T and R ISM profiles correctly as small (10% point estimate). However, T and R products differ by 12% in their ISM (mean) while having an average CV% of 37.2 and 42.7, respectively. In spite of this mean difference, the PBE test for ISM was passed in 6 5.5% of the cases. Hence, the discrepancy between the apparently correct classification by the PQRI WG (i.e., products that differ by >10% in their ISM are inequivalent) and that of the APSD equivalence test seems to be a negative characteristic of the PBE test (i.e. rewarding a less variable T product disguises mean differences). Scenario 32 is a borderline case for which the classification depends highly on the cut off value that is applied for comparative CI profile comparison testing. This scenario was a split decision among the PQRI WG members and application of the MmCSRS resulted in an estimated difference of 10% (point estimate) between the ISM profiles. Discussion The proposed APSD equivalence test based upon the MmCSRS ( Figure 4 1 ) could classify approximately 70% of the 55 CI profile scenarios ( 13 15 ) according to the opinion of the PQRI WG ( Figure 4 4 Table 4 3 and Table 4 4 ). A reasonable explanation could be provided for those scenarios for which the classification of the APSD equivalence test did not match that of the PQRI WG (see above). Thus, the APSD equivalence test based upon the MmCSRS seems t o be suitable to consistently categorize CI profiles as equivalent of inequivalent. Hence, the major objective of the overall project was achieved ( 23 28 ) The main reasons for successfully classifying the 55 PQRI CI profile scenarios were, first, apply ing of the MmCSRS to a reduced number of deposition sites (i.e., ISM sites) and, second, recognizing the necessity of scale a cut PAGE 118 118 off value for the MmCSRS by the variability of the R product (see above). When the original CSRS was used for classification o f the 55 CI profile scenarios, it was applied to all deposition sites and RVS was not performed ( 12 13 ) In fact, when applying the original CSRS to the ISM sites in combination with RVS, a similar high agreement with the PQRI WG clas sification can be reached as for the MmCSRS statistic (results are not shown). However, the improved characteristic of the MmCSRS when T and R products are identical (i.e., returning a value of one regardless of the shape and number of deposition sites of the CI profile ( 23 ) ) warrants the superiority of the MmCSRS. The proposed APSD equivalence test ( Figure 4 1 ) consist of three steps that should ensure that the two products emit an equivalent dose (first step), deposit an equivalent dose in the lung (second step), and have an equivalent regional lung deposition pattern (third step). However, it could be discussed whether the first step is necessary for drugs that do not have any significant oral bioavailability. On the other hand, a test for equivalent single actuation content (first step) may be required in a series of comparative in vitro tests anyway and this discussion would be redundant. When the cut off value plot that was used for classification of the 55 PQRI CI profile scenarios was constructed ( Figure 4 4 ), certain assumptions and simplifications were made that require further discussion and analysis (see above). First, the respective regulatory agencies need to set a cut off value for comparative CI profile comparison testing. Application of the pr oposed APSD equivalence test to different batches of R products and, subsequently, determining a value for which e.g., the tests results in an equivalent classification in 90% of the cases PAGE 119 119 could be an option. Furthermore, it may be debatable whether differ ent cut off values could be applied for different OIDPs. Second, the cut off lines are constructed on the basis of the average rank ordered profile (by decreasing magnitude of the normalized deposition on the ISM sites) that is displayed in Figure 4 3 and the assumptions of equal variability (in terms of CV%) on all ISM sites and no correlation between the deposition sites. Each of the three assumptions will influence the intercepts and slopes of the cut off lines and, therefore, possibly the result (i.e., pass or fail) of the equivalence test. The application of the average CI profile (see above; Figure 4 3 ) for construction of the cut off value lines seems to be justified by the fact that rank ordered (by decreasing magnitude of their normalized deposition) ISM profiles do not vary much across different impactor setups. Hence, a similar cut off value would result for different impactor setups. Constructing the cut off values lines based upon a uniform R profile (i.e., identical deposition on all ISM sites) would be the most conservative alternative as it would result in the least steep slopes ( 28 ) and, hence, the most difficult criteria to pass. On the other hand, if a cut off va lue for comparative CI profile testing would be based upon the performance of different batches of the same R product (see above), the smaller cut off value for a uniform R profile would be counteracted by a larger criterion (in % difference between two pr ofiles). A similar discussion is true for the assuming no inter site correlation when constructing the cut off value lines. It was previously demonstrated that the MmCSRS is smaller when no inter site correlation is assumed and, thus, constructing the cut off values when assuming no inter site correlation structure results in a criterion that is more difficult to pass ( 28 ) However, it should be remarked that only one particular inter PAGE 120 120 site correlation structure was tested and, hence, further simulation analysis is required to fully evaluate the effect of different inter site correlation structures. Assumin g equal variability (in terms of CV%) on all deposition sites for constructing the critical value plot was necessary to maintain a manageable level of complexity even though it is not realistic for real impactor data. As a consequence of this, a single met ric that provides a reasonable estimate for the variability of the R product over all deposition sites needs to be defined for RVS. We have introduced the mean CV% over the four ISM sites with the largest deposition as such a single metric for RVS (see abo ve) and used it for classification of the 55 PQRI scenarios. The fact that using the mean CV% over the four ISM sites with largest deposition helped classify the 55 PQRI scenarios according to the opinion of the PQRI WG supports this approach for RVS but s hould not be considered as validation of it. The current selection for RVS definitely puts even larger weight on the high deposition sites (among the ISM sites) than it is already done by the characteristic of the MmCSRS. Nonetheless, further simulation an alysis using other approaches for RVS should be performed before making a final selection for the best single metric for RVS. Third, two sided confidence intervals for the MmCSRS were constructed (see Appendix) when classifying the 55 PQRI scenarios using the APSD equivalence test. However, since the MmCSRS cannot be negative, it may be worthwhile discussing the construction of one sided confidence intervals for the MmCSRS for increasing the power to conclude BE. Conclusions In the proposed APSD equivalenc e test the MmCSRS is applied to deposition sites that are relevant for lung deposition (e.g., sites that are comprised in the definition PAGE 121 121 of ISM) and other tests ensure equivalence in emitted dose and dose that is deposited in the lung. The proposed APSD eq uivalence test and scaling cut off values for the MmCSRS by the variability of the R product could classify most of the 55 CI profile scenarios according to the opinion of the PQRI WG. Thus, the proposed APSD equivalence test based upon the MmCSRS seems to be a very promising approach for consistently discriminating equivalent from inequivalent CI profiles. However, further simulation analysis is necessary to fully understand the effects of RVS and inter site correlation structure on constructing cut off va lues for t he MmCSRS. PAGE 122 122 Table 4 1 Illustration of construction of test (T) and reference (R) CI profiles for deriving a cut off value for the MmCSRS Profile/ Site 1 2 3 4 5 6 7 8 R 33.1 33.1 12.2 12.2 3.61 3.61 0.974 0.974 T 36.4 29.8 13.4 11. 0 3.97 3.25 1.071 0.877 T and R CI profiles differ by +/ 10% on all deposition sites; deposition in mcg; R CI profile is displayed in Figure 4 3 Table 4 2 Estimated intercept and slope parameters and coefficients of determination (R 2 ) when regressing the MmCSRS against the squared inverse o f the coefficients of variation Difference T/R Intercept Slope R 2 10% 1.019 173.6 > 0.999 15% 0.968 395.3 > 0.999 20% 0.923 704.1 > 0.999 25% 0.896 1102.3 > 0.999 30% 0.886 1586.7 > 0.999 Difference T/R: Differences between T and R profiles; R profile is displayed in Figure 4 3 PAGE 123 123 Table 4 3 Results of application of APSD equivalence test to 55 PQRI scenarios # PQRI WG Total Mass PBE ISM PBE RVS PE LB UB C 10 C 15 C 20 C 25 C 30 1 100 73.3 3.5 28.85 1.71 1.2 2.19 1.23 1.44 1.77 2.22 2.79 2 79 81.5 5.8 34.39 1.5 1.03 1.95 1.17 1.3 1.52 1.83 2.23 3 7 81.4 0.3 31.14 1.18 0.82 1.5 1.2 1.38 1.65 2.03 2.52 4 0 46.4 0.0 32.7 1.67 1.15 2.19 1.18 1.34 1.58 1.93 2.37 5 100 76.2 65.3 30.84 1.33 0.92 1.7 1.2 1.38 1.66 2.05 2.55 6 79 92.9 64.6 38.73 0.82 0.55 1.05 1.13 1.23 1.39 1.63 1.94 7 36 74.6 1.9 37.66 0.86 0.59 1.09 1.14 1.25 1.42 1.67 2 8 0 22.0 0.0 29.77 1.71 1.18 2.22 1.21 1.41 1.72 2.14 2.68 9 0 41.8 0.0 33.65 1.65 1.15 2.12 1.17 1.32 1.54 1.87 2.29 10 79 83.5 85.2 37.58 1.47 1.02 1.91 1.14 1.25 1.42 1.68 2.01 11 50 87.1 78.2 33.36 2.95 2.05 3.92 1.17 1.32 1.56 1.89 2.31 12 21 93.8 89.6 36.92 2.93 1.95 4.04 1.15 1.26 1.44 1.7 2.05 13 71 88.2 83.6 32.71 1.74 1.2 2.26 1.18 1.34 1.58 1.93 2.37 14 64 53.7 33.5 33.51 2.1 1.45 2.77 1.17 1.32 1.55 1.88 2.3 15 50 63.3 48.3 31.47 2.58 1.81 3.38 1.19 1.37 1.63 2.01 2.49 16 29 94.1 96.7 39.64 1.98 1.34 2.67 1.13 1.22 1.37 1.6 1.9 17 64 83.6 76.7 31.68 2.16 1.48 2.87 1.19 1.36 1.62 1.99 2.47 18 29 96.0 76.8 37.57 2.1 1.46 2.77 1.14 1.25 1.42 1.68 2.01 19 14 91.1 65.3 33.67 2.58 1.83 3.33 1.17 1.32 1.54 1.87 2.29 20 100 98.4 75.1 34.38 1.19 0.81 1.57 1.17 1.3 1.52 1.83 2.23 21 100 99.5 94.8 36.8 1.16 0.77 1.55 1.15 1.26 1.44 1.71 2.06 22 21 100.0 90.7 34.57 1.25 0.85 1.66 1.16 1.3 1.51 1.82 2.21 23 14 100.0 67.9 34.53 3.09 2.12 4.14 1.16 1.3 1.51 1.82 2.22 24 83 100.0 90.9 25.45 1.07 0.73 1.41 1.29 1.58 2.01 2.6 3.34 25 86 100.0 8.7 27.72 1.12 0.77 1.47 1.24 1.48 1.84 2.33 2.95 26 29 100.0 65.5 29.37 0.97 0.63 1.34 1.22 1.43 1.74 2.17 2.73 27 29 99.7 79.4 30.54 1.98 1.43 2.53 1.21 1.39 1.68 2.08 2.59 28 50 98.2 74.9 33.51 1.3 0.92 1.67 1.17 1.32 1.55 1.88 2.3 29 93 99.8 87.2 32.67 1.02 0.7 1.31 1.18 1.34 1.58 1.93 2.37 30 14 100.0 100.0 13.78 3.69 2.75 4.61 1.93 3.05 4.63 6.7 9.24 31 29 100.0 100.0 14.4 2.76 2.02 3.5 1.86 2.87 4.32 6.21 8.54 32 50 100.0 100.0 16.48 1.44 1.03 1.82 1.66 2.42 3.52 4.95 6.73 33 100 100.0 100.0 13.08 1.17 0.82 1.49 2.03 3.28 5.04 7.34 10.16 34 64 99.8 94.8 17.41 1.7 1.2 2.2 1.59 2.27 3.25 4.53 6.12 35 100 100.0 98.1 22.32 1.28 0.89 1.63 1.37 1.76 2.34 3.11 4.07 36 100 100.0 100.0 19.56 1.04 0.73 1.3 1.47 2 2.76 3.78 5.03 PAGE 124 124 Table 4 3. Continued # PQRI WG Total Mass PBE ISM PBE RVS PE LB UB C 10 C 15 C 20 C 25 C 30 37 7 100.0 100.0 7.68 14.67 10.36 19.69 3.96 7.67 12.86 19.58 27.79 38 14 100.0 99.9 9.31 4.77 3.15 6.74 3.02 5.53 9.05 13.61 19.19 39 86 100.0 100.0 8.1 3.48 2.37 4.74 3.66 6.99 11.65 17.7 25.07 40 100 100.0 100.0 7.12 2.15 1.46 2.93 4.44 8.77 14.81 22.64 32.19 41 29 100.0 0.0 6.23 4.26 2.95 5.71 5.49 11.15 19.06 29.3 41.77 42 86 100.0 96.1 6.69 3.67 2.53 4.92 4.9 9.8 16.65 25.53 36.34 43 86 100.0 100.0 6.15 3.17 2.2 4.23 5.61 11.42 19.54 30.04 42.84 44 100 100.0 100.0 7.12 2.14 1.47 2.86 4.44 8.77 14.81 22.64 32.19 45 100 81.8 5.3 16.03 1.24 0.83 1.64 1.69 2.51 3.66 5.19 7.06 46 57 64.3 26.7 15.77 1.56 1.11 1.99 1.72 2.56 3.75 5.33 7.27 47 36 7.5 43.1 16.51 1.33 0.93 1.7 1.66 2.42 3.51 4.94 6.71 48 21 87.2 0.0 17.3 1.45 1.04 1.85 1.6 2.29 3.28 4.58 6.19 49 7 8.4 0.0 16.91 2.17 1.55 2.8 1.63 2.35 3.39 4.75 6.43 50 93 54.0 93.9 15.21 1.4 0.99 1.8 1.77 2.68 3.97 5.66 7.74 51 50 20.4 75.2 14.87 1.71 1.21 2.2 1.8 2.76 4.11 5.88 8.06 52 0 90.6 0.0 16.54 10.33 7.53 13.23 1.65 2.41 3.5 4.93 6.69 53 7 99.9 0.0 15.67 8.5 6.28 10.69 1.73 2.58 3.79 5.39 7.35 54 43 99.6 0.5 17.65 7.2 5.13 9.36 1.58 2.24 3.18 4.43 5.98 55 71 99.3 1.4 15.55 7.19 5.13 9.43 1.74 2.6 3.83 5.45 7.45 52* 0 90.39 0 14.75 9.97 7.16 12.96 1.82 2.78 4.16 5.96 8.18 53* 7 99.89 0 15.44 7.17 5.11 9.32 1.75 2.63 3.88 5.52 7.54 54* 43 99.61 0 15.67 7.21 4.98 9.68 1.73 2.58 3.79 5.39 7.35 55* 71 99.2 0 14.89 6.43 4.43 8.79 1.8 2.75 4.1 5.87 8.04 Results are based upon 20,000 replications per scenario; #: Scenario; PQRI WG: % of experts who evaluated the scenario as equivalent ( 13 ) ; Total Mass PBE: % of passes of PBE test for total mass equivalence; ISM PBE: % of passes of PBE test for ISM equivalence; RVS: Reference variance scaling (average); PE: Point estimate for MmCSRS (average); LB: Lower bound of 90% BCA confidence interval for MmCSRS; UB: Upper bound of 90% BCA confidence interval for MmCSRS; CX: Cut off value for MmCSRS for a X % criterion for equivalence testing of CI profiles; *: deposition sites 4 10 were used for ISM PAGE 125 125 Table 4 4 Classification of 55 PQRI scenarios based upon PQRI WG and APSD equivalence test results PQRI: P APSD Test : P PQRI: F APSD Test : F PQRI: F APSD Test : P PQRI: P APSD Test : F Scenario 6, 24, 29, 33, 34, 35, 36, 39, 40, 42, 43, 44, 50 3, 4, 7, 8, 9, 11, 12, 15, 16, 18, 19, 22, 23, 27, 28, 30, 31, 37, 38, 41, 47, 48, 49, 51, 52, 53, 54 26, 32 1, 2, 5, 10, 13, 14, 17, 20, 21, 25, 45, 46, 55 N 13 27 2 13 % 23.6 49.1 3.6 23.6 PQRI: Classification of PQRI WG; APSD Test: classification of APSD equivalence test; a pass for PQRI was assigned when >50% of the PQRI WG concluded equivalence; a pass for APSD test was assigned when > 50% pass the first and second steps and a 15% cut off value for the third step; P: pass; F: fail; N: number of scenarios PAGE 126 126 Figure 4 1 Proposed APSD equivalence test; a population BE test ( 29 ) could be applied for equivalence testing at steps one and two; MmCSRS based profile comparison test could alternatively be applied to deposition sites that are comprised in the definition of the fine particle mass PAGE 127 127 Figure 4 2 Real CI profiles, sites are ordered by decreasing magnitude of their normalized deposition on deposition sites that are comprised in the definition of the ISM for an Andersen CI; MDI: Metered dose inhaler; DPI: Dry powder inhaler PAGE 128 128 Figure 4 3 Average and reference CI profiles for constructing cut off value for MmCSRS based CI profile comparison test; sites are ordered by decreasing magnitude of their normalized deposition; deposition of average/reference CI profile (%; by sit e): 37.7/33.1 (1), 28.5/33.1 (2), 16.9/12.2 (3), 7.71/12.2 (4), 4.87/3.61 (5), 2.34/3.61 (6), 1.14/0.974 (7), 0.811/0.974 (8) PAGE 129 129 Figure 4 4 Cut off value plot and example confidence interval for the MmCSRS PAGE 130 130 Figure 4 5 Categorization of 55 PQRI scenarios based upon proposed APSD equivalence test; point estimates (filled circles) and 90% BCA bootstrap confidence intervals (segments; 2,000 bootstrap replicates) are displayed for those scenarios tha t received a pass in total mass and ISM PBE test s in >50% of the 20 ,000 simulations ; green colored scenarios were classified by >=70% of the PQRI WG as equivalent; orange colored scenarios were classified by >=30% and <70% of the PQRI WG as equivalent; red colored scenarios were classified by <30% of the PQRI WG as inequivalent; mean of the squared inverse of the coefficient of variation (CV%) across the four ISM sites with the la reference variance sc aling; d ifferently shaded areas and associated lines represent different cut off values for different equivalence criteria between two profiles (e.g., 20% difference on all ISM sites); results are presented in three graphs with different ranges of variance scaling and MmCSRS to allow visualization of the entire collection w ith sufficient resolution. PAGE 131 131 Figure 4 6 Average ISM ratio (T/R) and normalized mean ISM profiles for PQRI scenarios 1 4; full profiles of all PQRI scenarios are available elsewhere ( 14 15 ) ; blue lines: R product; red lines; T produc t PAGE 132 132 Figure 4 7. Average ISM ratio (T/R) and normalized mean ISM profiles for PQRI scenarios 5 8; full profiles of all PQRI scenarios are available elsewhere ( 14 15 ) ; blue lines: R product; red lines; T product PAGE 133 133 Figure 4 8. Average ISM ratio (T/R) and normalized mean I SM profiles for PQRI scenarios 9 12 ; full profiles of all PQRI scenarios are available elsewhere (14, 15); blue lines: R product; red lines; T product PAGE 134 134 Figure 4 9. Average IS M ratio (T/R) and normalized mean I SM profiles for PQRI scenarios 13 16 ; full profiles of all PQRI scenarios are available elsewhere (14, 15); blue lines: R product; red lines; T product PAGE 135 135 Figure 4 10. Average ISM ratio (T/R) and normalized mean ISM profiles for PQRI scenarios 17 20 ; full profiles of all PQRI scenarios are available elsewhere (14, 15); blue lines: R product; red lines; T product PAGE 136 136 Figure 4 11. Average ISM ratio (T/R) and normalized mean I SM profiles for PQRI scenarios 21 24 ; full pr ofiles of all PQRI scenarios are available elsewhere (14, 15); blue lines: R product; red lines; T product PAGE 137 137 Figure 4 12. Average ISM ratio (T/R) and normalized mean I SM profiles for PQRI scenarios 25 2 8; full profiles of all PQRI scenarios are available elsewhere (14, 15); blue lines: R product; red lines; T product PAGE 138 138 Figure 4 13. Average ISM ratio (T/R) and normalized mean I SM profiles for PQRI scenarios 29 32 ; full profiles of all PQRI scenarios are available elsewhere (14, 15); blue lines: R product; red lines; T product PAGE 139 139 Figure 4 14. Average ISM ratio (T/R) and normalized mean I SM profiles for PQRI scenarios 33 36 ; full profiles of all PQRI scenarios are available elsewhere (14, 15); blue lines: R product; red lines; T product PAGE 140 140 Figure 4 15. Average ISM ratio (T/R) and normalized mean I SM profiles for PQRI scenarios 37 40 ; full profiles of all PQRI scenarios are available elsewhere (14, 15); blue lines: R product; red lines; T product PAGE 141 141 Figure 4 16. Average ISM ratio (T/R) and normalize d mean I SM profiles for PQRI scenarios 41 44 ; full profiles of all PQRI scenarios are available elsewhere (14, 15); blue lines: R product; red lines; T product PAGE 142 142 Figure 4 17. Average ISM ratio (T/R) and normalized mean ISM profiles for PQRI scenarios 4 5 4 8; full profiles of all PQRI scenarios are available elsewhere (14, 15); blue lines: R product; red lines; T product PAGE 143 143 Figure 4 18. Average ISM ratio (T/R) and normalized mean I SM profiles for PQRI scenarios 49 51 ; full profiles of all PQRI scenarios ar e available elsewhere (14, 15); blue lines: R product; red lines; T product PAGE 144 144 Figure 4 19. Average ISM ratio (T/R) and normalized mean I SM profiles for PQRI scenarios 52 55 ; eight ISM sites; full profiles of all PQRI scenarios are available elsewhere (14, 15); blue lines: R product; red lines; T product PAGE 145 145 Figure 4 20. Average ISM ratio (T/R) and normalized mean I SM profiles for PQRI scenarios 52 55 ; seven ISM sites; full profiles of all PQRI scenarios are available elsewhere (14, 15); blue lines: R product; red lines; T product PAGE 146 146 CHAPTER 5 A PHARMACOKINETIC SIMULATION TOOL FOR INHALED CORTICOSTEROIDS 1 Background Inhaled corticosteroids (ICS) are first line medications for asthma treatment and a therapy option in the management of chronic obstructive pulmonary disease ( 2 30 ) A better understanding of pharmacokinetic (PK) properties that influence pulmonary selectivity of ICS has helped increase the efficacy and reduce systemic side effects of novel ICS ( 3 4 ) However the effects of certain physiological, formulation, and patient related factors on the systemic PKs of ICS remain poorly understood. For instance, changes in the lung physiology and anatomy during the course of a pulmonary disease affect the PK behavior o f some ICS while that of others is unchanged ( 31 32 ) Similarly the aerodynamic particle size distribution and regional lung deposition patterns (central to peripheral airways) affect the systemic PKs of some ICS but not tha t of others ( 33 ) Differences in dissolution rates do not only affect the time to reach the maximum plasma concentration (t max ) and the maximum plasma con centration (C max ) but also the area under the plasma concentration time profile (AUC). Thus, the PK behavior of inhaled drugs is much more complicated than that of traditional forms of administration. Moreover, changes in formulation and delivery device an d comparison of different ICS in the same device are often challenging. Clinical trial simulation ( 34 ) is a powerful tool for evaluating the outcomes of clinical or PK studies in a time and cost efficient way before resources are invested in conducting the actual s tudies. A trial simulation model generates realistic data by 1 Chapter 5 was originally published in the AAPS Journal Weber B, Hochhaus G. A pharmacokinetic simulation tool for inhaled corticos teroids AAPS J 2013 ; 15(1): 159 171 PAGE 147 147 specifying a mathematical model that adequately describes the functional relationship between the variable of interest and time (deterministic part of the model, here: PK profile of ICS) and by i ncorporating variability between and within subjects (random part of the model). This project was interested in providing such a simulation tool that allows incorporation of relevant physiological and formulation factors into the model and is able to predi ct the effects of such parameters on systemic PKs without having to perform actual PK studies. A freely available tool for simulation of PK trials after administration of ICS is provided that enables the user to explore the relationship between certain ph ysiological (e.g. differentiation between central and peripheral lung regions, different pulmonary absorption rates between central and peripheral lung regions ( 35 36 ) presence of mucociliary clearance mechanism in central lung regions ( 37 ) ), formulation (e.g. aerodynamic particles size distribution of the aerosol determining regional lung deposition patterns, dissolution properties of the ICS), and patient related factors (e.g. variability between and within subjects, differences in lung physiology between healthy subjects and patients) and the systemic PKs of ICS. The PK trial simulation tool is 2 to the statistical software R ( 21 ) and is available for download via http://www.cop.ufl.edu/pc/research/areas of research/inhaled glucocorticoids/icspkts r extension/ the users to simulate PK trials for any ICS (currently av ailable or hypothetical) delivered via different inhalers and different physiological settings in healthy subjects or patients by allowing the users to specify their own model parameters. Furthermore, the 2 Pharmacokinetic Trial Simulation PAGE 148 148 e of the commercially available ICS (budesonide (BUD), flunisolide (FLU), fluticasone propionate (FP), and triamcinolone acetonide (TA)). This PK trial simulation tool for ICS represents an innovation compared to previously published ICS PK models ( 3 ) and deterministic ICS PK simulation tools ( 38 ) as it allows simulation of PK trials by integrating variability between and within subjects and distinguish es between central and peripheral regions of the lung. This paper is structured as follows. First, a compartment model ( Figure 5 1 ) that incorporates physiological, formulation, and patient related factors of inhalation therapy (see above) is characterized. Second, a closed form expression for the plasma concentration time profile after ICS administration is derived based upon the compartment model (deterministic part of the PK trial simulation model). The availability of a closed form expression of the underlying mathematical model is beneficial for time efficient simulation. Third, the structure of the random part of the PK trial simulation model (i.e. between subjec t variability (BSV) and within subject variability (WSV)) is specified. Fourth, literature estimates of model parameters (i.e. typical values and associated variability terms (BSV and WSV) for the drug specific modules of the PK trial simulation tool are s ummarized. Fifth, the performance of the drug specific modules of concentration time profiles to actual plasma concentration data and/or literature data following administration of BUD, FLU, FP, and TA. In the discussion section possible PAGE 149 149 debated. Finally the structure and functions of the PK trial simulation tool and its modules are briefly explained by t wo hands on examples. Compartment Model Figure 5 1 displays a compartment model that adequately describes the fate of an ICS after administration by incorporating phy siological and formulation related aspects for inhalation therapy and patient factors. In detail, an inhaled drug particle, according to its aerodynamic particle size distribution, is deposited in the oropharynx (Dose Mouth ), is deposited in the lung (Dose L ung ), or is exhaled. The fraction of the emitted dose that is exhaled is negligible and was, thus, disregarded in the compartment model. It is pragmatic to distinguish the dose deposited in the lung into a fraction deposited in central lung regions and a f raction deposited in peripheral lung regions, given the impact of the physiological differences between the two regions on the fate of an inhaled drug ( 39 ) Even though in vitro/in vivo correlation between aerodynamic particle size distribution and regional lung deposition patterns has been established infrequently if ever, it is widely accepted that larger particles are more l ikely to be deposited in the oropharynx and central lung regions and smaller particles are more likely to be deposited in peripheral lung regions ( 7 ) Both central and peripheral lung regions were separated in one compartment where undissolved particles are present (LC 1 and LP 1 ) and one compartment where particles are in solution (LC 2 and LP 2 ). In detail, drug particles deposited in central lung regions (LC 1 ) are either cleared by the mucociliary clearance mechanism (k muc ) or will dissolve in the bronchial fluids (k diss ), pass through the pulmonary cells in the central lung regions (LC 2 ) and be absorbed into the systemic circulation (k pul,C ) ( 37 ) Drug particles deposited in peripheral lung regions (LP 1 ) dissolve (k diss ), pass through the pulmonary cells in the peripheral lung regions (LP 2 ) and are PAGE 150 150 absorbed into the systemic circulation (k pul,P ). The model allows explicitly for different absorpt ion rate constants for drug absorption from the central and peripheral lung regions if this distinction is justified ( 35 36 ) The fraction of the drug that is deposited in the oropharynx and the fraction that is removed by mucociliary clearance will be swallowed and can be absorbed systemically (k a ) through the gastrointestinal tract (A) depending upon the oral bioavailability (F BA ) of the drug. The amount of drug that reaches the systemic circulation will be distributed throughout the body (k 12 k 21 ) and eliminated (k 10 ) according to its PK properties. The model was parameterized in terms of CL and V C where CL represents the s ystemic clearance (in L/h) of the ICS, V C represents the volume of distribution (in L) of the central body compartment, and k 10 = CL/V C Patient factors are incorporated into the model by allowing for variability in the model parameters between and within subjects. Plasma Concentration Time Profile Closed Form Expression A closed form expression for the plasma concentration time profile after ICS administration was judged as beneficial for time efficient PK trial simulation. This expression was derived ba sed on a system of differential equations ( Eq. 5 1 Eq. 5 7 ) describing the fate of an ICS in the compartment model ( Figure 5 1 ) (5 1) (5 2) (5 3) (5 4) (5 5) PAGE 151 151 (5 6) (5 7) where t represents the time (in h), LC 1, LP 1 LC 2, LP 2, A, X, and P represent the amount of drug at time point t in the dissolution compartment of the central lung, dissolution compartment of the peripheral lung, solution compartment of the central lung, solution compartment of the peripheral lung, GI absorption compartment, central body compartment, and peripheral body compartment, respectively. The first order rate constants k diss k pul,C k pul,P k muc k a k 12 k 21 and k 10 were defined above. The assumption that the mucociliary clearance is a first order process, which seems to be justified for healthy subjects or mild asthmatic patients ( 40 ) was made for mathematical convenience. The system of differential equations was then solved using Laplace integration methods ( 41 ) Details are given in the Hence, a closed form expression for the plasma concentration time profile (C t ) after administration of an ICS and thus the determin istic part of the PK trial simulation model is given by (5 8) where all terms that were not introduced above are defined in the PAGE 152 152 Random Structure of PK Model Between and Within Su bject Variability After log transformation, individual PK parameters (e.g. F Lung CL, V C ) were variance values variance) of the PK parameters. The off correlation between the PK parameters, are zero. Hence, all individual PK parameters are independent of each other and follow a lognormal distribution. An exponential error model was selected as residual error model. (5 9) where C(obs) ij and C(pred) ij represent the observed and predicted plasma concentration at the j th time point in the i th ij are assumed to be independent and identically distributed normal random variables with mean equal to 2 Drug Specific Modules Literature Based Parame ter Estimates administration of the ICS BUD, FLU, FP, and TA. Estimates for the typical value parameters are given in Table 5 1 and are in accordance with a previously published deterministic PK model ( 42 ) (unless otherwise stated in Table 5 1 ). It should be noted that literature estimates for both the pulmonary disso lution and absorption processes assumption that the dissolution process is the rate limiting step seems reasonable given the lipophilic character of ICS and the fast pulmonary absorption of lipophilic substances PAGE 153 153 ( 35 36 ) Furthermore, an educated guess of 0.5 for the fraction of the lung dose that is deposited in central lung regions (i.e. central to peripheral lung deposition (C/P) ratio equals 1) was used as default values for all four modules. This ratio is a typic al value within the estimates reported in the literature for some of the formulations included, while for other of the included drugs estimates were not available. However, due to a lack of validated scintigraphy procedures literature data need to be seen critically ( ( 43 ) see also Discussion). Therefore, this ratio was used without further differentiation for all four drug specific modules. Estimates for the BSV and WSV terms either varied across the literature or were not available. Hence, BSV estimates for all parameters and WSV were set to default values of 20% and 30% (expressed as coefficient of variation (CV)), respectively, in all four drug specific modules. However, the users can adjust the BSV and WSV parameters and typical value parameters if desired. Performance Check of the Drug Specific Modules of PK Trial Simulation Tool Methods For all modules, the literature based model parameters ( Table 5 1 ) were used to generate 1,000 plasma concentration time profiles after inhalation of a single dose of 1000 mcg, 500 mcg, 250 mcg, and 100 mcg BUD, FP, FLU, and TA, respectively. For BUD and FP, these simulated plasma concentration time profiles were used to check the performance of the BUD and FP modules of the PK trial simulation tool by comparing the simulated data to PK data from four studies where healthy subjects received BUD and FP delivered via their respective dry powder inh alers (study I ( 44 ) study II ( 45 ) study III ( 46 ) study IV ( 47 ) ). Individual plasma concentration time profiles were available for study I. For studies II IV, only certain PK metrics (e.g. AUC 0 t C max t max ) w ere available from the literature. Using the simulated plasma concentration time PAGE 154 154 data, 90% prediction intervals were constructed by cutting off the lower and upper 5% of the simulated plasma concentrations per time point. For both, BUD and FP, the 90% pred iction intervals were then visually compared to data from 14 healthy subjects that received a single dose of 1000 mcg BUD and 500 mcg FP, respectively (study I). Moreover, typical PK metrics (i.e. AUC 0 inf AUC 0 t C max t max and the terminal half life) w ere calculated for the simulated data and compared to those of studies I IV. AUC and C max values from studies II IV were normalized to the simulated dose of 1000 mcg (BUD) and 500 mcg (FP) to match the administered dose of the simulated data and study I. For FLU and TA, where individual plasma concentration time data were not available, simulated (n = 1,000) AUC 0 inf C max and t max were compared to those (after dose adjustment) from literature ( ( 48 54 ) ) to check the performances of the FLU and TA modules. Results Figure 5 2 and Figure 5 3 display the visual comparison of the simulated plasma concentrations (90% prediction in tervals) to those of the 14 healthy subjects (study I) for BUD and FP, respectively. Comparison of the PK metrics of the simulated data to those of studies I IV is given in Table 5 2 and Table 5 3 for BUD and FP, respectively. For FLU and TA, the results of the performance checks are displayed in Table 5 4 Discussion A freely available tool for simulation of PK trials for ICS has been developed as an extension package to the software R. In its current form, the model allows simulation of pla sma concentration time profiles after administration of (I) two different hypothetical ICS and (II) two different formulations of four different ICS (BUD, FLU, FP, and TA) in a PAGE 155 155 parallel study design. A detailed example about the functions and outputs of th e Briefly, for all five modules (hypothetical ICS, BUD, FLU, FP, and TA) the user can specify certain PK model parameters (typical values, BSV, and WSV) for both drugs (ICS) or both formulat ions of either BUD, FLU, FP, and TA, the time points at which plasma samples outcome of a PK trial based upon the specified parameters values and returns 90% confidence int ervals for geometric means ratio of the two drugs/formulations for both AUC and C max and generates a plot displaying the average plasma concentration time profiles. Optionally, output tables containing e.g. individual or average plasma concentration can be generated. In the module for simulation of PK trials for hypothetical ICS, the users can specify all typical value parameters by themselves whereas certain typical value parameters (e.g. CL, V C k 12 k 21 k a ) are fixed to literature values in the drug sp ecific modules (BUD, FLU, FP, and TA) ( Table 5 1 ). Since literature estimates for most of the BSV and WSV parameters were either inconsistent or not available (e.g. d istribution rate constants) BSV and WSV parameters were set to default values of 20% and 30% (CV), respectively, in all modules. These values represent reasonable estimates for some parameters (e.g. BSV for CL and volume of distribution is commonly between 20% and 30% ( 55 ) ). The authors are aware that a BSV of 20 30% m ight not be representative for all model parameters. However, given the scarcity of reliable literature information on BSV and WSV, suggesting certain default values for those model PAGE 156 156 parameters and giving the users the options to adjust them to their belief s and needs seems appropriate. could be applied for simulation of PK trials of non ICS by adjusting the model parameters to represent other inhaled drugs. The PK trial simulat ion tool is based upon a compartmental model that is able to incorporate relevant physiological aspects of the lung (difference in absorption rate from central vs. peripheral lung, mucociliary removal of particles from central lung regions), physicochemica l properties of the drug (dissolution rate, deposition characteristics such as pulmonary deposition efficiency, central vs. peripheral deposition) and patient factors (reduction of mucociliary clearance rate constant or changes in deposition efficiency, se e Hands on Example I). It must be emphasized that while the model can adjust for such factors, the underlying model is neither a physiologically based PK model nor does it directly link the deposition profile of the drug particles in the lung to its physic ochemical properties (see below). The purpose of the model is to adequately reflect plasma concentration time profiles of ICS while allowing certain features of inhalation therapy (e.g. C/P ratio, mucociliary removal of undissolved drug particles in the ce ntral lung) to be considered. In addition, the variability between and within subjects of all PK parameters is considered. The PK trial simulation tool and the compartment model itself represents an extension of previously published inhalation models by By ron ( 39 ) Gonda ( 56 ) and Hochhaus et al. ( 3 ) Specifically, the models by Byron and Gon da focused rather on the kinetics in the respiratory tract and not in plasma and did not consider variability. The model by Hochhaus et al. did not PAGE 157 157 distinguish between central and peripheral regions of the lung and did not allow for variability between and within subjects. In the current form of the PK trial simulation tool, the user needs to specify deposition characteristics such as the emitted dose, the pulmonary deposited dose, and the C/P ratio. The authors are aware that particle deposition in the lu ng could be modeled with higher resolution using analytical equations for particle deposition efficiencies and specific flow conditions or computational fluid and particle dynamics methods ( 57 ) However, addition of such tools into the model would be of little benefit, as the purpose of the simulation tool is to model plasma and not regional lung concentration profiles after ICS administration. Since little is known about differences in the pulmonary absorption rates between different regions of the lu ng (other than some evidence pointing towards faster absorption from peripheral lung regions ( 35 36 ) which is already incorporated into the model), higher regional resolution for particle deposition exceeding central and peripheral regions, as generally provided by deposition models ( 57 ) would not affect the PK profile as the particles would still dissolve/be absorbed accordin g t o the same rate constants. Nonetheless, users could easily link these particle deposition models ( 57 ) with this PK trial simulation tool by translating the outputs of the deposition models into inputs of the simulation tool (i.e. fraction of the emitted dose that is deposited in the lung and the pulmonary fraction that is deposited in central or periphera l regions of the lung). Similarly, model parameters could be adjusted to include specific patient groups if known relationships between disease state and pulmonary deposition characteristics are known ( 46 58 ) Further, suitable in vitro deposition mode ls, such as cascade PAGE 158 158 impaction ( 59 ) or systems able to assess the dissolution rate of inhalable drug fraction ( 60 ) might be used to predict in vivo lung deposi tion or dissolution behavior. Indeed, we incorporated in vitro dissolution rate constants into the FP model (as the dissolution rate for this but not the other ICS was slow enough to be measured with sufficient accuracy in the in vitro setting (unpublished data). However, it needs to be realized that in vitro/in vivo correlation between CI profiles and regional lung deposition, as well as in silico/in vivo correlations remain generally to be established. A more detailed in vitro based prediction of particle deposition in the lung would definitely be incorporated in future extensions of the current version of the PK trial simulation tool, once validated models are available. The module that allows PK trial simulation after administration of hypothetical ICS should be considered as the main tool of this extension package as it allows the users to specify all model parameters based upon their own data, beliefs, and/or needs (see above). Nonetheless, modules for four specific ICS (BUD, FLU, FP, and TA) were incl uded in the simulation tool for convenience. For these modules, a set of default values for the model parameters is provided ( Table 5 1 ). Whereas drug related PK parameters (i.e. CL, VC, k 12 and k 21 ) are fixed to literature values, the users can adjust formulation related parameters (e.g. lung deposition parameters, dissolu tion rate constants). This enables the users, first, to explore the effect of different formulations or patient groups on the PK of a specific ICS and, second, to change the default values to values that would be supported by their data if needed. The defa ult values for the typical value parameters of the drug specific modules are based upon published literature data or unpublished experimental data ( Table 5 1 ) unless t hat for the C/P ratio and the PAGE 159 159 pulmonary absorption rate constants. Even though literature data on the C/P ratio is available for ICS ( 49 61 64 ) differences in the C/P ratio ha ve been described for different formulations of a given drug and for different patient groups ( 43 ) Because of the large variability in such estimates, the fact that no validated scintigraphy methods have been agreed on, and the lack of estimates for other ICS, an educated guess of 1 was used for the C/P ratio of healthy volunteers. However, the users can easily adjust these default values (see above). In addition, only general estimates for differences in the absorption rate across pulmonary membranes have been described in the literature ( 35 36 ) For glucocorticoids differences in the absorption rates for central and peripheral section of the lung have only resulted in semi quanti tative estimates. Again educated guesses resulted in the choices of 10 and 20 h 1 as pulmonary absorption rate constants for the central and peripheral regions of the lung, respectively. However, the user can change these defaults estimates if the properti es of a specific drug require it. To ensure that the model and the selected model parameters are valid, the predictive performance of the BUD, FLU, FP, and TA modules was checked by comparing simulated PK data and resulting metrics to those of actual studi es. package were checked by comparing simulated data to PK data from four studies where healthy subjects received BUD and FP delivered via their respective dry powder inhalers (see ab ove). For FP, the simulated plasma concentrations predict the outcomes of the studies I IV adequately with respect to mean and variability of both the individual plasma concentration profiles (study I, Figure 5 3 ) and the PK metrics (studies I IV, Table 5 3 ). The model overestimated somewhat the variability in C max PAGE 160 160 compared to that of study I (CV%: 37.7 vs. 19.8), while the variability in C max for Study III was under estimated (58.3 CV%). t max of the simulated data (0.89 h) is smaller than that of studies I, III, and IV (1 1.32 h). This might indicate that that the selected di ssolution rate constant (k diss ) of the FP module is slightly too large or that the literature based compartmental micro constants (k 12 k 21 ) need adjustment ( 42 ) The predicted AUCs are in very good agreement with the range of observed AUCs in the four FP studies ( Table 5 3 ), also indicating that the mucociliary clearance rate const ant (which affects the AUC of slowly dissolving drugs) is reasonable. For BUD, the overall predictive performance of the simulated data is not quite as good as that of FP but still satisfactory ( Table 5 2 and Figure 5 2 ). There was, however, a tendency of the simulation to slightly overestimate plasma concentrations of study 1 (t he 90% prediction interval overestimated somewhat the observed plasma concentrations from study I; see Figure 5 2). This is also reflected in the increased AUC 0 inf of the simulated data compared to that of study I (ratio of simulated vs. observed mean AUC 0 inf equals 1.67; Table 5 2 ). However, this was not an indicator for a poor predictive performance of the BUD module, as a much better agreement between the PK metrics of the simulated data and those of studies II IV was observed (average ratio of simulated vs. observed mean AUCs equals 1.02, range: 0.75 1.31; Table 5 2 ). The simul ated mean C max (1.39 ng/mL) was within the range of observed mean values (0.89 2.26 ng/mL; Table 5 2 ), although some tendency to lower concentrations and later t max v alues (t max,simulated : 0.65 h (mean), t max,observed : 0.21 0.5 h (range of means)) was observed. This difference in t max might suggest that the PAGE 161 161 dissolution rate constant of the BUD module (k diss = 17.8 h 1 ) might be too small 3 For most of the published BUD PK data after inhalation, however, the dissolution/absorption rate is difficult to determine since the peak concentrations occur very early (often at the time point where the first plasma sample was obtained). Similarly, it is almost impossible to correctly estimate dissolution rates in vitro for such fast dissolving drugs. The predictive performances of both the FLU and TA modules were both satisfactory as the simulated mean AUC 0 inf C max and t max were in good agreement w ith those of the published data ( Table 5 4 ). In particular, the means of simulated PK metrics were within the range of the means of the literature data with exception of t max of the FLU module. In summary, the predictive performances of all modules were satisfactory, in particular when considering that model parameters are either based upon different sources of literature data, in vitro data, or educated guesses (see Table 5 1 for more details). The slight differences between the predicted and observed C max and t max (see above) is very likely due to the uncertainty that is involved when estimating the pulmonary dissolution rates of the ICS, especially when this process is very fast, such as observed for BUD and FLU. All modules, including those for BUD and FP, explicitly allow the users to adjust the pulmonary dissolution rates as w ell as other deposition parameters to their own beliefs. Hence, parameters established by the user can be easily incorporated. Furthermore, the general module of this PK trial simulation package, in which the users can change all model parameters, has bee n provided to allow the highest degree of flexibility. Overall, the drug specific modules of the 3 Other reasons such as variability in systemic distribution micro constants (k 12 k 21 ) across studies cannot be excluded. PAGE 162 162 ICS without having to perform literature research on the input parameters that also allow adjustment of the model parameters if needed. physiological, formulation, and patient related factors on the systemic PKs of ICS while incorporating variability between and within subject. For instance, the PK trial simulation tool could be used to compare two identical formulations in different patient population by altering the model parameters that are related to lung anatomy and physiology (i.e. C/P ratio and the muc ociliary clearance rate constant). Furthermore, the PK trial simulation tool could be applied to compare the PK behavior of two different formulations of the same ICS that differ in their dissolution rates and/or aerodynamic particle size distribution (cen tral to peripheral airways) and to explore the effect of these differences on the AUC and C max In the these two on example to explain how to use the different mo dules of the PK trial simulation tool. Introductory videos showing how to download and install R, how to install the downloaded via http://www.cop.ufl.edu/pc/research/areas of research/inhaled glucocorticoids/icspkts r extension/ complicated stu dy designs (e.g. cross over designs) or could be used as a basis for a PK/pharmacodynamics (PD) model by linking the plasma concentrations to the suppression of the endogenous cortisol release ( 65 ) Moreover, Eq. 5 12 and Eq. 5 13 PAGE 163 163 could be used for predicting the pulmonary drug concentrations after ICS administration that could then be linked to a PD model of a pulmonary biomarker. Such a pulm onary PKPD model could be useful for evaluating the effect of different ICS or different formulations of the same ICS on their pulmonary efficacy. Summary A freely available tool for PK clinical trial simulation after ICS administration was provided as an compartment model that describes the fate of an ICS after inhalation. In its current form, parameters, which could represent physiological, formulation, and patient related factors) on PK behavior of ICS while taking variability between and within subjects into account. Addition al Equations Laplace transformation ( 41 ) of Eq. 5 1 Eq. 5 7 and rearrangements yields (5 10) (5 11) (5 12) (5 13 (5 14) (5 15) (5 16) PAGE 164 164 where s represents the Laplace operator, F BA was defined above, and LC 1,0 LP 1,0 and A 0 denote the initial amount of drug in the dissolution compartments of the central and peripheral lung, and the GI absorption compartment, r espectively. Particularly, (5 17) (5 18) (5 19) where Dose is the by the inhaler emitted dose, F Lung is the fraction of the emitted d ose that is deposited in the lung, and F C is the fraction of the lung dose that is deposited in central lung regions. Substitution of Eq. 5 10 Eq. 5 14 and Eq. 5 16 into Eq. 5 15 10 k 21 10 + k 12 + k 21 yields (5 20) Where (5 21) (5 22 ) (5 23) (5 24) Anti Laplace transformation of Eq. 5 20 yields (5 25) where (5 26) (5 27) PAGE 165 165 (5 28) (5 29) and (5 30) (5 31) (5 32) (5 33) (5 34) (5 35) (5 36) (5 37) (5 38) (5 39) (5 40) ICS pk TS R Extension Package Hands on Examples The structure and functions of explained in form of two hands max in healthy subjects and asthmatic patients. In the second example, the effect of having two PAGE 166 166 FP formulations that differ in their pulmonary dissolution rate constant on the PK documentation (supplemental material) and/or by accessing the official R help files. Moreover, the supplemental material Hands on Example 1: ICS Running the following code in R wil l simulate a PK trial when 500 mcg of an hypothetical ICS are administered to 25 subjects per treatment group (healthy subjects (Situation A) vs. asthmatic patients (Situation B)) and plasma samples are obtained at 0.17, 0.33, 0.5, 1, 1.5, 2, 3, 4, 6, 8, 1 0, 12 14, 16, 18, 20, 22, and 24 h after administration. The asthmatic patients are modeled by increasing the fraction of drug that is deposited in the central regions of the lung and by lowering the mucociliary clearance rate constant. ##################################################### #Number of Subjects (n) per Group ##################################################### n.subjects = 25 ##################################################### #Time points (h) where plasma samples are ob tained ##################################################### Time = c(0.17,0.33,0.5,1,1.5,2,3,4,6,8,10,12,14,16,18,20,22,24) ##################################################### #Situation A Model Parameters Typical Values (TV) and #Between Subject Va riability (BSV) ##################################################### Dose.A = 500 PAGE 167 167 TV.FLung.A = 0.2 TV.FC.A = 0.5 TV.FBA.A = 0.1 TV.kdiss.A = 0.3 TV.kmuc.A = 0.5 TV.kpulC.A = 0.4 TV.kpulP.A = 0.4 TV.ka.A = 0.65 TV.CL.A = 49 TV.VC.A = 87 TV.k12.A = 0.1 TV.k21.A = 0.05 BSV.FLung.A = 0.2 BSV.FC.A = 0.2 BSV.FBA.A = 0.2 BSV.kdiss.A = 0.2 BSV.kmuc.A = 0.2 BSV.kpulC.A = 0.2 BSV.kpulP.A = 0.2 BSV.ka.A = 0.2 BSV.CL.A = 0.2 BSV.VC.A = 0.2 BSV.k12.A = 0.2 BSV.k21.A = 0.2 ########################################### ########## #Situation B Model Parameters Typical Values (TV) and #Between Subject Variability (BSV) ##################################################### PAGE 168 168 Dose.B = 500 TV.FLung.B = 0.2 TV.FC.B = 0.8 TV.FBA.B = 0.1 TV.kdiss.B = 0.3 TV.kmuc.B = 0.25 TV.kpulC.B = 0.4 TV.kpulP.B = 0.4 TV.ka.B = 0.65 TV.CL.B = 49 TV.VC.B = 87 TV.k12.B = 0.1 TV.k21.B = 0.05 BSV.FLung.B = 0.2 BSV.FC.B = 0.2 BSV.FBA.B = 0.2 BSV.kdiss.B = 0.2 BSV.kmuc.B = 0.2 BSV.kpulC.B = 0.2 BSV.kpulP.B = 0.2 BSV.ka.B = 0.2 BSV.CL.B = 0.2 BSV.VC.B = 0.2 BSV.k12.B = 0.2 BSV.k21.B = 0.2 ##################################################### #Within Subject Variability (WSV) ##################################################### PAGE 169 169 WSV = 0.3 ##################################################### #PK Trial Simulation ##################################################### ICS(plots=FALSE,tables=FALSE) The following output displaying the AUC and C max for both healthy subjects and asthmatic patients and 90% confidence intervals of the geometric means rati os (healthy/asthmatic) for both AUC and C max Simulation was successful AUC Means (Arithmetic Means): Situation A Situation B [1] 2.23 1.96 Cmax Means (Arithmetic Means): Situation A Situation B [1] 0.43 0.34 AUC 90% Confidence Interval (Geometric Mean Ratio): [1] 0.99 1.28 Cmax 90% Confidence Interval (Geometric Mean Ratio): [1] 1.04 1.39 Furthermore, a graph showing the average plasma concentration time profiles for both healthy subjects and asthmatic pat ients is created ( Figure 5 4 ) Hands on Example 2 : FP Running the following code in R will simulate a PK trial when 500 mcg FP are administered to 35 subjects per formulation group (formulation A and B differ in their dissolution rate constants, B dissolv es 3 fold faster) and plasma samples are obtained at 0.17, 0.33, 0.5, 1, 1.5, 2, 3, 4, 6, 8, 10, 12 16, 20, and 24 h after administration. PAGE 170 170 ##################################################### #Number of Subjects (n) per Group ########################### ########################## n.subjects = 35 ##################################################### #Time points (h) where plasma samples are obtained ##################################################### Time = c(0.17,0.33,0.5,1,1.5,2,3,4,6,8,10,12,16,20,24) ##################################################### #Formulation A Model Parameters Typical Values (TV) and #Between Subject Variability (BSV) ##################################################### Dose.A = 500 TV.FLung.A = 0.16 TV.FC.A = 0.5 TV.kdis s.A = 0.302 TV.kmuc.A = 0.938 TV.kpulC.A = 10 TV.kpulP.A = 20 BSV.FLung.A = 0.2 BSV.FC.A = 0.2 BSV.kdiss.A = 0.2 BSV.kmuc.A = 0.2 BSV.kpulC.A = 0.2 BSV.kpulP.A = 0.2 BSV.CL.A = 0.2 BSV.VC.A = 0.2 BSV.k12.A = 0.2 PAGE 171 171 BSV.k21.A = 0.2 ############################ ######################### #Formulation B Model Parameters Typical Values (TV) and #Between Subject Variability (BSV) ##################################################### Dose.B = 500 TV.FLung.B = 0.16 TV.FC.B = 0.5 TV.kdiss.B = 0.9 TV.kmuc.B = 0.938 TV.kpulC.B = 10 TV.kpulP.B = 20 BSV.FLung.B = 0.2 BSV.FC.B = 0.2 BSV.kdiss.B = 0.2 BSV.kmuc.B = 0.2 BSV.kpulC.B = 0.2 BSV.kpulP.B = 0.2 BSV.CL.B = 0.2 BSV.VC.B = 0.2 BSV.k12.B = 0.2 BSV.k21.B = 0.2 ##################################################### #Within Subject Variability (WSV) ##################################################### WSV = 0.3 ##################################################### #PK Trial Simulation PAGE 172 172 ##################################################### FP(plots=FALSE,tables=FALSE) The following output displaying the AUC and C max for both formulations and 90% confidence intervals of the geometric means ratios (A/B) for both AUC and C max is Simulation was successful AUC Means (Arithmetic Means): Formulation A Formulation B [1] 0.71 0.73 Cmax Means (Arithmetic Means): Formulation A Formulation B [1] 0.20 0.38 AUC 90% Confidence Interval (Geometric Mean Ratio): [1] 0.85 1.09 Cmax 90% Confidence Interval (Geometric Mean Ratio): [1] 0.45 0.6 0 Moreover, a graph showing the average plasma concentration time profiles for both formulations is generated ( Figure 5 5 ). PAGE 173 173 Table 5 1 Ty pical value parameters for the BUD, FLU, FP, and TA modules of the PK trial simulation tool Parameter Unit BUD (DPI) FLU (MDI) FP (DPI) TA (MDI) Lung ) 0.3* 0.24* 0.16* 0.15* C ) 0.5* (!!) 0.5* (!!) 0.5* (!!) 0.5* (!!) BA ) 0.11 0.2 0**** 0.23 muc ) h 1 0.938* ( 39 ) 0.938* ( 39 ) 0.938* ( 39 ) 0.938* ( 39 ) diss ) h 1 17.8* 14* 0.189 (!) 1.2* pul,C ) h 1 10** 10** 10** 10** pul,P ) h 1 20** 20** 20** 20** a ) h 1 0.45 ( 66 ) 14 **** 0.91 ( 67 68 ) L/h 85 55 73 39 C ) L 100 70 31 154 12 ) h 1 20.01 0.41 1.78 *** 21 ) h 1 11.06 0.82 0.09 *** Additional References ( 61 64 69 71 ) ( 44 55 72 73 ) ( 74 ) Lung ) represent specific values for the inhalers (i.e. BUD: Turbohaler, FLU: MDI, FP: Diskus, TA: MDI). ** Parameters are arbi trarily chosen to represent fast absorption of dissolved lipophilic substances and to account for possible faster absorption from peripheral lung regions and can be changed by the user *** One compartment body model seems to be more suitable to describe PK of TA **** The oral bioavailability of FP is <1% and negligible for the plasma concentration time profile The dissolution rate constant (k diss ) for the FP module is based upon unpublished in vitro dissolution data and PK analysis of unpublished FP data !! Literature estimates for F C (i.e. central vs. peripheral lung (C/P) deposition ratio) ratio for the different formulations are either not available or not applicable for the model (see Discussion). Thus, an educated guess of 0.5 (i.e. C/P deposition rat io of 1) was used as a default value for the modules. Typical value parameters are based upon a publication by Krishnaswami et al. ( 42 ) unless otherwise stated (reference(s) in parenthesis); further literature references that are related to the selection of the typical value parameters are given as additional references; BSV and WSV terms are set (by default) to values of 20% and 30% (expressed as CV%), respectively, and can be changed by the user; DPI: Dry powder inhaler; MDI: Metered dose inhaler PAGE 174 174 Table 5 2 Simulated Data Study I Moellmann et al. ( 44 ) Study II Harrison et al. ( 45 ) Study III Mo rtimer et al. ( 46 ) Study IV Dalby et al. ( 47 ) n 1,000 14 12 20 26 C max (ng/mL) 1.39 (27.2) 0.89 (54.3) 2.02 ( ) 2.09 (49) 2.26 ( ) t max (h) 0.65 (92.3) 0.41 (84.3) 0.21 (114) 0.5 ( ) AUC 0 24 (ng/mL*h) 4.74 (27.2) 2.56 (60.0) AUC 0 inf (ng/mL*h) 4.77 (27.4) 2.84 (56.3) AUC 0 5/6 (ng/mL*h) 3.63 (26.4) 3.59 (41.4) AUC 0 8 (ng/mL*h) 4.06 (25.9) 5.39 ( ) AUC 0 10 (ng/mL*h) 4.32 (25.9) 3.3 (106.4) Terminal t 1/2 (h) 2.62 (39.3) 2.97 (48.4) *AUC 0 5 for simulated data, AUC 0 6 for literature data ; comparison of PK metrics (mean (CV% )) from simulated data using the PK trial simulation tool and literature, n: number of subjects, only data from healthy subjects where used from literature, AUC and C max data from literature were normalized to the simulated dose of 1000 mcg PAGE 175 175 Table 5 3 Simulated Data Study I Moellmann et al. ( 44 ) Study II Harrison et al. ( 45 ) Study III Mortim er et al. ( 46 ) Study IV Dalby et al. ( 47 ) n 1,000 14 12 20 26 C max (ng/mL) 0.11 (37.7) 0.10 (19.8) 0.07 ( ) 0.06 (58.3) 0.1 ( ) t max (h) 0.89 (65.4) 1.36 (44.4) 1.21 (75.2) 1 ( ) AUC 0 24 (ng/mL*h) 0.56 (31.0) 0.66 (23.2) AUC 0 inf (ng/mL*h) 0.63 (32.1) 0.78 (33.7) AUC 0 5/6 (ng/mL*h) 0.31 (32.3) 0.20 (57.5) AUC 0 8 (ng/mL*h) 0.36 (33.3) 0.36 ( ) AUC 0 10 (ng/mL*h) 0.41 (31.7) 0.75 (42.5) Terminal t 1/2 (h) 6.77 (30.4) 8.05 (53.1) *AUC 0 5 for simulated data, AUC 0 6 for literature data ; comparison of PK metrics (mean (CV% )) from simulated data using the PK trial simulation tool and literature, n: number of subjects, only data from healthy subjects where used from literature, AUC and C max data from literature were normalized to the simulated dose of 500 mcg PAGE 176 176 Table 5 4 package FLU Simulated Data FLU Literature Data ( 50 53 ) TA Simulated Data TA Literature Data ( 48 49 54 ) Mean Range Mean Range C max (ng/mL) 1.30 0.81 2.39 0.18 0.12 0.25 t max (h) 0.33 0.09 0.2 2.01 1.59 3.67 AUC 0 inf (ng/mL*h) 1.92 1.52 4.28 0.90 0.69 1.92 Comparison of PK metrics from simulated data using the PK trial simulation tool (mean) and literature (range of means), AUC 0 inf and C max data from literature were normalized to the simulated dose of 250 and 100 mcg for FLU and TA, respectively PAGE 177 177 Figure 5 1 Compartment model for characterization of plasma concentration after administration of ICS, F Lung : fraction of the emitted dose that is deposited in the lung; F Mouth : fraction of the emitted dose that is deposited in the oropharynx; F C : fraction of the lung dose that is deposited in central regions of the lung (LC 1 ); F P : fraction of the lung dose that is deposited in peripheral regions of the lung (LP 1 ); LC 2 and LP 2 : Co mpartments representing central and peripheral lung regions, respectively, where the drug is dissolved; F BA : oral bioavailability; k muc : mucociliary clearance; k a : drug absorption from the gut into the systemic absorption; k diss : dissolution of drug partic les; k pul,C : drug absorption from central lung regions into the systemic circulation (central body compartment); k pul,P : drug absorption from peripheral lung regions into the systemic circulation; k 12 k 21 : drug distribution between central and peripheral body compartments; k 10 : drug elimination from the systemic circulation: all rate constants (k) were assumed to be first order processes PAGE 178 178 Figure 5 2 : Observed plasma concentration after inhalation of a single dose of 1000 mcg BUD (n = 14) ( 44 ) grey shaded area: 90% prediction interval based upon simulated plasma concentrations after inhalation of a single dose of 1000 package PAGE 179 179 Figure 5 3 : Observed plasma concentration after inhalation of a single dose of 500 mcg FP (n = 14) ( 44 ) grey shaded area: 90% prediction interval based upon simulated plasma concentrations after inhal ation of a single dose of 500 mcg PAGE 180 180 Figure 5 4 Hand administration of 500 mcg of a hypothetic al ICS to 25 subjects per treatment group (healthy subjects (Situation A) vs. asthmatic patients (Situation B)) and plasma samples are obtained at 0.17, 0.33, 0.5, 1, 1.5, 2, 3, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, and 24 h after administration, asthmatic patients are modeled by increasing the fraction of drug that is deposited in the central regions of the lung and by lowering the mucociliary clearance rate constant PAGE 181 181 Figure 5 5 Hand K trial when 500 mcg FP are administered to 35 subjects per formulation group (formulation A and B differ in their dissolution rate constants, B dissolves 3 fold faster) and plasma samples are obtained at 0.17, 0.33, 0.5, 1, 1.5, 2, 3, 4, 6, 8, 10, 12 16, 20, and 24 h after administration. PAGE 182 182 CHAPTER 6 FINAL DIS C U SSION AND CONCLUSIONS Demonstration of bioequivalence (BE) of locally acting orally inhaled drug produc ts (OIDPs) remains challenging since different methods as those that have been established for systemically acting orally administered drug are required (see Chapter 1). Both the European Medicines Agency (EMA) and the Food and Drug Administration (FDA) have proposed approaches for establish ment of BE for locally acting OIDPs ( 7 75 ) Even though those approaches differ from each other in their requirements that are needed for market approval of generic inhalers, they rely on th e same in vitro experiments (e.g., cascade impactor (CI) profiles for determination of aerodynamic particle size distribution (APSD)) and in vivo studies (e.g., pharmacokinetic (PK) and pharmacodynamic (PD) studies for establishment of an equivalent system ic safety profile and equivalent pulmonary efficacy profile, respectively). The appropriateness of both approaches should be evaluated with respect to, first, the mission of both the EMA and the FDA to provide safe and cheap generic alternatives to the in novator products and, second, the scientific background and justification of the methods that are applied in those approaches. The following is a subject evaluation of the current EMA and FDA approaches for establishment of BE of locally acting orally inha led drug products that does not necessarily reflect the opinion of any of the co authors of the previous chapters. A Critical Evaluation of the Current EMA and FDA Approaches for Establishment of Bioequivalence of Locally Acting Orally Inhaled Drug Produc ts Making safe and cheap generic alternatives to innovator products available to the public is one of the missions of both the EMA and the FDA. However, safety and PAGE 183 183 cheapness are usually adversaries. Thus, a compromise between both appears to be the best so chemical entities, however, the safety concerns outweigh any concerns for cost effectiveness. Among other reasons, this has led to a very lengthy (approximately 12 years) and expensive ($2 billion) process for obtaining market approval for new drugs. On the other hand, the methods that have been established for demonstration of BE of systemically acting orally administered drugs ( see Chapter 1) allow the development of safe generics involving reasonable expenses. However, since those methods cannot readily be applied to local ly acting OIDPs (see Chapter 1) a need for methods that enable the development of safe and cheap generic OID Ps has been created. Both the EMA and the FDA have proposed approaches for establishing BE of OIDPs. Even though both approaches comprise similar methods, there emphasis on safety and/or cost effectiveness seems to be different. On one hand, the FDA appro ach (see Chapter 1) is very conservative and focuses on patient safety and compliance. It should be remarked here that patient safety and compliance is indispensable and not a negative thing at all. However, the restrictiveness of the FDA approach raises t he question whether there will ever be a generic dry powder inhaler on the US market that received market approval based upon the current approach. A non availability of generic OIDPs would not help reduce the health care costs and potentially affect the a ffordability of those drugs to low income families. On the other hand, considering the poorly established in vitro in vivo correlation (IVIVC) between CI data and pulmonary deposition, it seems questionable that generic PAGE 184 184 OIDPs could be on the European marke t solely based upon in vitro CI data without even testing it in a single human subject. The FDA requires a generic product that demonstrates an equivalent systemic safety and pulmonary efficacy profile to an innovator product and both having a similar dev ice design and formulation to pass a series of in vitro tests. The sensitivity of in vitro tests to potential differences in the performance of two products is well known. However, an in vitro difference does not necessarily result in an in vivo or a clini cally significant difference ( 76 ) Irrespective of those IVIVC considerations, the additional in vitro tests requirement raises questions on the reliability of the methods that are applied for demonstration o f an equivalent safety and efficacy profile. If in vitro tests are needed to show potential differences in product performances that were not demonstrated in in vivo studies (PK or PD), the relevance of those in vivo studies for BE establishment is questio nable. Whereas the appropriateness of PK studies for establishment of an equivalent systemic safety profile is scientifically accepted, there is limited evidence supporting the sensitivity of PK and PD studies for establishment of an equivalent pulmonary e fficacy profile and no consensus among experts ( 5 6 77 78 ) This, however, puts a different perspective on the EM A approach possibly relying only on in vitro cascade impactor data since most of the methods that are applied are not validated. On the other hand, an identical or equivalent CI profile and, therefore, an equivalent aerodynamic particle size distribution d oes not necessary warrant the assumption of an equivalent in vivo performance with respect to safety and efficacy since cascade impactor may not be sensitive to certain formulation characteristics that PAGE 185 185 affect the in vivo performance. It should be remarked though that EMA restricts the applicability of an in vitro test only approval by having to meet certain requirements. If the generic company cannot use, decides not to use, or fails to demonstrate BE by using in vitro data, the EMA allows similar methods as the FDA to establish BE between the generic and innovator products. The case where the in vitro test (e.g., cascade impactor data) fails to show BE deserves further scrutiny. There are two reasons why any statistical test applied to any in vitro data se t could fail to show BE. First, generic and innovator product are equivalent with respect to the characteristic that is tested for but the variability is too large or the sample size too small. Second, the generic and innovator product are indeed different from each other with respect to the characteristic that is tested for. In case of the former, performing a PK and/or PD study to establish an equivalent safety and/or efficacy profile seems reasonable and justified against the background that the unreason ably large sample size would be needed to pass the in vitro criteria. In case of the latter, however, the performance of PK and/or PD studies for establishing equivalence between generic and innovator product appears to be critical since a difference in a characteristic that is sufficient for demonstrating BE was shown. Impact of the Modified Chi Square Ratio Statistic the Aerodynamic Particle Size Distribution Equivalence Test, and Pharmacokinetic Trial Simulation Software on the Current EMA and FDA Gui delines Even though it remains to be demonstrated which methods and approaches are most suitable for establishing BE of locally acting orally inhaled drug products, the results and findings of this dissertation will have a significant impact on the develop ment of generic locally acting OIDPs. The modified chi square ratio statistic (mCSRS; Chapter 2, Chapter 3, and Chapter 4) and the related aerodynamic particle size PAGE 186 186 distribution (APSD) equivalence test (Chapter 4) could become the standard method for testi ng APSD equivalence and/o r comparative cascade impactor equivalence testing and, hence, be frequently used to obtain market approval in Europe and the United States. The PK trial simulation tool (Chapter 5) could be a valuable tool for evaluating the sensi tivity and robustness of PK data (e.g., the maximum plasma concentration and the area under the concentration time curve) for detecting differences in the pulmonary fate between generic and innovator OIDPs PAGE 187 187 LIST OF REFERENCES 1. Global Initiative for Asthma. Global strategy for asthma management and prevention. http://www.ginasthma.org/uploads/users/files/GINA_Report_2012.pdf Accessed 1 February 2013 2. Global Initiative for Chronic Obstructive Lung Disease. 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Guideline on the Requirements for Clinical Documentation for Orally Inhaled Products (OIP) Including the Requirements for Demonstration of Therapeutic Equivalence between Two Inhaled Products for Use in the Treatment of Asthma and Chronic Obstructive Pulmonary Disease (COPD) in Adults and for Use in the Treatmen t of Asthma in Children and Adolescents. http://www.ema.europa.eu/docs/en_GB/document_library/Scientific_guideline/20 09/09/WC500003504.pdf Ac cessed 13 June 2012 76. Suman JD, Laube BL, Dalby R. Validity of in vitro tests on aqueous spray pumps as surrogates for nasal deposition, absorption, and biologic response. J Aerosol Med. 2006;19:510 21. 77. Goyal N, Hochhaus G. Demonstrating Bioequivalen ce Using Pharmacokinetics: Theoretical Considerations Across Drug Classes. Respiratory Drug Delivery 2010. 2010;1:261 72. 78. Pearlman DS, Noonan MJ, Tashkin DP, Goldstein MF, Hamedani AG, Kellerman DJ, et al. Comparative efficacy and safety of twice daily fluticasone propionate powder versus placebo in the treatment of moderate asthma. Ann Allergy Asthma Immunol. 1997;78:356 62. PAGE 194 194 BIOGRAPHICAL SKETCH Benjamin Weber wa s born in Ulm, Germany in 1983. In 2008, Benjamin received a professional deg ree in Pharmacy from the University of Tuebingen, Germany He joined the working group of Dr. Guenther Hochhaus in the Department of Pharmaceutics (College of Pharmacy, University of Florida), pursuing a Doctor of Philosophy in Pharmaceutical Science and a Master of Statistics. In collaboration with the FDA, Benjamin Weber has been focusing on the development of new in vitro and in vivo methods for establishing bioequivalence of orally inhaled drug products. Benjamin has had publications in the European Jou rnal of Pharmaceutical Sciences, Drug Metabolism and Deposition AAPS Journal, Respiratory Drug Delivery, and Planta Medica. Benjamin has had poster presentations at several international scientific conferences. Benjamin was the w inner of the poster competition (Ph.D. students) at the 23rd Annual Research Showcase and Awards Recognition Day (2010) at the College of Pharmacy (University of Florida) and has been awarded a fellowship of the Oak Ridge Institute for Science and Education in 2010 and 2011 that allowed him to perform parts of his research at the Office of Generic Drugs, Center of Drug Evaluation and Research Food and Drug Administration in Rockville, MD. 