Development of Novel Statistical Methods and Decision Support Tools for the Management of Malaria in Western Africa

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Development of Novel Statistical Methods and Decision Support Tools for the Management of Malaria in Western Africa
Millar, Justin J
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[Gainesville, Fla.]
University of Florida
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Doctorate ( Ph.D.)
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University of Florida
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Forest Resources and Conservation
Committee Chair:
Ribeiro Do Valle,Denis
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Committee Members:
Psychas,Paul J
White,Ethan P
Glass,Gregory E
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Subjects / Keywords:
bayesian -- epidemiology -- malaria -- statistics
Forest Resources and Conservation -- Dissertations, Academic -- UF
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Forest Resources and Conservation thesis, Ph.D.


Malaria remains one of the most significant contributors to the global burden of infectious diseases, responsible for over 200 million cases and 400,000 deaths annually. Over 90% of malaria cases and death occur in sub-Saharan Africa, particularly within children less than five years old whom account for 61% of the total malaria-related deaths in 2017. The 2018 World Malaria Report indicated that there was no progress from 2015 to 2017 despite approximately $9 billion in global investment towards control and elimination. There is a growing consensus for the use of data-driven targeted interventions, which have been made more feasible in recent years due to the increased availability of malaria surveillance data and important environmental drivers from GIS and remote sensing source. However, as relevant data has become more available and refined the need more sophisticated statistical methods which can link disparate data, adequately represent the underlying dynamics, and characterize sources of uncertainty. Moreover, there is a significant demand for connecting statistical models to the actual decision process of designing effective interventions. In this dissertation I first utilize repurposed data from an insecticide spraying campaign in Bunkpurugu-Yunyoo in northern Ghana and publically available environmental data and develops a novel Bayesian-based approach for characterizing local risk factors for malaria within a single high burden district. Next I constructed a framework for comparing the cost-effectiveness of MDA versus MSAT, created models using publically available data from western Africa, and developed an interactive web application where stake-holders at set model parameters to perform scenario-based comparison of possible interventions. Finally, I fuse these two concepts by fitting semi-parametric model for comparing the influence of local health facilities in Bunkpurugu-Yunyoo on childhood malaria, and use this model to develop an interactive decision support tool which projects the impact of new health facilities. These developments were created in order to support data-driven decision making for targeted malaria interventions. ( en )
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Thesis (Ph.D.)--University of Florida, 2019.
Adviser: Ribeiro Do Valle,Denis.
Co-adviser: Adams,Damian.
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by Justin J Millar.

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© 2019 Justin John Millar


To Linda and Mark


4 ACKNOWLEDGMENTS Despite a single name on the cover page this dissertation is the culminated efforts of many, many people, without whom I could not possibly have completed this work. I am especially thankful for my advisor, Dr. Denis Valle. I am grateful I had the opportunity be one of your first graduate stude nts, you took an chance on bring ing in student with very little background in programming and Bayesian statistics. In the moment it can sometimes be difficult to recognize incremental progress, but in writing this dissertation and compiling all the work we This PhD has been an incredible, life altering experience, and I am trul y thankful for this opportunity and excited about our f uture endeavors. I would also like to a cknowledge my other committee members. Dr. Paul Psychas has had a mo numental impact on this work and on my ca reer development. N o t only was were you wil ling to share an incredible data source , a painstakingly earned resource, with a young research with no epidemiological experience , but you always were patience , encouraging , and supp ortive. The trip to Ghana you organiz ed was an incr edible e xperience, on a p rofessional and p ersonal level. I am incredibl y g rateful fo r your insights and guidance and look forwar d to our conti nuing endeavors . D r. Greg G lass , in additional to provi ding me with a strong foundation in s patial ep idemiology, you have c onstantly been encouraging and supportive . Your support serious ly me push p ast my o wn reservations about my abilit ies. I felt very fortunate t o have Dr. Damien Adam s on my committee. At times I felt quite d isconnected from our dep artment, but you were al ways en gaging whenever we ran into each other. You also provided an unique p r ospective on my work, a lways connecting dots in a way I ha dn t considered, which greatly improved my


5 research. And finally, I a m ex t remely grateful for Dr. Ethan W hite agreeing to com e onto the committee in a later stage of my degree. Y o u open ed me up a to tal ly new perspective to me, not just about programming skills and practices, but also more broadly about open and collaborative research. Also, int ro ducing me t o the Data Carpentry communi t y ha s had a profound im pact on m y pedagogical development. I m tha nkful for these opportunities and hope that we can continu e to work toget her in the future. This work also would not have been possible without the support and effort from my inc redible internation al collaborators. I n particular, I am e xceedingly thankful for Dr. Benjamin Abuaku, Professor Kwado Koram, Dr. Collins Ahorlu, Sammuel Oppong and the Ghana National Malaria Control program . Th e efforts these and man y other s made to collect the Bunkpurungu data were incredible , and I am grateful that you not only allowed me to c ollaborate with these data but al so provided valuable feed back on ou r manuscript. I als o want to tha n k the su pervisors from the Nation al Malaria Control Programme, Noguchi Memorial Institute for Medical Research , f or their support of my work with their data. I would also like to acknowledge the p rofound impact that my colleagues and community have had on my development . I came to Gainesville with almost no expe rience in progra mming and very litt le backgroun d in statistics and data science. S o many individuals and opportunities over these past four ye ars have provided m e with so mu ch knowledge , w ithout which I would not have been able to produce with wo rk. I would like to thank m y lab mates Punam Amratia, Kok B en Toh, Jacy Hyde, Christine Swan son , Dr. Pedro Albuquerque , Dr. Joanna M. Tucker Lima , Dr. Qing Zhao , and Dr.


6 Yusuf Jameel . I would also like to t hank Dan Max well, Shawn Taylor, Daijiang Li , François Michonneau , the UF R Meet up, the UF Carpentr y Club, the UF Informatics Institute , the Em erging Pathogens Institute , and the Carpentries . I need to personal ly thank my pa rtner, Kendall Everly. This journey has been incre d ible and challenging, and I cannot imag ine facing the all the difficult ies along this path wi thout you. You have been a cons tant support when I felt lost and a pu sh when I needed it . And most of all you have always believed in me . I am so grateful for the life we ve built together and cannot wait for ou r next future adventures. Finally, none of this would not be possible witho ut the immense support from m y incredible f amily. I am t h ankful for m y Florida family , who always made me feel connected and near to family , especially during the holida ys. I am thankful for Chasey, Kelly, and James, who have always been loving and support ive . It s incredible how the time and distance evaporates as soon as we re back toget her , and it s like we re kids ag ain. I am thankful for Moony, Olive, T h or, Titan, Bosco, Sampson, Shelly, and Shiloh for provid ing an endless supply of joy and comfor t. An d most of all, I am thankful for Linda and Mark. I am tha nkful for the inc redible sacrifice s you ve made for me, and for your unwavering b elief in me. I have had incredible opportunities and experiences because of you , and I know t he future holds even more . T hank you.


7 TABLE OF CONTENTS page ACKNOWLED GMENTS ................................ ................................ ................................ .. 4 LIST OF TABLES ................................ ................................ ................................ .......... 10 LIST OF FIGURES ................................ ................................ ................................ ........ 11 LIST OF ABBREVIATIONS ................................ ................................ ........................... 13 ABSTRACT ................................ ................................ ................................ ................... 15 CH APTER 1 INTRODUCTORY REMARKS ................................ ................................ ................ 17 The Present State of Malaria Burden and Man agement ................................ ......... 17 Malaria Epidemiology, Risk Factors, and Targeting Interventions .......................... 18 Modelling and Decision Support Challenges ................................ .......................... 19 Aims ................................ ................................ ................................ ........................ 20 2 DETECTING LOCAL RISK FACTORS FOR RESIDUAL MALARIA IN NORTHERN GHANA USING BAYESIAN MODEL AVERAGING ........................... 22 Abstract ................................ ................................ ................................ ................... 22 Introduction ................................ ................................ ................................ ............. 23 Methods ................................ ................................ ................................ .................. 25 Data Collectio n ................................ ................................ ................................ . 25 Ethical Approval ................................ ................................ ............................... 28 Statistical Methods ................................ ................................ ........................... 28 Base model ................................ ................................ ................................ 28 Complex models: seasonal differences and nonlinear associations .......... 30 Out of sample Predictions ................................ ................................ ................ 31 Results ................................ ................................ ................................ .................... 32 Descriptive Analysis ................................ ................................ ......................... 32 Risk Factor Outcomes ................................ ................................ ...................... 32 Base model ................................ ................................ ................................ 32 Seasonal differences ................................ ................................ ................. 33 Nonlinear associations ................................ ................................ ............... 34 Out of sample Predictio ns ................................ ................................ ................ 34 D iscussion ................................ ................................ ................................ .............. 35 Conclusion ................................ ................................ ................................ .............. 39 3 TO SCREEN OR NOT TO SCREEN: AN INTERACTI VE FRAMEWORK FOR COMPARING COST EFFECTIVENESS OF MASS SCREENING AND TREATMENT FOR MALARIA INTERVENTION ................................ ..................... 48


8 Background ................................ ................................ ................................ ............. 48 Methods ................................ ................................ ................................ .................. 51 Estimating Cost effectiveness ................................ ................................ .......... 51 Determining outcome probability based on prevalence, sensitivity, and specificity ................................ ................................ ................................ 53 Data collection ................................ ................................ ........................... 53 Modelling prevalence, sensitivity, and specificity ................................ ....... 53 Designing the Interactive Framework ................................ ............................... 55 Results ................................ ................................ ................................ .................... 56 General Comparisons ................................ ................................ ...................... 56 Context specific Results base d on National scale Survey Data ....................... 56 Effect of false negatives on cost effectiveness ................................ .......... 57 Differences between urban and rural communities ................................ .... 58 Estimating regional breakpoints for treatment and RDT costs ................... 58 Interactive Applications ................................ ................................ ..................... 60 Discussio n ................................ ................................ ................................ .............. 60 Conclusion ................................ ................................ ................................ .............. 63 4 ASSESSING AND PROJECTING THE INFLUENCE OF ACCESSIBILITY TO LOCAL HEALTH FACILITIES ON CHIL DHOOD MALARIA IN NORTHERN GHANA ................................ ................................ ................................ ................... 75 Introduction ................................ ................................ ................................ ............. 75 Methods ................................ ................................ ................................ .................. 77 Data Collectio n ................................ ................................ ................................ . 77 Field setting ................................ ................................ ................................ 77 Malaria status ................................ ................................ ............................. 77 Accessibility to health facilities ................................ ................................ ... 78 Additio nal risk factors ................................ ................................ ................. 78 Modelling Malaria Prevalence ................................ ................................ .......... 79 Projecting the Impact of New Health Facilities ................................ ................. 80 Results ................................ ................................ ................................ .................... 81 Accessibility to Health Facilities ................................ ................................ ........ 81 Model Interpretation ................................ ................................ ......................... 82 Predicting prevalence and cases ................................ ............................... 83 Shifting and adding new healt h facilities ................................ .................... 85 Discussion ................................ ................................ ................................ .............. 86 Implications for Ghana ................................ ................................ ..................... 86 Modelling Choices and Limitations ................................ ................................ ... 87 Geographic Resource Allocat ion and Decision Support ................................ ... 88 5 CONCLUDING REMARKS ................................ ................................ ................... 102 APPE NDIX A SUPPLEMENTAL MATERI AL FOR CHAPTER 2 ................................ ................. 104


9 B SUPPLEMENTAL MATERIAL FOR CHAPTER 3 ................................ ................. 109 LIST OF REFERENCES ................................ ................................ ............................. 114 BIOGRAPHICAL SKETCH ................................ ................................ .......................... 134


10 LIST OF TABLES Table page 2 1 Survey based variables. ................................ ................................ ..................... 42 2 2 Re mote sensing and GIS based Variables. ................................ ........................ 43 2 3 Model Comparisons based on the sum of the log likelihood. ............................. 46 3 1 Parameter definitions f or ex pected cost equations ................................ ............. 65 3 2 Summary of Data Sources ................................ ................................ ................. 66 4 1 Summary of GAM output. ................................ ................................ ................... 91


11 LIST OF FIGURES Fi gu re page 2 1 Map of study district, Bunkpurugu Yunyoo, in northern Ghana (red polygon show in insert map). ................................ ................................ ........................... 41 2 2 Mean sl ope e stimates (circles) and 95% credible intervals (horizontal grey bars) from probit regression parameters.. ................................ .......................... 44 2 3 Modelled patterns in malaria risk factors based on seasonal interaction terms.. ................................ ................................ ................................ ................ 45 2 4 Implied patterns in malaria prevalence and distance to urban center and distance to health facility. ................................ ................................ ................... 45 2 5 Regression parameter es tim at es using BMA, logistic regression, and Lasso regression models containing interactions terms and spline covariates . ........... 47 3 1 C onceptual framework for comparing the cost effectiveness of mass dr ug ad ministration (MDA) and mass screen and treat (MSAT) based on the potential outcomes a nd associated costs. ................................ .......................... 65 3 2 Comparison of the cost effectiveness of presumptive treatment and screen and tr eat a s a function of malaria prevalence. ................................ .................... 67 3 3 Rural community comparisons of regional value added (per individual) from diagnostic screening in Burkina Faso. ................................ ................................ 68 3 4 Regional estimates of early childhood malaria prevalence and RDT sensitivity and specificity in Burkina Faso. ................................ .......................... 70 3 5 Comparison of regional value added (per individual) fr om diagnostic screening in between urban and rural communities in Burkina Faso. ................. 71 3 6 Regional breakpoints for cost of treatment and diagnostic test (RDT) in Burkina Faso. ................................ ................................ ................................ ..... 73 4 1 Accessibility of health facility in Bunkpurugu Yunyoo, Ghana. . .......................... 90 4 2 Influence of accessibility to nearest health facility on early childhood malaria p rev al ence. ................................ ................................ ................................ ......... 92 4 3 Influence of additional risk factors on early childhood malaria prevalence . ........ 93 4 4 Distribution of early childhood malar ia pr evalence in Bunkpurungu Yunyoo, Ghana. . ................................ ................................ ................................ ............... 94


12 4 5 Distribution of cases of early childhood malaria in Bunkpurungu Yunyoo, Ghana. ................................ ................................ ................................ ................ 95 4 6 Com pa ring covariate ranges in training and testing datasets. ............................ 96 4 7 Predicting early chi ldhood malaria prevalence and cases in Bunkpurungu Yunyoo, Ghana. . ................................ ................................ ................................ . 97 4 8 Shifting the location of CHPS compounds. ................................ ......................... 99 4 9 Impact of adding new health facilities based on optimized location. ................. 100 4 10 Projected local impact of additional health facilities based on optimal location. 101


13 LIST OF ABBREVIATIONS ACT(s) Artemisinin based combination therapies BMA Bayesian Model Averaging CHPS Community Based Health P l anni ng and Services CI Confidence or credible intervals CSS Cascading Style Sheets DHS Demographic Heal th Survey(s) FN False negative FP False positive GAM Generalized additive model GEHIP Ghana Essential Health Intervention Project GIS Geographic info rmation systems GPS Global Positioning System HTML Hypertext Markup Language IRS Indoor residual spray ing ITN Insecticide treated bed netting Lasso Least absolute shrinkage and selection operator LLIN Long lasting insecticide treated bed net L ST L and surface temperature MODIS Moderate Resolution Imaging Spectroradiometer MAP Malaria Atlas Project MDA Mass dr ug administration MIS Malaria Indicator Survey(s) MSAT Mass screen and treat NDVI Normalized difference vegetation index


14 PMI Presid e Malaria Initiative RDT Rapid diagnostic Sn Sensitivity Sp Specificity UN United Nations WHO World Health Organization WQ Wealth quintile


15 Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy DEVELOPMENT OF NOVEL STATISTICAL METHODS AND DECISION SUPPORT TOOLS FOR THE MANAGEMENT OF MALARIA IN WEST AFRICA By Justin John Millar May 2019 Chair: Denis Ribeiro do Vall e Major: Forest Resources and Conservation Malaria remains one of the most significant contributors to the global burden of infectious diseases, responsible for over 200 million cases and 400,000 deaths annually. Over 90% of malaria cases and fatali t ies occur in sub Saharan Africa, particularly wit hin children less than five years old. The 2018 World Malaria Report indicated that there was no progress from 2015 to 2017 despite approximately $9 billion in global investment towards control and eliminat i on. There is a growing consensus for the use of d ata driven targeted interventions, which have been made more feasible in recent years due to the increased availability of malaria surveillance data and data on important environmental drivers from GIS and r emot e sensing source s . However, as relevant data has become more available the re is a pressing need for more sophisticated statistical methods which can link disparate data, adequately represent the underlying dynamics, and characterize sources of uncerta i nty. Moreover, there is a significant demand for connecting statistical models to the actual decision process of designing effective interventions. In this dissertation I repurposed data from an insecticide spraying campaign in Bunkpurugu Yunyoo in northe r n Gh ana and publicly


16 available environmental data to implement ed a novel Bayesian based approach for characterizing local risk factors for malaria within a single high burden district. Next , I constructed a framework for comparing the cost effectiveness o f mas s drug administration ( MDA ) versus mass scree n and treat ( MSAT ) , created models using publicly available data from western Africa, and developed an interactive web application where stake holders can set model parameters to perform scenario based comp a riso n of possible interventions. Finally, I fuse these two concepts by fitting a semi parametric model for comparing the influence of local health facilities in Bunkpurugu Yunyoo on childhood malaria, and use this model to develop an interactive decision s uppo rt tool which projects the impact of new heal th facilities. These developments were created in order to support data driven decision making for targeted malaria interventions.


17 CHAPTER 1 INTRODUCTORY RE MARKS The P resent S tate of M alaria B urden and M a nagemen t Mal aria is recognized as one of the greatest contributors to the global burden of infectious disease morbidity and mortality. In 2017, there were an estimated 219 million cases and over 400,000 malaria related deaths (1) . M alaria burden is not uniformly distributed . Over 90% of cases and fatalities occur in sub Saharan Africa, and children under the a ge of five comprise over half of all malaria related death worldwide (1,2) . Since 2000 , there has been a substantial global investment in control and elimination programs, with over $9 billion invested from 2015 to 201 7 alone (1) . This massive global effort has resulted in significant progress. From 2000 to 201 5 the i ncide nce of malaria in endemic Africa countries dropped by 40% , primarily driven by the use of insecticide treated ne ts (ITNs) and indoor residual spray (IRS) ( 3) . H oweve r, there are still many challenges towards reaching important benchmarks, such as those set by the Millennium De velopment Goals , and eventually reaching global eradication (4 6) . M uch of the global progress has been made in middle income, low endemicit y count ries, whereas as poorer, highly endemic countries have lagged behind their targets (5) . This is particularly of concern fo r countries in western Africa, which experience year round transmission and high disease prevalence. In addition to having the highe st dise ase i ntensity, many West Africa count r ies also have poor health systems and infrastructure , unstable government s , and /or large at risk population, all of which contribute to the bleak outlook for malaria eradication in West Africa relative to the re st of t he wo rld (7) . Regions with high disease intensity can continue to experience scale ups of ITN and I RS (8) .


18 The influence of residual malaria has led to e size fits approach to malaria interventions in favor of targeting strategies based on the local factors that contribute to transmission and o verall burde n (9 11) . Malaria E pidemiolog y , R isk F actors, and T ar getin g I nterventions Malaria infections are caused by the protozoan Plasmodium , a genus of obligate p arasites which are transmitted to their host s through hematophagic arthropod vectors. There are many species of Plasmodium , as well as many vectors and hos ts, h owever the majority of human malaria infections in West Africa are caused by Plasmodium falcipar um (and to a less er extent P. vivax ) ( 12) . The primary vectors in West Africa are the mosquito species Anopheles arabiensis , Anopheles funestus and Anopheles gambiae (13) . The malaria parasite vector host complex leads to a myriad of potential factors that can contribute malaria transmission and disease prevalence. Environmental factors, such as temperature, rainfall, a nd humidity, can influen ce th e survival and reproduction cycles of the vector species and the parasite (12,14) . Behavioral differences in v ecto rs , such as periodicity of activity and indoor versus outdoor feeding preferences, can influence vectoral capacity and susceptibility to certain interventions (15 19) . Hu man dynamics also influence malaria transmission and prevalence patterns. Socio e co nomic (e.g., wealth, education, health insurance) (20 26) , demographic (e.g. age, ethnicity ) (12,27 31) , and geographic (e.g. distance to cities a nd health facilities) (32 39) factors have all been linked to malaria transmission and/or burden . Previous intervention history , both at the population (e.g. mass distributions of ITNs/IRS) and individual level (e.g. bed net use, treatment with antimalarial drugs) can also influence transmission (3,40,41) .


19 The local expression of these factors will ultimate ly determine whether an intervention (e.g. vector control based strateg y versus MDA) will successfully disrupt transmission and/or reduce malaria burden, and therefore accurately characterizing local risk factors can provide valuable insights for guiding targeted interventions. These explanatory covariates can be incorporated into geostatistical model s to create risk maps, which can inform and guide contro l strategies where there is little to no directly observed data on malaria infection status (42,43) . M odelling and D ecision S upport C hallenges Historically , data limitations have impeded the development of comprehensive analyses on local malaria risk factors. Recently, however, p rioritization of robust surveillance systems, comprehensive field surveys, and data sharing practic es have led to a rapid growth of publicly available information on potential malar ia risk factors (44,45) . At the sa me time, high resolution remote sensing and GIS product s have also become more accessible to researchers. This proliferation of information has enabled malaria risk models to incorporate a wider variety of explanatory data (46 49) . However, comprehensive risk factors models face significant methodological challenges associated with high dimensionality, such as variable selection and overfitting (50) . Addressing these issue s will require the use of sophisticated statistical methods , which are able to produce models that are both highly pre d ictive and interpretable. Furthermore, in order for local risk factors analyses to effectively guide malaria intervention planning they must be designed with the decision makers in mind. A ccurate characterizations of uncertainty and clear representation o f model assumptions and inferences must be prioritized. This will be particularly important when introducing


20 statistical methods that may be unfamiliar to decision makers. Finally, it is important to recognize and limit a priori modelling choice, and inst e ad favor flexible models and frameworks which can be applicable beyond the initial considerations of the modeler. Aims The goal of this dissertation is to improve data driven decision making for designing targeted malaria interventions through two primar y contributions: 1. I mplementing new statistical frameworks for identifying local malaria risk factors 2. E xtending risk models into interactive decision support tools. In Chapter 2 I evaluate a comprehensive suite of malaria risk factors over multiple seasona l surveys from a single hyperendemic district in northern Ghana using a Bayesian approach for model selection . I demonstrate how this methodology can be used to simultaneously comp are a wide range of explanatory variables while maintaining interpretability , improving predictive performance over standard regression methods ( i.e., logistic and LASSO), and incorporate uncertainty in the selection process. In Chapter 3 I use publicly a vailable national survey data to fit Bayesian mixed effect models to estimat e malaria prevalence and diagnostic performance. I then demonstrate how these models can be extended into a decision support tool for comparing the cost effectiveness of two large scale malaria interventions : mass drug administrat ion (MDA) and mass screen and treat (MSAT) . This framework allows decision makers to set cost parameters via an interactive web application, and provides real time comparisons based on the data driven model s. Importantly, this entire workflow is done completely in the open source p rogram R, which is commonly used by epidemiologists and does not require knowledge of additional programming language.


21 Finally, in Chapter 4 I fuse these two approaches. Using the same data from Chapter 2, I estimate the travel time to the nearest health facility using a least cost path analysis and modelled this new covariate (along with other potential confounders) using a generalized additive model (GAM). I then used this m odel to propose candidate l ocation s for new Community Based Health Planning and S ervices (CHPS) compounds , which are optimized to reduce early childhood malaria burden, and construct a interactive tool which allows stakeholder s to propose a location for a new h ealth facility


22 CHAPTER 2 DETECTING LOC AL RISK FACTORS FOR RESIDUAL MALARIA IN NORTHERN GHANA USING BAYESIAN MODEL AVERAGING 1 Abstract There is a need for comprehensive evaluations of the underlying factors that contribute to residual malaria in sub Saharan Africa. However, it is dif ficult to c ompare the wide array of demographic, socio economic, and environmental variables associated wit h malaria transmission using standard statistical approaches. Additionally, many conventional analyses fail to account for seasonal differences and n on linear r elationships. We propose a Bayesian based model averaging approach for identifying and comparing potential risk and protective factors associated with residual malaria. We modelled the relative influence of a comprehensive set of demographic, socio econom ic, environmental, and malaria intervention variables on malaria prevalence , using Bayesian model averaging (BMA) for variable selection. Data were collected in Bunkpurugu Yunyoo, a rural district in northeast Ghana that exp eriences holoendemic seasonal ma laria transmission, over six biannual surveys from 2010 to 2013 . A total of 10,022 children between the ages 6 to 59 months were used in the analysis. Multiple models were developed to identify important risk and protective factors, accounting for seasonal patterns and non linear relationships. These models revealed pronounced no n linear associations between malaria risk and distance from the nearest urban center and health facility. Furthermore, the association between malar ia risk and age and certain ethn ic groups was significantly different in the rainy 1 A version of this chapter has been published as Millar, J., Psychas, P., Abuaku, B., Ahorlu, C., Amratia, P., Koram, K., Oppong, S. and Valle, D., 2018. Detecting local risk factors for residual m alaria in northern Ghana using Bayesian model averaging. Malar ia journal , 17 (1), p.343.


23 and dry seasons. Using a season to season validation approach, we find that BMA outperformed standard logistic regression and Lasso regression in out of sample predictive ab ility. This modelling framework offers an alternative approach to disease risk factor analysis that generates interpretable models, can reveal complex, nonlinear relationships, incorporates uncertainty in model selection, and produces accurate predictions. Maximizing the effectiveness o f targeted interventions aimed at reducing residual malaria wil l require more sophisticated statistical methods which are capable of handling a wider range of relevant data. To this end, we believe BMA represents a valuable tool for constructing more infor mative models for understanding risk factors for malaria, as we ll as other vector borne and environmentally mediated diseases. Introduction In spite of significant global reductions in malaria transmission and pr evalence over the past decade (3) , many districts and municipalities across sub Saharan Africa continue to experience high malaria burden (51,52) . In several inst ances, high disease burden has persisted des pite widespread coverage of conventional malaria interventions, such as insecticide treated bed netting (ITN) and indoor residual spraying of insecticides (IRS) (8,53) . An important factor contributing to residual malaria transmission is a high degree of spatial heterogeneity (8) . Malaria prevalence can differ dramatically (54) , even over relatively short distances (55) , which has the potential to undermi ne universal intervention guidelines (56) . Similarly, some subpopulations might have a substantial ly higher malaria risk than other groups. Identifying these hotspots and hot pops is critical for developing targeted approaches to guide holoendemic areas towards malaria elimination (9,55) .


24 Identifying local risk factors for malaria can be d ifficult due to the wide range of variables that can be relevant to malaria epidemiology (57) . Studies on malaria risk factors have often focused on particular types or categories of variables, such as models based on environmental data (58 60) , or demographic and socio economic factors (20,61 63) . However, as information becomes more accessible and av ailable at finer geographic and temporal res olutions, malaria risk m odels have sought to incorporate a greater variety of explanatory data (46 49) . Additionally , the importance of complex patterns, such as non linear relationships and seasonally dependent shifts, has emerged as a significant component to modelling malaria risk (64 , 65) . Incorporating a wider range of explanatory information into disease risk factors models can be difficult when using traditional statistical approaches such as standard logistic regression. Having a large number of predictors or independent variabl e s (i.e. potential risk factors) can lead to overfitting (50) , which can decrease the accuracy of out of sample predictions and increase the probability of detecting spurious relationships, which can undermine the applicability towards guiding interventions. Additionally, traditional statistical models oft e n make critical assumptions, such as linearity. These shortcomings have led to the application of sophisticated variable selection methods which are able to incorporate more independent variables and model complex relationships without sacrificing forecas t ing accuracy. Examples of variable selection methods that have been used for malaria related data include stepwise regression (48) , ridge regression (66) , and lasso regression (67,6 8 ) . Bayesian Model Averaging (BMA) is an alternative approach to variable selection (69) . Previous studies outside of the field of disease control have demonstrated that


25 BMA often outperforms other methods of variable selection (70 72) . This technique has been adopted in many ecological modeling applications (73) , such as weather forecasting (74,75) , phylogenetics (76) , and hyperspectral image analysis (72,77) . While BMA is not new to modelling disease risk factors (78,79) , recent applications (i.e. in the past fifteen years) are uncommon, and to our knowledge B MA has yet to be used in the cont ext of malaria or other arthropod transmitted diseases. Given the wide variety of factors that contribute to malaria, the increased attention to complex patterns, and the improved availability of data, BMA could represent a valuable statistical tool for en hancing risk models and designing targeted interventions. In this study, we used BMA to identify the underlying factors that shape the spatiotemporal patterns of malaria prevalence in a district located in the Guinea savan nah zone of northern Ghana that e xperiences high seasonal malaria transmission (80,81) . We demonstrate how BMA can be used to identify se asonal differences and nonlinear relationships in malaria risk factors, compare the performance of BMA to standard logistic and lasso regression, and describe how these results can be useful for designing targeted malaria intervention strategies. Methods Data Collection The individual le vel longitudinal dataset was collected in the course of operations research on IRS which was conducted by the University of Ghana with the support of (10,11) . The current study, which was carried out at the University of Florida in collaboration the University of Ghana, consisted fundamentally of enhancing that original dataset with remote sensed variables and conducting follow on analyses to address a differe nt set of research objectives.


26 Data were collected from the Bunkpurugu Yunyoo district, Northern Region, which is in the Guinea savannah zone of northeastern Ghana and experiences recurring high levels of seasonal malaria t ransmission Figure 2 1). Two hig hly efficient malaria vectors predominate in this area, namely Anopheles gambiae s.s. and Anopheles funestus (82) . During the study period had > 75% coverage with long lasting insecticide bed net (LLINs), having benefitted from two mass dis tribution campaigns in 2010 and 2 012. Annual IRS campaigns were conducted in 2011 and 2012 using alphacypermethrin 0.4% WP (ICON®10CS, Syngenta, Basel Switzerland), with a second application of IRS provided in the dry season in the eastern portion of the d istrict. The district is composed of rural communities supported by small scale farming and herding, and two modest urban centers: Bunkpurugu (population: 7,436) and Nakpanduri (population: 5,783). The major ethno linguistic groups are the Bimoba (approxim ately 60%) and Konkomba (approxim ately 30%) with smaller populations of Mamprusi, Kusasis, Dagombas, Fulanis and others. The Bimoba tend to predominate in the higher ground of the north and east portions of the district, including the two urban areas, whi le the Konkomba are more prevalen t in the lower lying area of the south and west, where they graze their cattle in the riverine plains. The Konkomba, who tend to be a geographically and economically marginalized group across northern Ghana, are recognized as more culturally conservative a nd in general tend to be less educated (83) . Childre n between the ages of 6 to 59 months were surveyed in six biannual surveys, three during the rainy season (late October to November) and three during the


27 dry season (late March to April), from 2010 to 2013. A new representa tive sample was selected for each survey using a multi stage randomized cluster sampling technique. Probability proportional to size estimates were used to randomly select representative communities based on a Ghana Health Service roster of communities in the district. This sample covered approximately 20% of the under five population in each survey, based on 2010 census data. Individuals under six months old were removed from this analysis to eliminate the influence of maternal immunity. Each survey was co nducted over a three week period. Malaria status was assessed via blood film microscopy. The survey also captured data on relevant demographic, socioeconomic, and malaria intervention variables (Table 2 1), using a modified Malaria Indicator Survey questio nnaire. GPS coordinates were reco rded for a central point in each community center. The original dataset was enhanced by collecting additional information on environmental variables using GIS software (ArcMap 10.4) and freely available remote sensing sourc es (Table 2 2). Childhood malari a prevalence in this district exhibited a high degree of spatial heterogeneity over the study period, in both the rainy and dry seasons (Figure 2 1). Correlations between all potential risk factors were calculated, and in cases of high correlations (R 2 > 0.49), a single representative covariate was selected. Selection of these covariates was based on the relevance of each covariate to malaria epidemiology and intervention strategies. The covariates dropped from all models were farming caretakers, indoor r esidual spraying (IRS) in past seven months, average daytime land surface temperature, normalized difference vegetation index (NDVI), cumulative rainfall, and historical precipitation trends. Because BMA requires each


28 indiv idual to have information for all covariates, all individuals with at least one covariate with missing data were dropped from the analysis. As a consequence, all of our analyses were based on 10,029 children (84.0% of total dataset). These data were distri buted across 80 communities in th e first survey and 71 communities in each of the subsequent surveys. The number of individuals in each survey ranged from 1,341 to 1,788. Ethical Approval Ethical approval for the data collection was granted by the Institutional Review Board (IRB) of the Noguchi Institute for Medical Research at the University of Ghana (NMIMR IRB CPN#009 10 11 revd 2013, FWA 001824/IRB 908). Approval for faculty and student involvement in the follow on analysis of de identified data was given by the University of Florida (IRB201500051). Statistical Methods Base model We constructed all malaria risk models in the same general Bayesian framework. Let be the binary mic roscopy outcome (1 = positive, 0 = negative) for individual in community at time . We mod el this variable using a Bayesian probit regression model, in which we assume that: if (1 1) otherwise (1 2) In other words, individual in community at time is positive for malaria only if i s greater than zero. This is determined by:


29 (1 3 ) (1 4 ) (1 5 ) Where is a vector of the intercept and potential risk factors, and is a vector with the corresponding regression parameters. The matrix in the prior for is a diagonal matrix with . Finally, the prior for is given by a uniform distribu tion. Similar regression frameworks have been used in disease risk factors analyses, inclu ding for HIV and tuberculosis (84,85) , as well as malaria (86) . The novelty of our approach is using BMA in the variable selection process. Rather than eva luating the contributions of individual covariates (e.g. stepwise regression), this model selection proces s generates multiple models and compares them in order to select the optimal subset of covariates. Briefly, this is done by constructing an initial m odel using a random subset of the covariates, proposing a new candidate model, and comparing the fit of bo th models based on marginal likelihoods. The candidate model is built off the chosen covari randomly chosen covariate that is in the present model with one that is not included) . The candidate model is then either accepted or rejected based on the marginal likelihood, and is repeate d at each iterative step of our Markov Chain Monte Carlo (MCMC) algorithm. This process allows the uncertainty associated with the model


30 selection pro cedure to be adequately represented. A more in depth description of this model and how it is fit are provi ded by Zhao et al. (72) and Denison (87) . Complex models: seasonal differences and nonlinear assoc iations In addition to the general risk factor regression, we created extended versions of the base model by including additional covariates in order to describe complex patterns, and again used BMA for variable selection. First we evaluated whether the ef fect of risk factors differed between the dry and rainy seasons. For example, distance to the nearest heal th facility may be a strong risk factor in the rainy season but may be an irrelevant covariate during the dry season. This was modelled by including a dditional elements in the design vector representing the interaction of each covariate with the binary variable representing the rainy season. This model allows the parameter estimates for each covariate to vary by season. Risk or protective fact ors that vary substantially with season may suggest that different malaria intervention strategies may be required for each season. Finally, we used this framework to describe potential non linear patterns in two relevant continuous variables, distance to nearest urban center and distance to nearest health facility. These variables were selected based on outcomes from the base model and their applicability towards design interventions. This model included linear spline variables. Including these splines allows regression c oefficients for these variables to shift at the knot values, which can reveal non linear associations in the specified risk factors. Seasonal interaction terms were also included in this model which allowed these parameters to also differ in each season.


31 Out of sample P redictions As illustrated in the preceding sections, allowance for greater model flexibility was achieved by including additional parameters. Specifically, the base model contained 29 covariates, adding interaction terms increased the numbe r of covariates to 56, and adding linear splines expanded the model to include a total of 73 covariates. Increasing the number of parameters in a model can lead to overfitting, making variable selection an increasingly important task. To assess the out of sample performance of BMA, we performed predictions by training the model on data from a particular year and estimating malaria status for a future year. Due to high seasonality in malaria risk in the district, only same season predictions were considered (i.e. rainy season predict ions were based on a rainy season training dataset). We compared these predictions to standard logistic regression, as well as least absolute shrinkage and selection operator (Lasso) regression. Lasso is an alternative method for variable selection which h as been shown to improve out of sample predictions (88) . To demonstrate how these models performed relative to the number of covariates, we tested season to season predictions for t he base model and the extended model, which contained seasonal interactions and spline terms. Out of sample predictive skill was evaluated based on the sum of the log likelihood, where the model with the largest log likelihood su m was considered to have th e best predictive ability. All statistical analyses were performed using R (v3.3.1) (89) , using a customized Gibbs sampler (see Supplemental Materials). Ea ch model was run for 10 ,000 iterations with the first 1,0 00 iterations dropped to account for the burn in period. Convergence on para meter estimates was confirm ed using trace plots. Regression estimates for each


32 potential disease factors were evaluated and considered statistically significant if the 95% credible interval did not contain zero. Results Descriptive Analysis There was a sl ight decreasing trend in ma laria prevalence over the course study, however the distribution of seasonal community prevalence remained relatively consistent over the course of the study (see Supplemental Materials). Mean community prevalence (and interquart ile ranges) in the three ra iny season surveys were 0.57 (0.39 0.75), 0.52 (0.33 0.73), and 0.46 (0.27 0.61), whereas in the three dry season surveys these values were 0.35 (0.15 0.50), 0.31 (0.14 0.47), and 0.23 (0.10 0.33). Note that the parasi temia rate remained high du ring the final rainy season despite high coverage of ITNs and two years of IRS. Risk Factor Outcomes Base model The basic risk factor model with BMA variable selection detected that many expected, classic patterns of malaria ri sk factors are present amon gst the early childhood populations in Bunkpurugu Yunyoo (Figure 2 2). The strongest risk factor associated with malaria infection was rainy season, as evident in the prevalence maps (Figure 2 1). Age was also a significant risk factors, as would be expec ted among young children (i.e. less than five years old) in an area of stable, holoendemic malaria. Among the distance measures, distance to nearest health facility and urban centers were significant risk factors, whereas distanc e to nearest roads and wate r bodies had little to no effect. The Konkomba communities experienced significantly higher malaria risk, relative to the Bimoba, and generally had a high mean prevalence overall. Note


33 that this represents the risk associated wit h ethnicity are adjusting f or other covariates in the model, such as education, wealth, and elevation. Statistically significant protective significant factor, however given th e relatively narrow range i n elevations (135 to 449 meters above sea level) this is likely a consequence of the two urban centers being in higher elevation, not because of high altitude effects on local climate. IRS in the past year was also a significant protective factor. The cate gorical variables for wealth quintiles did not have statistically significant effects individually, however as a group these variables indicated that the lower wealth quintile groups (below median and well below median) were posi tively associated with mala ria prevalence. Seasonal differences Modelling malaria risk with seasonal interaction terms (see Supplemental Materials) suggested most risk factors did not exhibit prominent differences between the rainy and the dry seasons, wi th a few notable exceptions . Age was an important risk factor for malaria in both seasons, however the slope estimate for this parameter was significantly lower in the rainy season than in the dry season, as illustrated in Fig 3. These patterns suggest tha t while all ages experience higher malaria burden in the rainy season, children in the upper end of the observed age range (50 to 59 months old) experienced nearly the same predicted prevalence in the dry season as they did in the rainy season (Figure 2 3) . Another important finding refers to ethnicity. All ethnic groups experienced increased malaria burden in the rainy season, however predicted mean prevalence based on seasonal ethnicity interaction terms indicate that the increase in malaria prevalence d uring the rainy season was more intense for the Konkomba communities than for the other ethnic groups (Figure 2 3). For example, the


34 odds ratio associated with the effect of Konkomba ethnicity compared to Bimoba ethnicity increased from 1.27 in the dry seas on to 1.60 in the rainy sea son. By comparison, the odds ratios associated with the effect of Mamprusi ethnicity compared to Bimoba ethnicity were 1.09 and 1.15 in the dry and rainy seasons, respectively. Other marginal differences included health insurance , which was less significan t of a protective factor in the rainy season, and personal medication use, which was a moderate risk factor in the dry season but had relatively no influence in the rainy season (see Supplemental Materials). Nonlinear association s The final model containin g linear spline covariates revealed interesting nonlinear associations between malaria prevalence and distance to nearest urban center, and distance to nearest health facility (Figure 2 4). Distance to nearest urban center was pos itively associated with mal aria infection in a roughly linear pattern until about twelve to fourteen kilometers (km), after which malaria risk began to plateau. Similarly, the implied malaria risk was greater for communities that were further away from the nearest health facilities, however there was a less steep relationship after approximately two to four km. These non linear patterns in malaria risk and proximately to urban centers and health facilities were consistent in the rainy and dry seasons. Out o f sample Predictions Based on the sum of the log likelihood, BMA and Lasso regression both outperformed standard logistic regression for all predictions (Table 2 3). Both approaches improved the out of sample predications compared to standard logistic regr ession by shrinking the reg ression coefficient estimates towards zero ( Figure 2 5). A notable difference between these approaches is that BMA allows for near zero


35 parameter estimates, whereas Lasso will force marginal factors to equal zero. For the base se t of covariates, BMA and La sso had similar likelihood values, however BMA had higher likelihood values for all predictions based on the extended set of covariates, which included seasonal interactions and linear splines. Discussion Our findings lend strong support for the usefulness of Bayesian Model Averaging (BMA) as a statistical tool for revealing complex patterns in malaria risk factors. Many of the outcomes from BMA reflect well established patterns in malaria etiology across sub Saharan Africa. For e xample, it is well known th at this region of Ghana experiences strong seasonal patterns in malaria transmission (80,81) . Our risk model des ignated the largest paramet er estimate to the seasonality covariate, and the effect of seasonality was significant in all models. Additionally, age was also identified as an important risk factor, which follows typical prevalence age patterns from 6 to 59 months in holoendemic setti ngs (90) . Protective factors i dentified in our models, including access factors in similar settings (91,92) . These expected findings provide evidence for the validity of our methodology. The finding of a strongly protective effect of personal health corners, underscores the val u national health insurance scheme since 2006 (93) . Increasing model flexibility can reveal nuanced patterns and provide insight for informing targeted interventi o n strategies (94) . The incorporation of linear splines and seasonal interaction terms relaxed assumptions of linearity and temporal consistency, respectively, and both sources of model fl e xibility identified risk factor relationships that


36 may influence the effectiveness of potential interventions. A prominent outcome from our analysis was the major influence of the two modest urban centers in the northern region of the district. The link b e tween urbanicity and malaria transmission has been extensively discussed in the literature (12,95 97) , but understanding the relative impact of the modest urban centers present in the region on health can be challenging (98) , particularly at small spatial scales. For instance, large scale prevalence maps, such as those produced by the Malaria Atlas Project and the and t h e NMCP Oxford 2013 report on malaria stratification, typically categorize all Bunkpurugu Yunyoo within a narrow range of high prevalence (3,80) . However, our results indicate that even within a single holoendemic district, relatively modest urban centers (populations < 8,000) can have a considerable impact on malaria prevalence and spat i al distribution, even ten kilometers or more past the edges of such towns. The revealed non linear relationship between malaria risk and distance to urban centers suggested that the risk associated with living far from the urban center eventually reaches a plateau around twelve kilometers in Bunkpurugu Yunyoo. This is an interesting finding considering that the increased housing density, reduced non polluted water resources, and other urban characteristics resolved about two to three kilometers from the c e nters of the towns, based on field observation and satellite imagery. In addition, IRS coverage was universal across the district and ITN use was the same or improved at the more remote locations. This implies that ecologic and entomologic factors are les s likely to be driving this phenomenon, while socio economic factors may be important. Based on correlations between distance from nearest urban center and other risk factors, potential drives may include easier access to schooling (as


37 suggested by increas e d caretaker education rates), more reliable access to health insurance, elevated community wealth, or underlying factors associated with community ethnic composition. Further analysis of these data and integration with other data source is needed to furth e r explicate this finding, which may be informative for designing interventions specifically tailored to more urban versus rural communities. Similarly, our results suggest that the association between malaria risk and distance to nearest health facility b e comes less pronounced after about two to four kilometers. Comparable rate stabilization patterns at similar distances have been described in health facilities in rural regions of Kenya (99) . Distance to nearest health facility is known to be an important factor in treatment seeking behavior and health ou t comes (100 102) , and carefully characterizing the effect of this distance on health outcomes may be critical for the strategic alloc a tion of health facilities and community based health planning and services. The strength of the association of specific risk factors with malaria parasitemia rates can vary between seasons, which may have important implications for designing interventions . For example, our results indicate that the seasonal difference in malaria prevalence in Bunkpurugu Yunyoo was much less pronounced for older children (50 59 months old) than in young children. These results suggest that interventions designed to reduce burden during peak transmission (i.e. the rainy season) are likely to have a greater effectiveness in infants and young toddlers in terms of keeping them malaria free than those approaching school age, for whom there is a less substantial difference in pr e valence between the rainy and dry seasons. In addition, the seasonal increase in malaria risk was greater for the Konkomba communities than in other


38 ethnicities, suggesting that this is a particularly vulnerable population. Notably this effect emerges eve n after accounting for factors such as distance from urban center, wealth, education, roofing structure, and outside sources of drinking water. This suggests that other factors not captured in this study, such as cultural practices, genetic differences, a n d/or vector related factors (e.g. proximity to livestock hosts), may be contributing to greater childhood malaria burden in this ethnic group. Malaria interventions are often designed and implemented on a seasonal basis, which can be extremely effective m e thod for reducing cost and maximizing impact depending on the local malaria dynamics (103 106) . However, malaria risk factor analyses that do not account for seasonal differences in the effect of some risk factors will fail to capture patterns that might be important for the effectiveness of these seasonal based interve n tions. Including additional covariates to improve model flexibility can reveal meaningful risk factor patterns, but also increases the risk of overfitting, which necessitates the use of sophisticated statistical approaches. In this analysis, both BMA and Lasso regression improved upon the standard logistic regression by shrinking regression coefficients, but there are key differences between these approaches. Lasso regression is adept at constructing sparse models, but suffers when the number of covariat e s is too large and has a tendency to underperform for non sparse data (107) . Additionally, constructing confidence intervals for Lasso re gression coefficients continues to be an ongoing area of research (108 110) . Conversely, credible intervals are easily constructed from BMA, and increasing the number of parameters did not reduce predictive performance. This indicates that increasing the model flexibility in this analysis did not lead to overfitting when using BMA for variable selection.


39 There are other statistical techniques, such as artificial neural networks and support vector machines, which general can detect nonlinear and other relationships, and of t en have better predictive performance than standard logistic regression. However, it is typically difficult to make direct interpretations about the role of individual covariates using these techniques (111) . This is a significant limitation i n the context of modelling disease risk factors, as explicating specific parameters is how individual risk factors are classified and compared, and then used to inform intervention strategies. Model flexibility, interpretability, predictive performance, a nd uncertainty are each important attributes for developing disease risk models. Bayesian frameworks require a deeper understanding in statistical theory and programming, are often times computationally intensive, and may lack accessible tools/software. H o wever, Bayesian approaches offer many advantages for modelling epidemiological data, including high flexibility and intuitive expressions of inference and uncertainty (112) . In this study, BMA consistently outperformed standard logistic regression in out of sample prediction , similar to results in simulation studies (70 72) and studies in other ecological contexts (72 77,113) , including epidemiological risk analysis (78,79) . However further applications of BMA to model risk factors for malaria and other vector borne diseases are stil l needed to confirm our findings. To our knowledge, this is the first instance of using BMA for variable selection to model malaria risk factors. We believe that this methodology offers a flexible framework with many advantages over other methods for model l ing disease risk factors. Conclusion Our risk factor models for residual malaria in young children from a holoendemic district in northern Ghana revealed complex patterns of disease drivers, including


40 nonlinear relationships between malaria status and dis t ance from the nearest urban center and health facility, as well as seasonal differences in risk associated with age and ethnicity. Models quickly become increasingly more complex with additional explanatory variables and regression parameters that allow f o r more flexible modeling of the association of malaria risk to these variables, underscoring the need for reliable methods for model selection. The BMA approach produced easily interpretable models that outperformed standard logistic and lasso regressions in out of sample predictions. We believe that the novel statistical modeling approach shown here for identifying and describing risk factor has potential for expanding the understanding of local drivers of disease, more efficiently targeting and prioriti z ing existing interventions, and informing new interventions, for malaria and other vector borne diseases.


41 Figure 2 1. Map of study district, Bunkpurugu Yunyoo, in northern Ghana (red polygon show in insert map). Interpolations depict malaria prevalenc e in young children (ages 6 59 months) in Bunkpurugu Yunyoo, Ghana during the rainy and dry seasons in the left and right maps, respectively. Six biannual surveys were collected from 2010 2013 an d pooled by season. Black circles denote the sampled comm unities and yellow stars denote local urban centers. Interpolations were made using inverse distance weighted function in ArcGIS 10.3.


42 Table 2 1. Survey based variables. Demographic and Socio Econ omic Variable: Details: Age From 6 to 59 months old Ca Education Binary variable; either (1) for high school education and above or (0) otherwise In years Ethnicity Four groups; (1) Bimoba, (2) Konkomba, (3) Mamprusi, and (4) Other, based on language of caretaker Farming Caretaker * Binary variable; either caretaker occupation being farming (1) or otherwise (0) Gender Binary variable; either male (1) or female (0) Surface Water Source Binary variable; either (1) source of drinking water from exposed surface water or (0) otherwise Thatch Roofing Binary variable; either housing structure had a thatched roof (1) or otherwise (0) Wealth Quintile Constructed from multiple variables, using the methodology of the Ghana Demographic Health Survey (2008) (114) Malaria Inter vention Variable: Details: Health Insurance Personal Binary variable; either personal access to health insurance (1) or not (0) Health Insurance Community Binary variable; community coverage of sampled population or (0) otherwise IRS in past seven months * Binary variable; either individual household having been treated with IRS in past seven months (1) or not (0) IRS in past year Binary variable; eith er individual household having been treated with IRS in past year (1) or not (0) Indoor Residual Spraying (IRS) Community Coverage community coverage or (0) otherwise Insecticide Treated Nets (ITN) Personal Bina ry variable; either (1) if net was used in previous night or (0) otherwise ITN Community Coverage % community coverage or (0) otherwise Personal Medication Use Binary variable; either (1) used in the past two weeks or (0) otherwise


43 Table 2 2. Remote sensing and GIS based Variables. Variable: Source/Satellite: D etails: Distance t o Health Facility GIS Derived Euclidean distance from active health facility at time of survey (based on survey location) Distance to Main Roads GIS Derived (115) Euclidean distance from ma jor roads Distance to Urban Centers GIS Derived Euclidean distance from center with 5,000 individuals Distance to Water Bodies GIS Derived (116) Euclidean distance from rivers and standing water bodies Elevation CGIAR SRTM (117) Meters above sea level Land Surface Temperature Day* NASA (Terra) MOD13A3 (Aqua) MYD13A3 (118) Average monthly daytime temperature (in degrees Celsius) 30 days prior to a survey Land Surface Temperature Night NASA (Terra) MOD13A3 and (Aqua) MYD13A3 (118) Average monthly nighttime temperature (in degrees Celsius) 30 days prior to a survey Norma lized Difference Vegetative Index* NASA (Terra) MOD13A3 and (Aqua) MYD13A3 (119) The maximum monthly index 30 days prior to a survey Population Density WorldPop (120) Pop ulation density per 100 m grid, log transformed 5 y.o.) * WorldPop (120) Pop ulation under 5 years of age density per 100 m grid, log transformed Rainfall (Historical) * WorldClim (121) Average of the cumulative sum of precipitation from three months to one month prior to the survey date from past 50 years Rainfall (Cu rrent)* FEWSNET (122) Average of the cumulative sum of precipitation from three months to one month prior to survey Slope GIS Derived (from Elevation) * Removed from model s due to high correlations (R2 0.49) with one or more other variables.


44 Figure 2 2 . Mean slope estimates (circles) and 95% credible intervals (horizontal grey bars) from probit regression parameters. Variables whose 95% credible intervals do not incl ude zero are considered signif ica nt (labelled in bold). Risk and protective factors are shown in red and blue, respectively.


45 Figure 2 3. Modelled patterns in malaria risk factors based on seasonal interaction terms. The left panel depicts mean slope es timate (lines) and 95% credibl e i ntervals (polygons) for the predicted malaria prevalence based on age in the rainy and dry seasons. The right panel depicts the mean (points) and 95% credible intervals (vertical bars) for the predicted malaria prevalence b ased on ethnic group in the ra iny and dry seasons. Figure 2 4. Implied patterns in malaria prevalence and distance to urban center (left) and distance to health facility (right). Results for the rainy and dry seasons are shown in blue and yellow, respe ctively. The black circles dep ict where slopes are allowed to change (i.e., knot locations), selected at 20% quantiles of the observed data.


46 Table 2 3. Model Comparisons based on the sum of the log likelihood. Base model (p = 29) Sum of log likelihood: Training Testing Logistic Lasso BMA Rainy 2010 Rainy 2011 1072.27 1049.24 1028.24 * Rainy 2011 Rainy 2012 1055.39 1037.49 1032.57 * Rainy 2010 Rainy 2012 1153.62 1110.05 1057.07 * Dry 2011 Dry 2012 969.88 919.45 * 921.54 Dry 2012 Dry 2013 915.95 897.03 * 903.60 Dry 2011 Dry 2013 967.83 920.28 915.81 * AVERAGE: 1022.49 988.92 976.47 Model with interactions and splines (p = 73) Sum of log likelihood: Training Testing Logistic Lasso BMA Rainy 201 0 Rainy 2011 1079.63 1042.02 1027.85 * Rainy 2011 Rainy 2012 1066.56 1035.44 1030.75 * Rainy 2010 Rainy 2012 1156.76 1092.52 1050.55 * Dry 2011 Dry 2012 1065.27 1029.66 921.05 * Dry 2012 Dry 2013 922.40 902.79 902.32 * Dry 2011 Dry 2013 107 9.34 1059.24 917.82 * AVERAGE: 1061.66 1026.95 975.06 p refers to the number of covariates in the model. * indicates the model with the best fit.


47 Fig ure 2 5 . Regression parameter estimates using BMA (black), logistic regression (red), and Lasso regression (gray) models containing interactions terms and s pline covariates (73 independent variables). Parameter estimates were ordered according to the logistic regression resu lts to better illustrate the shrinkage of coefficients associated with the BMA and Lasso algorithms.


48 CHAPTER 3 TO SCREEN OR NOT TO SCRE EN: AN INTERACTIVE FRAMEWORK FOR COMPARING COST EFFECTIVENESS OF MASS SCREENING AND TREATMENT FOR MALARIA INTERVENTION Background Malaria continues to be a significant global health issue which disproportionately impacts young children from rural communiti es in sub Saharan Africa. Mass administration of anti malarial drug treatmen ts (MDA) to entire populations has been used as an intervention strategy for reducing the global malaria burden (123,124) , particularly during elimination efforts in the early to mid 20 th century (125) . Recently, however, interest in MDA as a viable malaria in tervention strategy has reemerged, in particular in conjugation with emergency responses to non malarial epidemics (e.g . the 2014 15 Ebola outbreak in West Africa) (126 129) . Contemporary MDA interventions, primarily through intermit t ent preventive treatment and seasonal chemoprevention campaigns, have been used to interrupt malaria transmission in low endemic settings (130) , as well as reduce malaria burden in vulnerable subpopulations, such as young children and pregnant women, in high endemic regions (131,132) . Traditional MDA interventions are based on presumptive treatment, meaning all individuals in a population or subpopulation receive treatment regardless of symptoms or other diagnostic information. Presumptive treatment ensures that all sick individuals receive treatment, however it also leads to overtreatment, which may undermine the cost effectiveness of MDA. In addition to w asting antimalarial drugs, a significant cost if MDA is based on modern anti malarial medicine such as artemisinin based combination therapy (ACT) (133,134) , there are additional costs associated with increased risk of resistance development by the parasite (135) .


49 An alternat i ve approach to MDA is mass screen and treat (MSAT), which consists of first screening the population with a diagnostic test and then only treating individuals with a positive test outcome. This intervention strategy follows the World recommends that all quality assured antimalarial medicines be distributed on the basis of confirmed test results. Because microscopic evaluations and molecular techniques (e.g., polymerase chain rea c tion) are often not a viable option in remote regions and/or at large operational scales, diagnosis is increasingly based on rapid diagnostics tests (RDT) throughout much of sub Saharan African (123,136) . RDT screening has been repeatedly shown to be a viable, cost effective option for diagnosing m alaria (137,138) . The widespread use of RDTs has significantly reduced the use of antimalarial drugs, helping to reduce the risk of resistance emergence (139,140) . Context is an important consideration, as the baseline likelihood of infe c tion is differen t in a clinical setting than in a mass administration, however MSAT relying on RDT outcomes has been shown to be a cost effective method for reducing malaria burden (141) . Determining when and where MSAT is more cost effective than MDA is an important challenge (130) . On the one hand, despite the potential of MSAT to reduce costs and overtreatment, there have been notable failur es in field studies (142 144) whereas, on the other hand, large scale antimalarial distributions are likely to accelerate the emergence of drug resistance (145,146) but see (147) . The emergence of resistance is a p articularly important concern given the growing consensus that repeated interventions are necessary for sustaining the impact of MDA and MSAT (130,148 150) . A recent Cochrane review has indicated that 182 studies have assessed the impact of


50 (124) , however, to our knowledge, few guidelines have emerged to help decision makers dete rmine when MSAT is a more cost effective strategy than MDA. In general, MSAT is thought to b e the preferred approach in high to mid transmission settings (151) , which was supported by the study from Crowell et al. (125) . In contrast, however, Walker et al. (152) found that MDA wa s more cost effective than MSAT in all but the highest transmission settings, and noted that the slight cost deficit in these areas was likely offset by the additional period prophylaxis provided to post intervention infected individuals (153) . Gerardin et al. (154) , on the other hand, argued that, in control/pre elimination settings, th e cost of overtreatment by MDA may mitigate the detection advantage (i.e. ensuring all infec ted individuals are treated), and therefore undermine the cost effectiveness of MDA compared to MSAT. Corroborating these findings with field research has been diff icult, as much of the observed data on recent MDA and MSAT applications is held in grey lite rature and unpublished reports (124,130) . Multiple factors can influence the effecti veness of MSAT relative to MDA. For example, unlike presumptive treatment, inaccurate diagno s tic results in MSAT can lead to both overtreatment and undertreatment. Although RDT have high overall sensitivity (above 93%) and specificity (above 95%), a compre hensive review of field studies found substantial heterogeneity in RDT performance (155) . Additionally, t he detection mechanism differs among different types of RDTs . For example, commonly used HRP 2 based RDTs such as Paracheck® will fail to detect infections caused by non Plasmodium falciparum species or by P. falciparum parasites which carry mutations to th e HRP 2 gene, resulting in false negative results (156,157) . False positive results can


51 also arise given that the HPR 2 protein can persist in the host for up to 2 to 3 weeks after parasitaemia has cleared (157) . Ultimately, the potential cost savings advantage of MSAT over MDA depends on baseline likelihood of infection (i.e. prevalence), RDT sensitivity and specificity, the direct costs of treatment and RDTs, and the indirect costs associated false positive an d false negative results (56,154) . However , many of these factors can vary substantially between regions throughout sub Saharan countries (56,155) and, as a result, it can be difficult to generalize which strategy is likely to be the most cost effective interventions in each region (158) . Nevertheless, identifying the optimal strategy in each region is important for stakeholders and policy implementers as national malaria control programs move away from size fits (65) . In thi s chapter , we outline a conceptual framework for comparing the cost effectiveness of malaria intervention strategies based on the probability of their possible outcomes and the costs associated with those outcomes, focusing on the comparison between MDA an d MSAT. First we demonstrate this comparative framework using hypothetical scenarios for each of these factors. Next, we create probabilistic models for estimating malaria prevalence and RDT performance using routinely collected national scale survey data (e.g., Demographic Health Surveys (DHS) and Malaria Indicator Surveys (MIS)) to present a real world application. Finally, using these models, we build an interactive web application which allows end users to determine the most cost effective interve ntion in each region based on the inputted economic values. Methods Estimating C ost effectiveness The expected cost per person associated with MDA and MSAT interventions can be estimated as a function of the costs of these interventions, the costs associat ed wit h


52 the potential outcomes , and the probability of those outcomes. The possible outcomes for an individual participant in an MDA campaign are either true positive or false positive, whereas an individual participant in an MSAT campaign may also be true negat ive or false negative (Figure 3 1). To determine the probability of each of these potential outcomes , we calculate the likelihood of malaria infection , the sensitivity , and specificity of the screening d iagnos tic test (model variables are defined in Tabl3 3 1) . Cost items include cost of the diagnostic test used for screening ( ), the cost of antimalarial treatment ), and the indirect costs of false negatives ( ) and false positives ( ) . Notice that the indirect costs of false negative or positive diagnostic outcomes may incorporate multiple sources of cost (i.e., lost wages due to illness). The per person expected cost of MDA is given by: The per person expected cost of MSAT is: where, based on t he law of total probabilities, is given by This framework could be augmented through the inclusion of additional layers of complexity, such as the inclusion of overal l program level costs and/or an expanded set of possible outcomes (e.g. likelihood of developing severe malaria and the associated costs), if data on these costs and outcomes were available for individual regions.


53 Determining outcome probability based on p revalence , sensitivity, and specificity Data collection Information on malaria status of children five years old and under were sourced from Demographic and Health and Malaria Indicator surveys (DHS and MIS, respectively). These data are freely available, use stan dardized sampling procedures, and contain information on a broad range of malaria indicators, such as age, urbanicity, and fever history. Recent surveys were selected for Burkina Faso (159) (160) , Ghana (161) , Guinea (162) , Nigeria (163) , and Togo (164) . These West African countri es were selected because they each contain relatively recent standardized country wide surveys and included information on RDT and microscopy (assumed to be (165,166) ). Individual survey sam ple sizes ranged from 2,713 to 6,112 individuals, distributed across 6 to 13 regio ns per country (Table 3 2). Modelling prevalence, sensitivity, and specificity Malaria prevalence was estimated separately for each country using Bayesian mixed effect logis tic regression models. Microscopy cting malaria infections in th is region (165,166) , and RDT was considered the screening diagnostic test. Let represent the binary infection status (as determined by microscopy) of individual from cluster i n region . We assume that is given by where is the probability of infection (e.g., prevalence). We constructed the model using just two basic covariates that could be relevant for the developm ent of region specific policy , namely age in months and a binary classification of urban/rural


54 environment . Using the logit link function , we model infection probability as This equation includes a cluster level random effect intercept , regional level fixed effects (i.e., intercepts and slopes and ), and co untry level fixed effects (i.e., country level slopes and urbanicity ). In relation to RDT, let represent the binary test outcome (1 for positive, 0 for negative) of individual from cluster in region . We assume that: where and denote the RDT sensitivity and specificity, respectively. Both of these par ameters were modelled with the sa me set of predictor variables and link function as . Individual models for prevalence, sensitivity, and specificity were created for source R statistical software (89,167) . These models relied on the default prior distributions (flat priors for the fixed effects, and half student t with 3 degrees of freedom and a scaling factor of 1 for the standard deviation of the random effects). Each model was fitted using 4 independent chains with a 1,000 iteration s burn in phase and a 1,000 iteration s sampl ing phase. Parameter convergence was determined using the potential scale reduction factor (convergence at ) (168) .


55 Designing the I nteractive F ramework Based on the outlined cost functions and associated outcome probabilities, we developed an interactive framework which allows use rs to compare the cost effectiveness o f MDA and MSAT in each region (as defined by DHS/MIS) within each (169) , a package that enables the creation of web based interactive applications directly from R code (instead of HTML, CSS, or JavaScript), which can then be freely hosted and accessed on the internet. Web applications like this can facilitate engagement with stakeholders and policy makers with limited statistical and programming backgrounds. Examples of other epidemiological inte ractive tools developed in shiny can b e found in (170 173) . By using probabilistic models for specifying the outcome probabilities we are able to compare intervention scenarios while accounting for uncertainty. Aside from inputting costs, the interface allows us ers to select covariate values (i.e. country, age range, and based visualization of the cost effectiveness comparison (174) . The code used to create this tool is available at { https://gi msat }, and the application can be accessed at { https :// general/ } 2 . We also constructed a the user to specify a range for RDT sensitivity and specificity and compare MDA vs MSAT over all possible prevalence rates (rather than modelling these parameters from data), which is accessible at { msat }. 2 shiny::runGitHub(" mda msat", "justinmillar", subdir = "base").


56 Results General C omparisons Using general cost and diagnostic accuracy parameters from the W HO (175) , MSAT is preferred in nearly all but the highest disease burden settings when the cost of fals e negatives is ignored (Figure 3 3A). However , screening becomes less cost effective in higher prevalence scenarios onc e the cost false negatives is assumed to be equal to the cost of treatment (e.g., an RDT negative individual eventually receives treatmen t; cost of $2.4 (175) ) (Figure 3 3B). The individual level cost of MSAT can be further undermined if the overall economic burden of false negative includes additional costs. For instance, if we assume that a person with fal se negative results also incur s a day of lost wages (cost of $23.95, based on hourly rate and assuming eight hours per workday based on t he median monthly income in sub Saharan from World Bank estimates (176) ), then screen and treat yields a significantly higher costs (Figure 3 3C). Finally, the primary effect of includ ing a cost associated with false positive is raising the cost of presumptive treatment in lower burden settings, which is eventually offset by costs associated with misdiagnosis in the screen and treat scenario as prevalence increases (Figure 3 3D). Contex t specific R esults based on N ational scale S urvey D ata Individual models for malaria prevalence and RDT sensitivity and specificity rates for young children (6 to 59 months old) were fitted for all six country datasets. In each model, all parameters reache d convergence based on the potential scale reduction factor. The followings sections illustrate the influence of the re gression parameter estimates, cost scenarios, and parameter uncertainty on the cost effectiveness comparison for Burkina Faso.


57 Effect of false negatives on cost effectiveness Designating costs specifically related to incorrect diagnostic results can have profound impacts on the cost effectiveness of the screen and treat intervention. Consider the rural communities in Burkina Faso (Figure 3 3), which fall within the mid to high transmission setting where MSAT is considered to be viable and potentially cos t effective (based on literature review) and where both clinical trials and mathematical studies have examined the effectiveness of MSAT (142,149,177) . We choose a favorable cost setting for MSAT by setting RDT cost to $0.60 and antima larial treatment cost to $2.55. These costs correspond to the lower and higher ends of RDT and antimalarial prices, respectively, based on the WHO report (175) . Figure 3A shows the estimated value added from screening per individual for rural communities in Burkina Faso ass uming no cost associated with false negatives or false positives. As expected, we fin d that under these conditions MSAT is favored in most regions in Burkina Faso, and there are no regions that favor MDA. However, MSAT becomes less cost effective once we a ttribute cost to false negative outcomes. When the cost of false negatives is set to the cost of the antimalarial treatment, which corresponds to a scenario where all truly infected individuals will eventually pay to receive treatment, MSAT becomes less co st effective. MSAT is only favored in three regions and there are more regions where MDA may be more cost effective or the economic difference between MDA and MSAT is unclear (Figure 3 3B). MSAT becomes even less cost effective as the cost associated with of false negatives increases . Under the hypothetical scenario where a false negative Faso ($6.37 per day , based on (17 6) ), MDA is favored in all but two regions , despite


58 relatively high prevalence rat es (ranging from 0.26; CI: 0.18 0.36 to 0.66; CI: 0.53 0.77) (Figure 3 3C) . Differences between urban and rural communities As outlined earlier, there are many factors which influence malaria prevalence and RDT performance, and therefore may influence the cost effectiveness of confirmative versus presumptive treatment. One factor that strongly determine these variables is the differences between urban and rural communit ies. Although there is considerable regional level variability in malaria prevalence within rural communities in Burkina Faso, rural communities consistently have higher prevalence than their urban counterparts (Figure 3 4). Interestingly, regional RDT sensi tivity and specificity rates also consistently decline from rural to urban communit ies. These differences between urban and rural communities can determine which intervention strategy will be the most cost effective. Figure 5 depicts the same cost scenario s as Figure 3 for both rural and urban communities in Burkina Faso. These compariso ns generally indicate that higher prevalence rural communities will tend to favor MSAT while lower prevalence urban communities tend to favor MDA, although these comparisons greatly depend on cost assumptions. The Nord region was the only region where both urban and rural communities favored MSAT in all cost scenarios. Interestingly this was not linked to particular prevalence rates, which were not too different from the othe r regions (0.16 and 0.47 for urban and rural communities, respectively), but instea d to having the highest sensitivity and specificity rates for both community types. Estimating regional breakpoints for treatment and RDT costs In addition to comparing the cost effectiveness of presumptive and confirmative interventions based on specific values for the direct costs of treatments and diagnostic


59 tests, it may also be valuable to identify the breakpoints for these costs. For example, under different scenarios o f false positive and false negative costs, we can use the estimated regional malari a prevalence, RDT sensitivity, and RDT specificity to determine the cost of RDT and treatment for which MDA (or MSAT) would be more cost effective. Figure 6 illustrates this using the scenarios in the previous examples for Burkina Faso, assuming no cost as sociated with false negatives (Figure 6A) and negatives (Figure 6B) . Notice that, as expected, for a given cost of RDT, the cost effectiveness will tend to favor MSAT as the price of treatm ent increases. Similarly, for a given cost of treatment, MDA is favored as RDT cost increases. This breakpoint tends to be lower in rural communities, which typically have h igher prevalence rates, and increases when we include indirect costs associated wit h false negative results. For example, the dashed veritcal and horizontal lines demonstrate this relationship using the RDT and treatment cost for the previous example ($0.6 0 and $2.55, respectively). Based on these costs , MDA will be favored in most rural districts whereas MSAT may be more cost effective in the urban communities for some districts. These figures illustrate the critical role of the ratio of treatment cost and screening cost in determining the cost effectiveness of these interventions and th at regional characteristics (prevalence and diagnostic test performance) strongly mediate the relationship between this cost ratio and intervention cost effectiveness. For e xample, the Hauts Basin region is highlighted to demonstrate how including a indire ct cost associated with false negative results in a substa nti al shift towards favoring MSAT.


60 Interactive A pplications In order to expand the utility of this framework beyon d these hypothetical scenarios, we constructed two interactive tools using the Shiny package in R. The first general/ . Following the conceptual framework (Fig. 1), this tool a llows the user to set the direct costs of treatment and diagnostic test (RDT), the indirect costs of false positive and false negative outcomes, and a rang e for the potential diagnostic sensitivity and specificity. The tool relies on these user defined inp uts to estimate the cost of MDA and MSAT across all possible prevalence, generating an output similar to the plots in Figure 3. The second tool is based on the data from national surveys and modelling outcomes from prevalence, sensitivity, and specificity, and is avaiable at example/ . This tool allows the user to s elect the country and setting (e.g., age range and urban or rural communities), as well as the same c ost parameters in the first tool. The outputs are similar to the comparisons shown in Figures 3 4, 3 5, and 3 6. Discussion As described in the comprehensi ve review by Newby et al. (130) , many studies have been published on the impact and effectiveness of MDA and MSAT. Impl ementation of both interventions have experienced both successes and failures. Moreover, simulations based on mathematical models comparing the cost effectiveness of MDA and MSAT have in some cases provided conflicting recommendations (125,152 154) . Rather than using math ematical models, our contribution to this important question of resource allocation focuses on using statistical models to quantify the probability of diff erent outcomes associated with each intervention. In addition, we use these


61 statistical models to pow er interactive decision support tools, in which users set the cost parameters and interact directly with inference from our statistical models in an open s ource, cross platform format. We have prioritized a methodology that would be maximally flexible and accessible, including using familiar publicly available data and relying on relatively simple statistical models and tools developed in open source and fr ee software. Unfortunately, there are several notable limitations associated with the data that we us ed. First, in order to model malaria status and diagnostic sensitivity and specificity, we assumed microscopy to be the gold standard. While microscopy is still considered to be the gold standard in western sub Saharan Africa (165,166) , it has been well established that microscopy based diagnosis are imperfect (166,178,179) , and that several factors (e.g., paras ite density) can influence the accuracy of microscopy (180) . If data on more precise diagnostic tests (such as polymerase chain reaction) were available at national scales, then better estima tes of RDT sensitivity and specificity could be generated, leading to improved cost effectiveness com parisons. Second, the approach for calculating cost effectiveness of MDA and MSAT presented in this article is intentionally simplistic because data that would support a more comprehensive national level analysis for multiple West African countries were n ot available. For instance, in addition to the individual level costs there are also fixed programmatic level costs of implementing each intervention, whic h are unlikely to be equivalent for MDA and MSAT (e.g., RDT based intervention required additional tr aining, storage, etc.). Furthermore, we discuss the individual level cost of receiving the intervention, but do not take into account how these interventio ns influence


62 morbidity/mortality metrics (e.g., disability adjusted life year ). In particular, determ ining which metric to use for the cost effectiveness comparison is important for defining the goal of the intervention (e.g., interrupting transmission or reducing malaria burden). Finally, if national level data on malaria prevalence and RDT performance were available for febrile patients seeking help at health facilities, tools like the one described in this article could be developed for clinical setting to determine where and when test and treat would be a better option than presumptive treatment. In t his case, one could also account for other potential outcomes, such as developing severe malaria (which may have a specific associated cost), not adhering to a diagnostic test result, and the development of adverse side effects to treatment. The WHO recen tly identified a pressing need for modelling based approaches to guide the selection of optimal interventions under difference epidemiological conditions (38). Decision support tools designed specifically for malaria control, particularly usin g mapping app roaches and geostatistical models, have become more prevalent in recent years as national survey data have become more broadly accessible (181 184) . Our framework aims to provide a decision support tool for stakeholders to decide whether MDA or MSAT will be more effective in different regions. We have demonstrated that such tools can be created and adapted using a standar d, open sourc e program, helping to bridge the gap between scientific knowledge generation and real world decision making. These decision support tools are critically important as national malaria control programs have identified the need to move away from size fit s require tools for identifying optimal interventions based on location conditions (185) . The


63 applications prese nted in this article contribute to the growing pool of decision support tools for guiding malaria control interventions. Similar to the work by Lubell et al. (181) , one valuable characteristic of the support tool presented is interactivity. Standard results presented in scientific articl es are limited to the parameters or scenarios selected by scientists, which often do not necessarily match those that would have been chosen by decision makers. Furthermore, often decision makers must consider additional infor mation that is either unknown or unaccounted for by the original developer, which is only possible if users can explore different scenarios within the decision support tool. Additional properties of the tools presented in this article are that they rely so lely on a freely available ope n source program, can be hosted on web applications (which makes them platform independent), and can be completely built using software regularly used in epidemiological research. Finally, by using Bayesian based frameworks fo r modelling the data and inter active inputs for defining cost parameters, our application allows stakeholders to make informed decisions by taking into account uncertainty in the outcomes under different cost scenarios. Conclusion We present a flexible fr amework for comparing the cost effectiveness of malaria interventions (specifically MDA and MSAT), and use this framework along with publicly available malaria data from national scale surveys to construct an interactive decision support tool. The methodol ogy used to create this tool a ddresses critical issues (e.g. cross platform, open source, real time interactivity) with previous decision support tools for guiding malaria interventions, and can be built using widely used open source software. The tool pr ovides a platform for decision makers (who may not have robust


64 statistical backgrounds) to interact with statistical models, and adjust the parameter to fit their context and external knowledge in order to support data driven decision making. We believe th at similar decision support to ols designed to fit specific malaria interventions and contexts will be a valuable asset for guiding data driven decision making for malaria control and elimination in a way that recognizes the inherent differences between reg ions .


65 Figure 3 1. Flow diagram representing the conceptual framework for comparing the cost effectiveness of mass drug administration (MDA) and mass screen and treat (MSAT) based on the potential outcomes and associated costs. Direct and indir ect costs are shown in blue an d red, respectively. FP and FN stand for false positive and false negative, respectively. Table 3 1 . Parameter definitions for expected cost equations Equation Parameters Description Cost of treating one person (e.g. cost of one antimalarial drug) Cost of one rapid diagnostic test (RDT) Cost associated with one false positive outcome Cost associated with one false n egative outcome Likelihood of microscopy outcome (1 = infected, 0 = uninfected) Likelihood of RDT outcome (1 = positive, 0 = negative) Likelihood of false positive (based on microscopy gold standard) Likelihood of false negative (based on microscopy gold standard)


66 Table 3 2. Summary of Data Sources Country Survey Type Collection Period Sample Size Regions Burkina Faso Malaria Indicator Survey (159) 2014/09 2014/11 6112 13 Cote Demographic Health Survey (160) 2011/12 2012/05 3344 11 Ghana Demographic Health Survey (161) 2014 /09 2014/12 2713 10 Guinea Demographic Health Survey (162) 2012/11 2013/02 3198 11 Nigeria Malaria Indicator Survey (163) 2014/10 2014/12 5127 6 To go Demographic Health Survey (164) 2013/11 2014/04 3215 6


67 Figure 3 2 . Comparison of the cost effectiveness of presumptive treatment (red) and screen and treat (blue) as a function of malaria prevalence. Each panel d epicts a different scenario relative to the costs associated with false positive (FP) and false negative (FN) o utcomes, as specified in the legends. The lower estimated cost (y axis) indicates the more cost effective strategy for a given prevalence rate (x axis). RDT sensitivity and specificity ranged from 0.82 0.96 and 0.80 0.90, respectively, and the cost of treatment and RDT were set to $2.40 and $0.60, based on a WHO report (175) . The gray shaded region indicates overlap in expected cost, where the more favorable strategy is un clear due to the range of possible values for RDT sensitivity and specificit y.


68 Figure 3 3. Rural community comparisons of regional value added (per individual) from diagnostic screening in Burkina Faso. Regional maps of the mean value added and value add ed estimates are shown on the left and right panels, respectively. Positive values (blue) indicate regions where screen and treat (MSAT) is favored whereas negative values (red) indicate regions where presumptive treatment (MDA) is favored. Error bars indi cate 95% credible intervals. When these intervals contain both positive and negative values, there is no significant difference regarding cost effectiveness between strategies (gray). Cost of diagnostic test (RDT) and treatment were set at $0.60 and $2.55, respectively. Panel A depicts added value estimates ignoring any potential costs associated with false negative results. Panel B depicts value added estimates when cost associated with false negative results is set to the cost of receiving delayed treatme nt. Panel C depicts value added estimates when cost associated with false ne gative results includes the cost of receiving delayed treatment and one day of lost wage (based on minimum wage ( 176) . In all of these scenarios, we assume no cost associated with false positive outcomes




70 Figure 3 4. Regional estimates of early childhood malaria prevalence and RDT sensitivity and specificity in Burkina Faso. Mean value estimate (circles) and 95% credible interval (vertical bars) for each region are based on 1,000 po sterior draws from each model. Each region has a unique shade and is connected by a dotted line to depict differences in parameter estimates between urban and rural communities.


71 Figure 3 5. Comparison of regional value added (per individual) from diagnos tic screening in between urban (left plots) and rural (right plots) communities in Burkina Faso. Positive values (blue) favor screen and treat (MSAT), negative values (red) favor p resumptive treatment (MDA), and 95% interval ranges that contain both positi ve and negative values indicate no significant difference (gray). Cost of diagnostic test (RDT) and treatment were set at $0.60 and $2.55, respectively. Panel A depicts added value estimates ignoring any potential costs associated with false negative resul ts. Panel B depicts value added estimates when cost associated with false negative results is set to the cost of receiving delayed treatment. Panel C depicts value added estimates when cost associated with false negative results includes the cost of receiv ing delayed treatment and one day of lost wage (based on minimum wage (176) . In all of these scenarios, we ass ume no cost associated with false positive outcomes.




73 Figure 3 6. Region al breakpoints for cost of treatment and diagnostic test (RDT) in Burkina Faso. Cost points above the line favor screen and treat treatment (MSAT) in that region, whereas cost points below the line favor presumptive treat (MDA). Rural and urban communities are depicted on the left and right columns, respectively. Panel A assumes no cost associated with false negative results, and Panel B incorporates a cost associated with fals e negative results which includes the cost of one day of lost wages (based on mi nimum wage (176) ). The blue line represents the Hauts Basins region, which is referred to in text. In all of these scenarios, we assume no cost associated with false positive outcomes.




75 CHAPTER 4 ASSESSIN G AND PROJECTING THE INFLUENCE OF ACCESSIBILITY TO LOCAL HEALTH FACILITIES ON CHILDHOOD MALARIA IN NORTHERN GHANA Introduction Despite the significant progress in reducing the global malaria burden, there are still many regions which experience high prevalence and transmission rates. These remaining pockets of high burden disproportionally impact young children in sub Saharan Afri ca (1) . In addition to pre exposure interventions such insecticide treated nets (ITNs) and ind oor residual insecticidal spray (IRS), post exposure interventions such as access to effective diagno sis and treatment with artemisinin based combination therapy (ACTs) have had a significant impact on reducing malaria related morbidity and mortality (3) . Regions wit h high coverage of ITN and IRS which continue to experience on lo cal conditions (8,9) . To this end, optimizing accessibility to local health facilities is likely to be an important component of effective malaria control and progression towards elimination. In an effort t o reduce childhood mortality and reach universal healthcare, Ghana im plemented the Community based Health Planning and Services (CHPS) program in 2000 (186) ] . The primary function of the CHPS program is to train and place community health officers in underserved communities. These officers provide vital medical services, includ ing the distribution to antimalarial treatments (187) . Early implementations of the CHPS program indicated significant progress towards reducing childhood mortality, and showed promising potential for scalability (188,189) . In 2013, the Ghana Essential Health Intervention Project (GEHIP) was enacted in order to


76 facilitate the expansion of the CHPS program in northern Ghana (187) , which nearly halved the under five mortality rates relative to the comparison distri ct over a five year period (190) . Moreover, this program had a low implementation cost and demonstrated efficient allocation of resources (191) , indicating that it may be a viable supplemental malaria control strategy for areas of Ghana with residual transmission. Determining the optimal location of the CHPS facil ities describe above is very important. Indeed, a ccessibility to health facilities has long been rec ognized as a significant factor for controlling malaria burden (192,193) . While there are many other factors that contribute to accessibility, suc h as cost (194,195) and social network systems (196) , geographic distance is often recognized as a sign ificant impediment to effective treatment (38,197 199 ) . As a result, distance to nearest health facility is highly associated with childhood mortality in sub Saharan Africa (39,100,200,201) . Importantly , simple Euclidean distance has been de monstr ated to underestimate the actual distance travelled, and therefore travel time is often a better metric for measuring geographic distance (100,202,203) . This study models the influence of travel time to the nearest health f acilit y on early childhood (under five years old) malaria prevalence within a single hyperendemic district in northern Ghana. Furthermore, we determine how the CHPS compounds in this district impact geographic accessibility, and project the potential impac t of a dding additional facilities. Finally, we construct an interactive tool to help aid decision makers in determining the optimal location for a new facility.


77 Methods Data Collection Field setting The data for this study were collected in Bunkpurugu Yu nyoo, a rural district in northeastern Ghana which is hyperendemic for malaria and experiences high transmission during the rainy season. The primary malaria vectors in the region are Anopheles gambiae sensu stricto (s.s.) and Anopheles funestus (82) . This area has received mu ltiple distributions of long lasting insecticide treated bed nets and indoor residual insecticide spray, however malaria burden remains high (i.e., prevalence greater than X%) , especially for young children (less than 5 years old) (80,81) . Malaria status The malaria status of children up to 59 months was collected over six biannual from 2010 to 2013 as part of operations research conducted by the U niversity of Ghana (10,11) . This study uses individual level malaria data from the three surveys conducted during the three rainy seaso ns fro m 2010 to 2012. Each survey was conducted within a three week period in late October to November. The sampling protocol closely followed that utilized by the Demographic and Health Survey, where households are selected for each survey using a multi stage randomized cluster sampling technique, with villages sampled with probability proportional to population size and households randomly selected within these villages . This sample covered approximately 20% of the under five population in each survey, b ased o n 2010 census data. Malaria status was determined using blood film microscopy. Location coordinates were recorded at a central location in each community with a handheld GPS. Individuals under 6 months old were removed from


78 the analysis, and only com muniti es with at least 20 observations were used to fit the statistical model. Accessibility to health facilities We calculated a ccessibility using the global travel time surface provided by the Malaria Atlas Project (MAP) (203) . This comprehensive data set estimates how long it takes humans to travel through a landscape by combining multiple p olitical, infrastructural, and environm ental sources to create a 1 k m 2 for the entire globe. Using this friction surface, we calculated the time it takes to travel to the nearest health facility based on the least cost path an alysis (204) , which accumulates the cost of moving through each pixel to estimate a more accurate path (and therefore time/distance) than Euclidean distance. The least cost pat h analysis was (89,205) . Raster s were created both with and without including the active CHPS compounds, and a one way paired t test wa s used to determine if the CHPS compoun ds significantly reduced the travel time for the surveyed communities. Additional risk factors In addition to accessibility to health facilities, we also included in our model several other factors that are likely to strongly influence malaria risk. For ex ample, t here are two modest urban centers in this district, Bunkpurugu and Nakpanduri, with approximate populations of 5,500 and 7,500 , respectively , and the effect on malaria of proximity to these settlements has bee n shown to be important (206) . Similarly, t he district has an escarpment along the northern reach and c ommunities atop the escarpment, including the urban centers, tend to be drier and hav e lower malaria burden, whereas the low lying communities are more rural, have denser vegetation, and


79 much higher burden. Finally, the distribution and density of the study population (6 to 59 months old) tends to be more heavily concentrated in and around the urban centers but are distributed across the rural communities throughout the district. Aside from being a potentially important malaria risk factor, population density enables us to calculate the expected number of infected individuals, which is one of the key outcome variables when determining the optimal location of health facilities. Distance to the nearest urban center (in meters) was based on Euclidean distance, and calculated in R (207,208) . Elevation (meters above sea level) was based on the 90 m resolution digital elevation map from Consortium for Spatial Information (117) . Vegetation was represented using n ormalized difference vegetative index (NDVI) was based on the maximum monthly index 30 days prior to a survey from MODIS (119) . Density of the under five year old population was sourced from the five year stratified WorldPop 2014 population estimates (209 211) , with an original raster resolution of approximately 100 m (0.0083 decimal degrees). Modelling Malaria Prevalence Raster data for each of these variables were ex tracted to the survey point data (212) . At each spatial point t he variable value was based on the mean bilinear interpolation of the neighboring grid cells in the associated raster. These data where then used to fit a generalized additive model (GAM) with a logit link (213) . This methodology allows for nonlinear effects of the selected predictors, being more flexible than a standard logistic regression. Accessibility to health facilities w as modelled using natural splines at fixed intervals (henceforth r s were set to 5, 10, 15, 30, 45, and 60 minutes travel time based on the distribution of the


80 observed data and functional applicat ion (e.g. regular intervals that could be useful for guiding field operations) . Distance to nearest urban center was modelled using an additive cubic spline, which incorporated a smoothing penalty to reduce overfitting. The remain variables were modelled a s standard linear predictors. These design decisions were based on the comprehensive risk factor analysis of these data (excluding the accessibility data) available at (206) . An overview of the methodological theory and implementation of GAMs is available at (214) . In order to estimate prevalence in unsampled regions of the district, a 1 k m 2 resolution grid was created over the district, and predictor variables were e xtracted from the raster data. Accessibility to health facilities and distance to nearest health facility were calculated using the centroid of each grid cell (207) , population density was based on a sum of the underlying raster cells, and the remaining variables were extracted as a bilinear interpolation of the mean neighboring raster cells. The fitted GAM model was then used to predict malaria prevalence across the district. Projectin g the Impact of New Health Facilities The fitted model was used to estimate the potential impact of new health facilities in Bunkpurugu Yunyoo. The optimal location of new health facilities was determined using a Nelder Mead optimization algorithm. To avoi d finding only local minima, the algorithm was initialized with 20 random selected coordinates using the centroids of the We adopted a sequenti al strategy to identify the optimal placement of health facilities . In other words, we first determined the optimal location of the first health facility. Based on the existing health facilities, including this recently created health facility, we then det ermined the optimal location of the second health facility. This p rocedure was done repeatedly until the optimal placement of 5 new


81 health facilities was determined. Instead of simultaneously determining the optimal location of all 5 new health facilities, we adopted this sequential approach because it more closely mimic s how these health facilities would be created in the real world (e.g., resources would probably only be available for the creation of one health facility at a time). Separate optimizations were performed to minimize the following metrics: prevalence acros s the district, the number of expected cases (which was estimated using the prevalence predictions and the under five population density raster data), and the average travel time to the near est health facilities. Finally, to enable decision makers to expl ore the impact of other possible locations for new health facilities, we created an interactive web based application using (169) . This application allows an end user to propose a location for a new health facility, and then , after recreating the accessibility surface , it displays the projected prevalence and expected number of cases using the GAM. The application is freely accessible online at health facilities / . Results Accessibility to Health Facilities Based on the MAP friction surface (203) , the average time to the nearest hea lth facility in Bunkpurungu Yunyoo was 37.3 minutes (15.9 to 52.1 minutes IQR) (Figure 1). The spatial distribution of travel times largely reflects the known distribution of roads, elevation, and land cover patterns in the district, in conjunction with th e general Euclidean distances. A notable exception, however, were the northern most pixels, which exhibited the highest travel times despite not havi ng exceptional high Euclidean distances from the nearest health facility or prominent land cover features t hat would impede human transport. This is most likely due to these pixels having close proximity


82 to border with Togo, as the MAP friction protocol pl aces a cost penalty on country boundaries. However, this border is known to be porous, with migration occur ring frequently. Additionally, there were no sample communities in this region of the district. Therefore, any model interpretations and predictions within this part of the district should be made with caution. The three active CHPS compounds during the s ampling period were each located along the east west extent between the two urban centers (Figure 1A). Despite their close proximity to each other , t hese compounds reduced travel times for 29 of the 135 sampled communities (21.5%), with a reduction of aver age travel time to the nearest health facility from 23.7 to 13.9 minutes (Figure 1B Model Interpretation The output from the fitted GAM suggests that accessibility to health facilities is a significant nonlinear predictor for early childhood malaria in Bun kpurungu Yunyoo. All but one of the natural spline covariates used to model travel time to the nearest health facility were significant effects (p va lue < 0.05) (Table 4 1). Figure 4 2 illustrates the nonlinear relationship between travel time to nearest h ealth facility and malaria prevalence when the other model covariates are set to the ir median value s . The predicted malaria prevalence increased rapi dly as travel time to the nearest health facility increased even over relatively short estimated travel tim es (e.g. from 0 to 5 minutes). After this sharp increase , predicted prevalence rates were relatively flat until experiencing another increase as trav el times exceed ed 30 minutes, and levelled off again as travel times approached an hour or more. Figure 4 3 illustrates the predicted prevalence rates for the other independent variables when all other covariates were held to their median value s . The cubic natural


83 spline used to estimate the effect of Euclidean distance to the nearest urban center was also a s ignificant predictor for early childhood malaria prevalence (Table 1). T his nonlinear relationship was fitted non parametrically using a ge neralized smoothing (215 ,216) . Predicted prevalence rose gradually as distance to the nearest urban center increased, plateaued around 8 km then increased again a round 13 km, and finally level ed off around 17 km. Elevation was the only significant linear predictor (Table 4 1), w ith predicted malaria rates being lower at the higher elevations. NDVI and population density were not significant predictors for early chi ldhood malaria in Bunkpurungu Yunyoo (Table 4 1). Predicting p revalence and c ases Early childhood malaria prevale nce rates were estimated for the entire district using the fitted GAM and the 1 km 2 aggregated data on the predictors (Figure 4 4A ) . Preval ence rates were relatively low (approximately 15 to 25%) near the two urban centers, and exceptionally high in the lo w lying rural areas in the southern portion of the district. The confidence intervals associated with these predictions were greatest in th e northern most pixels, followed by a patchy distribution in the southern portion of the district (Figure 4 4B). The uncertainty in the northern pixels is likely due to the exceptionally high estimated travel times to nearest health facility, which were no t well represented in the training dataset, whereas the patchy uncertainty in the south was most like ly driven by oth er covariates, such as very low population density and elevation relative to the sample communities. The distribution of prevalence rates a cross the district was roughly bimodal, with peaks around 50% and 80% (Figure 4 4B). The expected number of cases wa s estimated using the predicted prevalence and the under five population density data (Figure 4 5A). Unlike the predicted


84 prevalence rates, the distribution of expected cases was far more patchy due to the uneven distribution of young children in Bunkpurun gu Yunyoo. The greatest number of expected cases were clustered on the two urban centers, followed by some of the communities distributed a long the east west expanse between the urban centers. Expected cases were high in these areas despite having the lowe st estimated prevalence due to substantially higher population densities. This is also where the uncertainty (based on the width of the con fidence intervals) was the highest (Figure 4 5B). The estimated number of cases was relatively normally distributed, with most pixels containing 1 to 10 expected cases (Figure 4 5B). Making predictions outside the range of the training data can lead to spu rious results [48] . This issue can be magnified when using complex models such as GAMs which may contain higher order polynomial terms [49 ] . Figure 4 6 illustrates the value range captured by the training data (survey samples) relative to the total range throughout the district for each model covariate. The final panel in Figure 4 6 shows the grid cells for which at least one model covariate was outside the range observed in the survey. In total, nearly a quarter (24.7%) of the grid cells contained covaria tes outside the coverage of our observation, primarily driven by high NDVI values (8.1%), extremely low population densities (7.8%), and at the high and low elevation extremes (7.3%) in the northern and southern regions of the district, respectively. Trave l time to nearest health facility was the most well represented model covariate (3.1% outside of training range). Predictions on malaria pr evalence and expected number of cases in these pixels are extrapolations from the observed data, and should be evalua ted with ca u tion. A more conservative approach for assessing and projecting the impact of health


85 facilities on malaria prevalence and expec ted number of cases would be to remove extrapolated predictions (Figure 4 7A and 4 7B, respectively). Shifting and a d ding new health facilities After removing the extrapolated pixels, GAM parameter estimates were used to project the impact that changing t he spatial distribution of health facilities might have on childhood malaria in Bunkpurungu Yunyoo. First, we assesse d how the existing CHPS compounds could be repositioned to optimally reduce prevalence rates, expected number of cases, and travel time to nearest health facility (Figure 4 8). The placement which had the greatest impact in reducing the expected number of cases was strikingly similar to the actual locations of the CHPS. Prevalence rates across the district were reduced by shifting one of the CHPS to the high burden areas in the southern region, and accessibility to health facilities was improved by shiftin g another CHPS compound to the very southern edge of the district. As expected, the addition of new health facilities is projected to reduce malaria prevalence, expected number of cases, and estimated travel time, however our results suggest that there ar e diminishing returns as more and more new facilities are sequentially added (Figure 4 9). The addition of new facilities is not projected to have a dramatic impact on the average prevalence and travel time across the district, however new facilities are e xpected to have meaningful localized impact (Figure 4 10). The addition of five new health facilities could reduce up to 3 70 cases of early childhood malaria. Selecting new locations to have the greatest reduction in expected number of cases results in the prioritization of the northern region of the district between the two major settlements (similar to the current placement of CHPS), whereas prevalence and


86 travel time were reduce d by placing new facilities in the central and southern regions of the distri ct (Figure 4 10). Discussion Implications for Ghana Our model indicates that the local health centers and CHPS compounds in Bunkpurungu Yunyoo, Ghana are providing a protective effect against malaria prevalence in young children, even after accounting f or potential confounding risk factors such as distance to urban center. It is also important to consider that this effect is also detected in a subpopulation that has nearly universal access to ITS and IRS, suggesting that access to antimalarial treatment may be a n important supplemental intervention to the se standard pre exposure tools. The CHPS compounds in the district significantly reduced travel times for many of our sampling communities, despite only having a modest impact on travel times across the district as a whole. Moreover, our model also suggests that the current locations of CHPS compounds were relatively optimized to reduce the expected number of under five malaria cases. Millennium Development Goal to reduce under five mortality (217) . Despite the promising early implementat ions, scaling of CHPS program has faced difficulties (218) extension through GEHIP offer promising opportunities t o improve progress towards reducing childhood mortality (189,190) . In the context of malaria control, our findings further support previous work suggesting tha t the local health facilities (including the CHPS compo unds) have a significant influence on childhood malaria burden Bunkpurungu Yunyoo (206) , which we hope contributes to the further adoption and prolif eration of this program.


87 Modelling C hoices and L imitations Other studies throughout sub Saharan Africa have also described significant relationships between distance and/or travel time to health facili ties and malaria prevalence, however most often accessi bility is either defined in discrete categories (i.e. near or far based on a cutoff threshold) or as a single linear predictor (see review in (193) ). Relying on a flexible GAM with natural splines allowed for the detection of important nonli near effect s . These patterns may have important consequ ences for policy decisions, not only for selecting where to place new health facilities but also for other malaria interventions that implicitly rely on the spatial distribution of health centers. A si milar GAM construction has also been used to model trea tment seeking behavior in malaria endemic counties at a national and sub continental scale (219) . This study relies on a static model, which places some notable limitations on the potential application. A more dynamic approach, such as an agent based model (220,221) , may have great predictive and forecasting capabilities (222) . For example, our model is not abl e to forecast the number of cases a new health facility may eliminate as a function of time. However, dynamic models often require a priori definitions for how each model covariate shapes the response variable. For highly d ynamic systems, such as malaria t ransmission, these a priori choices are may be based on external studies and/or expert opinion, which can lead to spurious projections may not have accounted for the no nlinear effect of travel time to nearest health facility, which may have led to poor guidance for designing localized intervention strategies. Relying on local patterns will be particularly important for countries such as G hana,


88 which are moving away from size fits (223) , however further research is necessary to support these nonlinear patterns. C onversely, it would be possible t o consider similar model constructions which contain even less parameterization. For instance, rather than designating knots for the travel time covariate, we also evaluated a model which use d an additive approach similar t o the distance to urban center co variate . The resulting nonlinear relationship between predicted prevalence and time travel was similar to the defined knot model , however this approach produced a worse fitting model in terms of adjusted R 2 and deviance exp lained. Additionally, using the d esignated knots values were selected based on the distribution of the observed data and to have operational applicability, which we believe further enhances the utility of the model. Geographic R esource A llocation and D ec ision S upport Several geographic systems based approaches for guiding the allocation of health resources have been previously proposed (224 226) . Tanser (227) states that outcomes, such as optimizing access versus optimizing coverage. An important caveat to the opti mized candidate locations is that the evaluation of new facilities were based on reducing burden of a specific disease for a specific age class. Additionally, relying on different criteria (e.g. prevalence versus expected cases) may result in different opt imization outcomes. While there a re compelling reasons to prioritize reducing malaria prevalence in children under five years in this region, health facilities also serve many other vital community functions which may also be important to consider when ide ntifying new locations. Balancing these criteria is far from trivial and , as illustrated for


89 the optimization based on prevalence versus expected number of cases, changes to the objective function can lead to very different outcomes . Extending the utility of statistical models by implemen ting decision support tools powered by these models is key to address the complexities associated with identifying the optimal allocation of health resources. Furthermore, in addition to the many design decisions regarding the statistical model and decisio n support tool, there will always be additional external information that cannot be captured within the model. More specifically, i t is rarely possible for a scientist to account for all of the criteria that a decision make r must consider (e.g., is the are a for the new health facility in a region with civil unrest?) , and therefore an effective decision support tool should be designed to provide a platform for the decision maker to use inferences in conjunction with their additional criteria to make an infor med decision. We believe that our decision support tool will be a valuable contribution to the growing repository of new ly develop ed open source software for guiding health resource allocation (228,229) , and specifically to spatial decision support systems for guiding malar ia interventions (182 184) . A recent review found that less than 20% of febrile malaria positive children under five years old had received an ACT (230) . Further development of these spatial decision support tools such as th ese are critical important to improving this statistic and controlling this preventable disease.


90 Figure 4 1. Accessibility of health facility in Bunkpurugu Yunyoo, Ghana. Panel A depicts the location of traditional health centers (blue pluses), CHPS c ompounds (red pluses), surveyed communities (gray circles), and the travel times (in minutes) to the nearest health facility based Weiss et al. [14] using least cost path analysis. Map grid cells a re 1 k m 2 resolution. Panel B depicts the reduction in travel time for each surveyed community provided by the CHPS compounds.


91 Table 4 1. Summary of GAM output. Parametric coefficients Variable Estimate Std. Error p value (Intercept) 0.753 0.922 0.414 Travel time splines 0 to 5 minutes 0.969 0.265 <0.001 5 to 10 minutes 0.608 0.338 0.072 10 to 15 minutes 0.861 0.295 0.003 15 to 30 minutes 1.009 0.358 0.005 30 to 45 minutes 1.178 0.389 0.002 45 to 60 minutes 1.801 0.589 0.002 > 60 minutes 0.818 0.347 0.018 Elevation 0.004 0.001 <0.001 NDVI <0.001 <0.001 0.862 Under 5 Population Density <0.001 <0.001 0.961 Non parametric coefficients Est. DFs p value s(Distance to Urban Center) 4.866 <0.001


92 Figure 4 2. Influence of accessibility to nearest health facility on early childhood malaria prevalence. The predicted prevalence rates based on travel time (in minutes) to the nearest health facility from the GAM results. The relationship was modelled using natura l s plines, with designated knot values (dashed line) where the function can shift. All other covariates were set to their median values.


93 Figure 4 3. Influence of additional risk factors on early childhood malaria prevalence. The predicted prevalence rat es based on the GAM results. Euclidean distance to the nearest urban center (meters) was modelled using cubic splines, the other covariates were modelled as linear predictors. For each covariate prediction all other covariates were set to their median v alu es.


94 Figure 4 4. Distribution of early childhood malaria prevalence in Bunkpurungu Yunyoo, Ghana. Panel A depicted the predicted prevalence rates based on the GAM results. Existing health centers and CHPS compounds are depicted by blue and red crosses, r espectively, and sample community are depicted with gray dots. The upper plot in Panel B depicted th e uncertainty in the prevalence estimates based on width of the confidence intervals (C.I.), and the lower plot depicts the proportional distribution of pre valence rates across the district. Each grid cell is approximately 1 k m 2 .


95 Figure 4 5. Distributio n of cases of early childhood malaria in Bunkpurungu Yunyoo, Ghana. Panel A depicted the predicted prevalence rates based on the GAM results and the under f ive year old population density. Existing health centers and CHPS compounds are depicted by blue and red crosses, respectively, and sample community are depicted with gray dots. The upper plot in Panel B depicted the uncertainty in the estimated number of cases based on width of the confidence intervals (C.I.), and the lower plot depicts the proportional distribution of cases/km 2 across the district (note x axis is on log scale). Each grid cell is approximately 1 k m 2 .


96 Figure 4 6. Comparing covariate ra nges in training and testing datasets. The covariate data for the 1 k m 2 grid of the entire district contains values outside of the range of the observed dataset. The points in the dotplots represent individual observations for the district based on the 20 12 remote sensed and GIS derived data (n = 1390). Light gray points were within the range of observed survey data, whereas dark gray points were outside the observed survey data used to train the model and therefore may lead to spurious predictions. The ma p indicate grid cells for which all covariates were within the training data range (white) and those were at least one covariate was outside of the observed range in the training data.


97 Figure 4 7. Predicting early childhood malaria prevalence and cases in Bunkpurungu Yunyoo, Ghana. Panels A and B depict the malaria prevale nce and number of cases, respectively, for children under 5 years old based on the GAM using 2012 covariate information. Active health centers (blue) and CHPS compounds (red) are shown in as cross marks, and observation communities are shows as gray points . Low prevalence/cases are shown in purple, high prevalence and gray grid cells contained covariate values outside the range of the observed data (and therefore no predictions were mad e. Panels C and D depict predictions of prevalence and number of cases, respectively, were covariate values within the training data (light gray) and outside the trainin g data (dark gray) for each 1 km 2 grid cell (n = 1390).




99 Figure 4 8. Shifting the location of CHPS compounds. The expected number of case, prevalence rates, and travel time to nearest health center were estimated as if there were only health centers (blue circles) and no active CHPS compounds (red circles) using the GAM and friction su rface. All other model covariates were left unchanged . Then the location of three new facilities were proposed and optimized to reduce three important metric s: expected number of cases (left panel), prevalence (middle panel), and ti me to health facility (r ight panel) . The numbered circles depict the optimal location of the new health facilities, where numbers indicate the sequence that these health facilities are placed .

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100 Figure 4 9. Impact of adding new health facilities. Total number of cases, averag e prevalence rate (km 2 ), and average travel time to nearest health facilities were based on the GAM predictions. Health facilities were sequentially added and the location of each new health facility was determined using a Nelder M ead algorithm to minimiz e each type of outcome .

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101 Figure 4 10. Projected local impact of additional health facilities based on optimal location. The location of new potential health facilities were optimized to reduce prevalence rates ( k m 2 ), expected to tal number of cases, and average travel time to nearest health facility (minutes), independently, using a Nelder Mead optimization. The interpolated region in each map depicts the difference between the predictions with and without the additional facilitie s. The existing health c enters and CHPS compounds are shown in blue and red circles, respectively.

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102 CHAPTER 5 CONCLUDING REMARKS The primary goal of this dissertation is to improve the capacity for models to help guide malaria control efforts. My contributions towards this goal revolved around a dapt ing new and underutilized statistical frameworks which directly address some of the limitations of standard methods, and to demonstrate how these models can be extended into decision support tools in order to broaden their applicabili ty. In Chapter 2 I used BMA to simultaneously model a comprehensive s uite of potential malaria risk factors over a relatively small geographic area (a single district). The goal of informing targeted management presents a difficult statistical challenge, as model interpretability is important for informing how local factors may influence the success of a potential intervention, predictive performance is valued for accurately project ing the impact of an intervention, and uncertainty must be precisely charac terized in order to properly contextualize and compare policy options. Additionally, an ideal method for modelling malaria risk must also be able to detect complex, nonlinear patterns. To this end, I believe that BMA represents a valuable statistical tool for modelling local malaria risk factors. In Chapter 3 I focused on h ow models can be used to construct a decision support tool by using DHS national surveys to model malaria prevalence and RDT performance and us ed these models to compare the cost effecti veness of MDA versus MSAT. I believe this framework demonstrates how s tatistical models can be used to enable evidence based decision making . A more traditional approach towards this analysis would likely focus solely on defining cost scenarios a priori , a nd use a sensitivity analysis to describe uncertainty. Instead our mod els present an intuitive

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103 representation of the uncertainty in the modelled parameters, and the interactive tool allows the use r to set cost parameters , thereby unlocking the ability of s takeholders to define their own scenarios in real time. Importantly, t his entire framework was constructed using a free and open access software (i.e., R), enabling others to adapt or extend these tools for other settings . In Chapter 4 I merged these two approaches by first fitting a GAM to describe the relationship between accessibility to health facilities and early childhood malaria prevalence in Bunkpurungu Yunyoo, and then using this model to create a decision support tool which projects the potential impact of adding new health facilities on reducing local malaria burd en. The interactive tool is an important component to this analysis, as there are likely additional factors not included in our models which may limit the feasibility of the optimized he alth facility locations. Statistical models have served a vital role i n guiding the management of malaria in West Africa. As more malariometric data continues to be available and interventions become more targeted to fit local epidemiological conditions, t here will continue to be a need for advances in statistical methods an d tools that allow stake holders to incorporate cutting edge models into control efforts. It is my hope that the contributions in this dissertation serve to further enhance data driven d ecision making for the control and eventual eradication of malaria.

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104 A PP ENDIX A SUPPLEMENTAL MATERIAL FOR CHAPTER 2 Functions for implementing Bayesian Model Averaging in R tnorm < function (n,lo,hi,mu,sig){ #generates truncated normal variates base d on cumulative normal distributio n #normal truncated lo and hi if ( length (lo) == 1 & length (mu) > 1 )lo < rep (lo, length (mu)) if ( length (hi) == 1 & length (mu) > 1 )hi < rep (hi, length (mu)) q1 < pnorm (lo,mu,sig) #cumulative distribution q2 < pnorm (hi,mu,sig) #cumulative distribution z < runif (n,q1,q2) z < qnorm (z,mu,sig) z[z == Inf ] < lo[z == Inf ] z[z == Inf ] < hi[z == Inf ] z } # -----------------------------rmvnorm= function (n, mean = rep ( 0 , nrow (sigma)), sigma = diag ( l ength (mean)), method = c ( "eigen" , "svd" , "chol" ) ) { if ( ! isSymmetric (sigma, tol = sqrt (.Machine $ double.eps), check.attributes = FALSE )) { stop ( "sigma must be a symmetric matrix" ) } if ( length (mean) != nrow ( sigma)) { stop ( "mean and sigma have non conforming size" ) } sigma1 < sigma dimnames (sigma1) < NULL if ( ! isTRUE ( all.equal (sigma1, t (sigma1)))) { warning ( "sigma is numerically not symmetric" ) } method < match.arg (method) if (method = = "eigen" ) { ev < eigen (sigma, symmetric = TRUE ) if ( ! all (ev $ values >= sqrt (.Machine $ double.eps) * abs (ev $ values[ 1 ]))) { warning ( "sigma is numerically not positive definite" ) } retval < ev $ vectors %*% diag ( sqrt (ev $ values), length (e v $ values)) %*% t (ev $ v ectors) } else if (method == "svd" ) { sigsvd < svd (sigma) if ( ! all (sigsvd $ d >= sqrt (.Machine $ double.eps) * abs (sigsvd $ d[ 1 ]))) { warning ( "sigma is numerically not positive definite" )

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105 } retval < t (sigs vd $ v %*% ( t (sigsvd $ u) * sqrt (sigsvd $ d))) } else if (method == "chol" ) { retval < chol (sigma, pivot = TRUE ) o < order ( attr (retval, "pivot" )) retval < retval[, o] } retval < matrix ( rnorm (n * ncol (sigma)), nrow = n) %*% retval retval < sweep (retval, 2 , mean, "+" ) colnames (retval) < names (mean) retval } # -----------------------------update.betas= function (param){ p= ncol (param $ cov) Sigma.inv= diag ( x= 1 ,p) Sigma.inv[ 1 , 1 ]= 1 / 1000 prec= t (param $ cov) %*% param $ cov + ( 1 / param $ sigma2) * Sigma.inv var1= solve (prec) pmedia= t (param $ cov) %*% param $ z rmvnorm ( 1 ,var1 %*% pmedia,var1) } # -----------------------------update.sigma2= function (param){ p= ncol (param $ cov) a1=(p 1 ) / 2 Sigma.inv= diag ( x= 1 ,p) Sigma.inv[ 1 , 1 ]= 1 / 1000 b1=( t (param $ betas) %*% Sigma.inv %*% param $ betas) / 2 1 / rgamma ( 1 ,a1,b1) } # -----------------------------update.z= function (param){ cond=dat $ y > 0 media=param $ cov %*% param $ beta res= rep ( NA ,n) res[cond]= tnorm ( sum (cond), lo= 0 , hi= Inf , mu= media[cond], sig= 1 ) res[ ! cond]= tno rm ( sum ( ! c ond), lo= Inf , hi= 0 , mu= media[ ! cond], sig= 1 ) res } # -----------------------------log.marg.likel= function (cov,z,sig2){ w=z p= ncol (cov) Sigma.inv= diag ( x= 1 ,p) Sigma.inv[ 1 , 1 ]= 1 / 1000 prec= t (cov) %*% cov + ( 1 / sig2) * Sigma.inv var1= solve (prec)

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106 m u=var1 %*% t (cov) %*% w (p / 2 ) * log (sig2) ( 1 / 2 ) * ( t (mu) %*% prec %*% mu) + ( 1 / 2 ) * determinant (var1) $ modulus [ 1 ] } # -----------------------------samp.move= function (paramz){ indin.old=paramz $ indin p= length (indin.old) z= runif ( 1 ) p0= 1 if (p == 1 ) { in birth (paramz $ indin,paramz $ indout) # death prob 2 > 1 is (1/3) and birth prob 1 > 2 is 1. p0= 1 / 3 } if (p == maxp) { if (z < 1 / 2 ) { death (paramz $ indin) # birth prob T 1 > T is (1/3) and death prob T > T 1 i s 1/2 p0= 2 / 3 } if (z >= 1 / 2 ) swap (paramz $ indin,paramz $ indout) } if ( 1 < p & p < maxp) { if (z < 1 / 3 ) { birth (paramz $ indin,paramz $ indout) # death prob from T > T 1 is (1/2) and birth prob from T 1 > T is (1/ 3) if (p == maxp 1 ) p0= 3 / 2 } if ( 1 / 3 < z & z < 2 / 3 ) { death (paramz $ indin) # birth prob from 1 > 2 is 1 and death prob from 2 > 1 is 1/3 if (p == 2 ) p0= 3 } if ( 2 / 3 < z) swap ( paramz $ indin,par amz $ indout) } pold= log.marg.likel (xmat.orig[,indin.old],paramz $ z,paramz $ sigma2) pnew= log.marg.likel (xmat.orig[,],paramz $ z,paramz $ sigma2) + log (p0) prob= exp (pnew pold) z= runif ( 1 ) seq1= 1 : maxp k= which ( ! seq1 %in% eq1[k] if (z < prob) return ( list ( xmat= xmat.orig[,], indin=, indout= return ( list ( xmat= xmat.orig[,indin.old], indin= indin.old, indout= paramz $ indout )) }

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107 # ----------------------------death= function (indi nz){ if ( length (indinz) == 2 ) return (indinz[ 2 ]) # cannot delete intercept k= sample ( 2 : length (indinz), size= 1 ) indinz[ k] } # -----------------------------swap= function (indinz,indoutz){ if ( length (indinz) == 2 ) k=indinz[ 2 ] # cannot swap intercept if ( length (indinz) != 2 ) k= sample ( 2 : length (indinz), size= 1 ) tmp=indinz[ k] include= sample (indoutz, size= 1 ) sort ( c (tmp,include)) } # -----------------------------birth= function (indinz,indoutz){ k= sample (indoutz, size= 1 ) sort ( c (indinz,k)) } # ----------------------------Gibbs sampler code rm ( list= ls ( all= T)) set.seed ( 1 ) source ( 'scripts/functions.R' ) dat= read.csv ( 'datafiles/GibbsInput.csv' , T) nvillage= length ( unique (dat $ village)) npeople.village= table (dat $ village) n= nrow (dat) ind= grep ( 'cov' , colname s (dat)) xmat.orig=cov= data.matrix ( cbind ( 1 ,dat[,ind])) maxp= ncol (cov) # initial values betas= c ( 0.2 , rep ( 0 ,maxp 1 )) sigma2= 1 cond=dat $ y > 0 z= ifelse (cond, runif (n), runif (n, min= 1 , max= 0 )) indin= 1 : 10 indout= 11 : maxp param= list ( z= z, sigma2= sigma2, betas= matrix (betas[ indin], length (indin), 1 ), indin= indin, indout= indout, cov= cov[,indin]) ngibbs= 10000 vec.betas= matrix ( NA ,ngibbs,maxp) vec.outros= matrix ( NA ,ngibbs, 1 ) # run gibbs

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108 for (i in 1 : ngibbs){ print ( c (i,param $ indin)) if ( ! 1 %in% param $ indin) break ; tmp= s amp.move (param) param $ cov=tmp $ xmat param $ indin=tmp $ indin param $ indout=tmp $ indout param $ betas= t ( update.betas (param)) param $ sigma2= update.sigma2 (param) param $ z= update.z (param) tmp= rep ( 0 ,maxp) tmp[param $ indin]=param $ betas vec.betas[ i,]=tmp vec.outros[i,]=param $ sigma2 }

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109 APPENDIX B SUPPLEMENTAL MATERIAL FOR CHAPTER 3 Table B 1. Regional estimates for average prevalence, sensitivity and specificity. Country Region Urbanicity Prevalence Sensitivity Specificity Burkina Faso Bou cle de Mou houn Rural 0.587, 0.456 0.704 0.872, 0.86 0.884 0.572, 0.496 0.643 Burkina Faso Boucle de Mouhoun Urban 0.232, 0.145 0.33 0.737, 0.719 0.754 0.37, 0.302 0.437 Burkina Faso Cascades Rural 0.57, 0.45 0.677 0.893, 0.878 0.908 0.592, 0.516 0.665 B urkina Fas o Cascades Urban 0.21, 0.136 0.292 0.776, 0.752 0.798 0.409, 0.336 0.481 Burkina Faso Centre Rural 0.264, 0.176 0.362 0.915, 0.906 0.924 0.311, 0.238 0.387 Burkina Faso Centre Urban 0.065, 0.038 0.1 0.786, 0.772 0.8 0.125, 0.088 0.167 Burkina Faso Centr e Est Rural 0.453, 0.329 0.576 0.847, 0.825 0.866 0.577, 0.513 0.637 Burkina Faso Centre Est Urban 0.163, 0.1 0.236 0.678, 0.647 0.708 0.35, 0.294 0.404 Burkina Faso Centre Nord Rural 0.44, 0.309 0.57 0.891, 0.878 0.903 0.46, 0.403 0.515 Burki na Faso Ce ntre Nord Urban 0.15, 0.089 0.223 0.762, 0.741 0.781 0.285, 0.239 0.33 Burkina Faso Centre Ouest Rural 0.638, 0.5 0.756 0.951, 0.944 0.958 0.632, 0.56 0.698 Burkina Faso Centre Ouest Urban 0.271, 0.17 0.384 0.869, 0.856 0.882 0.443, 0.369 0.514 Burkina Faso Centre Sud Rural 0.483, 0.352 0.611 0.889, 0.874 0.902 0.454, 0.383 0.524 Burkina Faso Centre Sud Urban 0.169, 0.102 0.25 0.731, 0.705 0.755 0.286, 0.228 0.346 Burkina Faso Est Rural 0.557, 0.415 0.689 0.836, 0.822 0.85 0.386, 0.317 0.453 Burkina F aso Est Urban 0.234, 0.142 0.337 0.699, 0.68 0.717 0.209, 0.163 0.258 Burkina Faso Hauts Basins Rural 0.543, 0.406 0.666 0.867, 0.853 0.88 0.4, 0.328 0.471 Burkina Faso Hauts Basins Urban 0.194, 0.118 0.282 0.741, 0.723 0.759 0.187, 0.144 0.234 Burkina Faso Nord Rural 0.471, 0.351 0.584 0.965, 0.957 0.971 0.676, 0.608 0.736 Burkina Faso Nord Urban 0.163, 0.103 0.234 0.9, 0.882 0.913 0.483, 0.41 0.554 Burkina Faso Plateau Central Rural 0.379, 0.262 0.501 0.921, 0.912 0.93 0.455, 0.386 0.52 Bu rkina Faso Plateau Central Urban 0.12, 0.071 0.18 0.825, 0.812 0.838 0.232, 0.184 0.282

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110 Table B 1. C ontinued. Country Region Urbanicity Prevalence Sensitivity Specificity Burkina Faso Sahel Rural 0.578, 0.456 0.69 0.793, 0.78 0.806 0.388, 0.315 0.462 Burkina Faso Sahel Urban 0.234, 0. 152 0.323 0.657, 0.64 0.674 0.254, 0.196 0.314 Burkina Faso S ud Ouest Rural 0.658, 0.533 0.765 0.935, 0.922 0.946 0.601, 0.534 0.66 Burkina Faso Sud Ouest Urban 0.28, 0.181 0.386 0.859, 0.837 0.878 0.325, 0.268 0.382 C ote d'Ivoire Centre Rural 0.19, 0.1 28 0.259 0.865, 0.844 0.881 0.43, 0.269 0.593 Cote d'Ivoire C entre Urban 0.059, 0.036 0.086 0.839, 0.816 0.857 0.176, 0.09 0.284 Cote d'Ivoire Centre Est Rural 0.227, 0.135 0.336 0.919, 0.883 0.943 0.673, 0.507 0.807 C ote d'Ivoire Centre Est Urban 0.074 , 0.04 0.118 0.885, 0.842 0.916 0.385, 0.23 0.548 Cote d'Ivoi re Centre Nord Rural 0.187, 0.119 0.268 0.903, 0.864 0.929 0.456, 0.284 0.628 Cote d'Ivoire Centre Nord Urban 0.062, 0.036 0.095 0.888, 0.846 0.917 0.197, 0.0 98 0.322 Cote d'Ivoire Centre Oues t Rural 0.242, 0.167 0.325 0.752, 0.721 0.775 0.442, 0.294 0.5 91 Cote d'Ivoire Centre Ouest Urban 0.087, 0.054 0.127 0.625, 0.592 0.652 0.192, 0.106 0.295 Cote d'Ivoire Nord Rural 0.151, 0.089 0.228 0.91, 0.89 0.923 0.3 77, 0.251 0.511 Cote d'Ivoire Nord Urban 0.048, 0.026 0.077 0.881, 0.859 0.896 0.133, 0.074 0.20 4 Cote d'Ivoire Nord Est Rural 0.178, 0.117 0.246 0.864, 0.821 0.896 0.512, 0.344 0.67 Cote d'Ivoire Nord Est Urban 0.057, 0.035 0.085 0.834, 0.785 0.87 0.23 3, 0.127 0.358 Cote d'Ivoire Nord Ouest Rural 0.157, 0.101 0.221 0.806, 0.721 0.865 0.498, 0.326 0.662 Cote d'Ivoire Nord Ouest Urban 0.054, 0.033 0.081 0.759, 0.67 0.829 0.233, 0.124 0.363 Cote d'Ivoire Ouest Rural 0.236, 0.176 0.299 0.887, 0.854 0.911 0.533, 0.361 0.69 Cote d'Ivoire O uest Urban 0.083, 0.058 0.112 0.847, 0.808 0.876 0.245, 0.132 0.379 Cote d'Ivoire Sud Ouest Rural 0.198, 0.141 0.263 0.819, 0.778 0.852 0.55, 0.385 0.7 Cote d'Ivoire Sud Ouest Urban 0.067, 0.044 0.094 0.756, 0.706 0.795 0.253, 0.142 0.382 Cote d'Ivoire Sud sans Abidjan Rural 0.19, 0.108 0.291 0.92, 0.896 0.936 0.3 91, 0.25 0.536

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111 Table B 1. C ontinued. Country Region Urbanicity Prevalence Sensitivity Specificity Cote d'Ivoire Sud sans Abidjan Urban 0.06, 0.03 0.099 0.8 9, 0.86 0.91 0.155, 0.084 0.241 Cote d'Ivoire Ville D'Abidjan Rural 0.164, 0.108 0.228 0.747, 0.71 0.776 0.323, 0.206 0. 45 Cote d'Ivoire Ville D'Abidjan Urban 0.049, 0.03 0.072 0.64 8, 0.605 0.684 0.108, 0.058 0.17 Ghana Ashanti Rural 0.267, 0.188 0.352 0.937, 0.841 0.982 0.143, 0.092 0.209 Ghana Ashanti Urban 0.072, 0.046 0.106 0.745, 0.524 0.892 0.029, 0.017 0.046 Ghana Brong Ahafo Rural 0.316, 0.214 0.426 0.97, 0.955 0.979 0.385 , 0.248 0.53 Ghana Brong Ahafo Urban 0.132, 0.081 0.196 0.906, 0.875 0.9 24 0.119, 0.064 0.192 Ghana Central Rural 0.421, 0. 302 0.542 0.958, 0.903 0.986 0.306, 0.204 0.416 Ghana Central Urban 0.165, 0.102 0.24 0.851, 0.706 0.94 0.092, 0.054 0.14 Ghana E astern Rural 0.36, 0.267 0.458 0.967, 0.936 0.982 0.288, 0.193 0.392 Gha na Eastern Urban 0.138, 0.092 0.193 0.871, 0.791 0.9 2 0.091, 0.053 0.138 Ghana Greater Accra Rural 0.22, 0.129 0.329 0.92, 0.801 0.977 0.145, 0.079 0.232 Ghana Greater Accra Urban 0 .072, 0.036 0.118 0.722, 0.496 0.88 0.035, 0.017 0.061 Ghana Northern Ru ral 0.381, 0.256 0.512 0.944, 0.825 0.99 0.459, 0.35 7 0.559 Ghana Northern Urban 0.127, 0.072 0.196 0.864, 0.656 0.97 0.16, 0.109 0.22 Ghana Upper East Rural 0.14, 0.069 0.234 0.885 , 0.746 0.96 0.134, 0.072 0.214 Ghana Upper East Urban 0.058, 0.026 0.10 5 0.615, 0.413 0.79 0.039, 0.019 0.068 Ghana Upper West Rural 0.38, 0.237 0.531 0.976, 0.961 0.984 0.49, 0.365 0.612 Ghana Upper West Urban 0.116, 0.059 0.189 0.896, 0.86 0.916 0.15 2, 0.094 0.222 Ghana Volta Rural 0.273, 0.171 0.39 0.924, 0.789 0.984 0. 249, 0.188 0.318 Ghana Volta Urban 0.098, 0.054 0.1 54 0.775, 0.524 0.932 0.083, 0.058 0.112 Ghana Western Rural 0.435, 0.306 0.564 0.883, 0.688 0.974 0.26, 0.202 0.324

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112 Table B 1. C ontinued. Country Region Urbanicity Prevalence Sensitivity Specificity Ghana Wester n Urban 0.18, 0.108 0.266 0.64, 0.336 0.872 0.082, 0.058 0.11 Guinea Boke Rural 0.249, 0.181 0.324 0.741, 0.654 0.811 0.338, 0.241 0.44 Guinea Boke Urban 0.133, 0.09 0.181 0.378, 0.288 0.469 0.098, 0.062 0.142 Guinea Conakry Rural 0.095, 0. 07 0.123 0.78 9, 0.677 0.871 0.095, 0.072 0.122 Guinea Conakry Urban 0.023, 0.015 0.034 0.519, 0.377 0.654 0.015, 0.01 0.022 Guinea Faran ah Rural 0.76, 0.668 0.835 0.872, 0.818 0.911 0.463, 0.369 0.553 Gu inea Faranah Urban 0.402, 0.295 0.509 0.591, 0.493 0.682 0.238, 0.174 0.309 Guinea Kankan Rural 0.592, 0.502 0.674 0.876, 0.845 0.901 0.581, 0.471 0.679 Guinea Kankan Urban 0.307, 0.234 0.384 0.514, 0.456 0.568 0.223, 0.154 0.298 Guinea Kindia Rural 0.59, 0.5 0.671 0.76, 0.672 0.832 0.276, 0.209 0.35 Guinea Kindia Urban 0.253, 0.188 0.321 0.371, 0.278 0.468 0.094, 0.064 0.126 Guinea Labe Rural 0.362, 0.276 0.448 0.572, 0.422 0.706 0.17 1, 0.13 0.214 Guinea Labe Urban 0.18, 0.128 0.236 0.27, 0.167 0.387 0.047, 0.034 0.062 Guinea Mamou Rural 0.465, 0.3 72 0.554 0.64 7, 0.532 0.748 0.208, 0.155 0.268 Guinea Mamou Urban 0.199, 0.141 0.26 0.336, 0.238 0.44 0.096, 0.068 0.127 Guinea N'Zereko re Rural 0.701, 0.613 0.776 0.831, 0.752 0.89 0.484, 0.389 0.576 Guinea N'Zerekore Urban 0.348, 0.261 0.437 0.544, 0. 425 0.653 0.2 27, 0.164 0.296 Nigeria North Central Rural 0.568, 0.421 0.702 0.755, 0.724 0.782 0.218, 0.147 0.295 Nigeria North Central Urban 0.158, 0.089 0.241 0.59, 0.553 0.625 0.102, 0.065 0.147 Nigeria North East Rural 0.313, 0.211 0.42 0.858, 0.844 0.87 0.248, 0.164 0.34 Nigeria North East Urban 0.14, 0.087 0.205 0.718, 0.7 0.738 0.125, 0.077 0.18 Nigeria North West Rural 0.458, 0. 336 0.576 0.828, 0.81 0.846 0.354, 0.265 0.444 Nigeria North West Urban 0.16, 0.099 0.23 0.683, 0.657 0.707 0.159, 0. 11 0.216

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113 Table B 1. C ontinued. Country Region Urbanicity Prevalence Sensitivity Specificity N ig eria South East Rural 0.332, 0.216 0.453 0.883, 0.873 0.893 0.182, 0.118 0.258 Nigeria South East Urban 0.144, 0.084 0.217 0 .787, 0.774 0.8 0.093, 0.056 0.1 38 Nigeria South South Rural 0.381, 0.259 0.505 0.867, 0.855 0.879 0.4, 0.306 0.494 Nigeria South South Urban 0.145, 0.087 0.216 0.741, 0.724 0.757 0.18, 0.125 0.242 Nigeria South West Rural 0.461, 0.326 0.594 0.896, 0.88 4 0.906 0.27, 0.191 0.356 Niger ia South West Urban 0.166, 0.097 0.248 0.819, 0.804 0.832 0.109, 0.07 0.155 Togo centrale Rural 0. 57, 0.408 0.716 0.862, 0.743 0.938 0.191, 0.149 0.236 Togo centrale Urban 0.209, 0.116 0.322 0.543, 0.348 0.721 0.081, 0.06 0.105 Togo grande agglomeration de lome Rural 0.27, 0.177 0.372 0.806, 0.729 0.86 0.165, 0.146 0.187 Togo grande agglomeration de lome Urban 0.068, 0.037 0.107 0.469, 0.366 0.57 0.04, 0.032 0.048 Togo kara Rural 0.569, 0.41 0.714 0.864, 0.793 0.916 0.23 7, 0.135 0.358 Togo kara Urban 0.275, 0.16 0.406 0.559, 0.433 0.673 0.051, 0.026 0.086 Togo maritime (sans agglomeration de lome) Rural 0.372, 0.241 0.507 0.793, 0.593 0.919 0.112, 0.069 0.166 Togo maritime (sans agglomeration de lome) Urban 0.145, 0.08 1 0.224 0.481, 0.252 0.707 0.054 , 0.032 0.083 Togo plateaux Rural 0.533, 0.394 0.663 0.884, 0.771 0.954 0.271, 0.251 0.291 Togo p lateaux Urban 0.254, 0.159 0.362 0.575, 0.365 0.762 0.11, 0.099 0.122 Togo savanes Rural 0.292, 0.187 0.407 0.824, 0.74 0.88 6 0.104, 0.085 0.123 Togo savan es Urban 0.086, 0.048 0.132 0.507, 0.386 0.62 0.053, 0.042 0.065

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134 BIOGRAPHICAL SKETCH Justin was born in Lansing , Michigan and raised in Det roit . He received a Bachelor of Science in e cology and e volution from Michigan State University in 2007, a M aster of Sc ience in b iolo gy from the University of Mississippi in 2012, and a Doctor of Philosophy from the University of Florida in 2019. His early research was focused on marine ecolog y and microbial biogeography . During his PhD , his research interest ed shifted to e pidemiology and applied s tatistics . H e developed an niche in Bayes ian statistics, ge ospatial modelling, reprod ucible research and decision science. His re search motivations were to construct statistical model to help guide local control effo rt s of malaria and other disease s , and to make inferences from models accessible to local imple ment ers by developing interactive dec ision support tools. He believed that the end point of a model should n t be a publication or pres entation, but a product tha t c ould actually empower dat a driven dec ision making .