Bayesian spatial models applied to malaria epidemiology INAUGURALDISSERTATION zur Erlangung der W¨urdeeines Doktors der Philosophie vorgelegt der Philosophisch-Naturwissenschaftlichen Fakult¨at der Universit¨atBasel von Federica Giardina aus Pescara, Italien Basel, December 2015 Original document stored on the publication server of the University of Basel edoc.unibas.ch Genehmigt von der Philosophisch-Naturwissenschaftlichen Fakult¨atauf Antrag von Prof. Dr. M. Tanner, P.D. Dr. P. Vounatsou, and Prof. Dr. A. Biggeri. Basel, den 10 December 2013 Prof. Dr. J¨orgSchibler Dekan Science is built up with facts, as a house is with stones. But a collection of facts is no more a science than a heap of stones is a house. (Henri Poincar´e) iv Summary Malaria is a mosquito-borne infectious disease caused by parasitic protozoans of the genus Plasmodium and transmitted to humans via the bites of infected female Anopheles mos- quitoes. Although progress has been seen in the last decade in the fight against the disease, malaria remains one of the major cause of morbidity and mortality in large areas of the developing world, especially sub-Saharan Africa. The main victims are children under five years of age. The observed reductions are going hand in hand with impressive increases in international funding for malaria prevention, control, and elimination, which have led to tremendous expansion in implementing national malaria control programs (NMCPs). Common interventions include indoor residual spraying (IRS), the use of insecticide treated nets (ITN) and environmental measures such as larval control. Specific targets have been set during the last decade. The Millennium Development Goal (MDG) 6 aims to halve malaria incidence by 2015 as compared to 1990 and to achieve universal ITN coverage and treatment with appropriate antimalarial drugs. In 2010, the Global Malaria Action Plan (GMAP), created by the Roll Back Malaria (RBM) Partnership, called for rapid scaling-up to achieve universal coverage with some form of vector control. Transmission of malaria depends on the distribution and abundance of mosquitoes, which are sensitive to environmental and climatic conditions, such as temperature, rainfall, vegetation and land use. Geostatistical models can be used to estimate the environment- disease relation at fixed locations over a continuous study area, and predict the burden of malaria at places where data on transmission are not available. Data are correlated in space because common exposures of the disease influence malaria transmission similarly in neigh- boring areas. Geostatistical models take into account spatial correlation by introducing location-specific random effects. Bayesian model formulation is a natural and convenient choice for model fit via the implementation of Markov chain Monte Carlo (MCMC). This thesis develops novel statistical methodology for (i) producing accurate disease v burden estimation (malaria parasitemia risk and number of infected) at high spatial res- olution and (ii) assessing the coverage and effectiveness of vector control interventions. Produced maps and estimates make a significant contribution to the monitoring and eval- uation of the progress toward the targets of disease reduction and intervention coverage scaling-up. Contemporary information on malaria prevalence for this work was provided mostly by Malaria Indicator Surveys (MIS) and Demographic Health Surveys (DHS) with malaria modules. MIS are nationally representative surveys developed by RBM that collect para- sitaemia data on children below the age of 5 years and are usually carried out during high malaria transmission seasons. Historical data were extracted from the Mapping Malaria Risk in Africa (MARA) database, that contains over 10,000 geographically positioned sur- veys from gray or published literature across all sub-Saharan Africa. Malaria confirmed cases data were gathered by the Health Management Information System (HMIS) in Zam- bia. In Chapter 2, Bayesian geostatistical Zero-Inflated Binomial (ZIB) models were de- veloped to produce spatially explicit parasitaemia risk estimates and number of infected children below the age of 5 years in Senegal. Geostatistical ZIB models were able to ac- count for the large number of zero-prevalence survey locations (70%) in the Senegalese MIS 2008 dataset. Model validation confirmed that the ZIB model had a better predictive ability than the standard Binomial analogue. Bayesian variable selection methods were incorporated within a geostatistical framework in order to choose the best set of environ- mental and climatic covariates associated with the parasitaemia risk. Several ITN coverage indicators were calculated to assess the effectiveness of interventions. Chapter 3 explores different modelling specifications of zero-altered models and suggests model formulations in a geostatistical setting. In particular, the work addresses the problem of selecting variables and assessing the need of incorporating a spatial structure in the modelling of the mixing probability and the non-degenerate distribution. Specific prior distributions for spatial process selection based on non-zero random effects variances are proposed and analyzed through a set of simulated data. The proposed approach was applied to obtain simultaneous estimation of suitability of malaria transmission and of conditional risk in Senegal. The renewed interest in malaria eradication suggests that more sparse data will be produced from parasitological as well as entomological surveys. The impact of environmental predictors on malaria risk is commonly modeled as a linear effect, constant throughout the study area. However, more flexible functional forms, such vi as piece-wise linear or splines may be required to capture non-linear relationships between the predictors and malaria risk. The area under study is often large, covered by different regions, (e.g. ecological zones) and the relationship between the disease and its risk factors may not be constant across the area. Furthermore, the spatial correlation is likely to vary not only as a function of distance but also of their geographic position. Chapter 4 develops Bayesian spatial variable selection methods with spike-and-slab prior structure that allow the choice of different predictors and their functional forms in non-stationary geostatistical models for mapping disease survey data. Penalized spline effects are re- parameterized as mixed effects terms and their selection is based on non-zero random effects variance identification. Spatially varying weights are proposed to achieve smoothness across irregularly shaped regions. These methods are applied on the analysis of data from the Mali DHS to obtain spatially explicit estimates of the disease burden in the country. Few studies have linked malaria survey data with Remote Sensing (RS)-derived land cover/use (LC) variables. Chapter 5 assesses the effect of the spatial resolution of RS- derived environmental variables on malaria risk estimation in Mozambique. A proximity measure to define LC variables to be included as covariate in a geostatistical model for malaria risk is proposed and applied to the Mozambican DHS dataset in 2011. The model was validated using a LC layer at 5 m resolution produced by MALAREO, a Seventh Framework Programme (FP7) funded project which covered part of Mozambique during 2010-2012, and freely available Remote sensing sources. The predictive performance was compared. When prevalence estimation relies on the compilation of historical data, surveys are commonly heterogeneous in season and sampled population (age groups). In Chapter 6, age and time heterogeneity between surveys is addressed by proposing a general formulation that couples spatial statistical models and mathematical transmission models allowing uncertainty incorporation. The proposed methodology is applied to obtain age/season- specific high resolution disease risk estimates in Zambia. By 2013, six African countries had completed two rounds of MIS: Angola, Liberia, Mozambique, Rwanda, Senegal, and Tanzania. In Chapter 7, a spatio-temporal analysis was performed to estimate changes in malaria parasitemia risk across these countries. Additionally, the coverage and effectiveness of control measures (i.e., ITN and IRS) was quantified at national and subnational level in reducing malaria risk, after taking into account climatic factors. The analysis was performed with a Bayesian geostatistical model and spatially varying coefficients to study disease/interventions associations. Bayesian vii variable selection procedures were developed to select the most relevant ITN measure in reducing malaria risk and spatial kriging over the study area was performed to produce intervention coverage maps. For the first time, smooth maps of probability of decrease in parasitemia were produced. The methods described throughout this thesis may not be applied directly from field practitioners or NMCP personnel, since they require specialized knowledge. However, we are currently working on the implementation of the models with entirely free softwares and user-friendly interfaces to be distributed to the NMCPs and facilitate their work in monitoring and evaluating the progress in the fight of the disease. viii Zusammenfassung Malaria ist eine durch M¨ucken ¨ubertragene, ansteckende Krankheit, welche durch para- sit¨areProtozoen der Gattung Plasmodium ausgel¨ostund durch den Biss infizierter weib- licher Anopheles M¨ucken auf Menschen ¨ubertragen wird. Trotz des Fortschritts im Kampf gegen die Krankheit w¨ahrendder