Bayesian spatio-temporal modelling of the relationship between mortality and malaria transmission in rural western Kenya

Sub-Saharan Africa (SSA) still bears the highest burden of the global mortality despite recent dramatic decreases. The majority of these deaths occur in children younger than 5 years and malaria infection is thought to be a leading cause of these deaths. Because of this belief, many studies have documented the effects of malaria transmission on childhood, but everyone living in malaria endemic areas is exposed to malaria parasites and is at risk of dying of malaria or malaria related causes. Besides the immediate threat to human survival, consequences of repeated clinical malaria infection places enormous economic and emotional impact on the households and systems. Over a century, a number of malaria control strategies have been implemented to reduce or eradicate the malaria burden. However, some of these interventions were never successful in SSA due to weak health systems, political goodwill and anti-malarial drug resistance among other factors. A global health initiative to roll back malaria (RBM) was initiated in 1998 aiming to halve the malaria-related mortality by year 2010 and to eliminate the disease by 2030 though evidence-based malaria control approaches. However, monitoring of the progress and achieving the above objective requires (i) reliable all-cause and malaria specific mortality which is often lacking in most of this region, and (ii) precise knowledge on the nature of the relationship between mortality and transmission which remains unclear. INDEPTH, a network of health and demographic surveillance systems (HDSS), initiated the malaria transmission intensity and mortality burden across Africa (MTIMBA) project in the year 2002 with the aim to improve our understanding of this relationship in its malaria endemic member sites. The HDSS exist in various parts of the low and middle-income countries where routine vital registration systems are weak or nonexistent, and routinely monitor demographic and health events at household level in a geographically defined area. It also collects information on causes of death, entomological data in randomly selected houses (locations) among others. The MTIMBA data are characterized by the presence of spatio-temporal correlation and the sparsity of the entomological data. Spatial correlation arises because locations in close proximity have similar risks due to common exposures. Sparse data occurs when large number of survey locations has zero (no) mosquitoes or proportions of infected mosquitoes. Standard statistical models are not appropriate to analyze these data because they assume independence between locations, leading to incorrect parameter estimates. In addition, excess zeros introduce overdispersion. Ignoring the extra zeros result in poor fit. Geostatistical temporal models adjust for spatial and temporal correlation by introducing location and time specific random effects respectively. Zero-inflated analogues of these models assume that a proportion of zeros arise from a count distribution and the remaining ones are observed with probability one. Spatio-temporal models have large number of parameters. Bayesian methods can fit highly parameterized models by employing Markov chain Monte Carlo (MCMC) simulation algorithms, hence overcome the computational problems of the likelihood-based methods. The objectives of this thesis was (i) to develop data driven Bayesian geostatistical models to assess the relationship between mortality and malaria transmission and (ii) apply these models to analyze the MTIMBA data extacted from KEMRI/CDC HDSS database with the aim to (a) estimate transmission heterogeneity and produce smooth maps of transmission intensity of the study area (b) assess the spatio-temporal changes and obtain smooth surfaces of socioeconomic status and (c) assess the relationship between malaria transmission and mortality across ages taking into account intervention efforts, socioeconomic status and demographic factors. In chapter 2, Bayesian zero inflated binomial (ZIB) geostatistical models were developed and compared with standard binomial analogues to analyze sparse sporozoite rate (SR) data adjusting for environmental/climatic factors and seasonality. The models also included spatial and temporal correlation. Smooth maps of SR during wet and dry season were produced. The results showed that ZIB models fit the data better and estimate predictors with lower uncertainty compared to standard binomial models. The analysis also revealed spatial and seasonal heterogeneity in SR. SR was high during the wet season and in most parts of the northern and in a few locations in the southern part of the study area. Rainfall and altitude (distance above sea level) were the main drivers of SR in this area. The method used to obtain high resolution entomological inoculation rate (EIR) surfaces is discussed in chapter 3. EIR is a product of sporozoite rate (binomial data) and mosquito density (count data). Therefore we developed Bayesian zero inflated negative (ZINB) geostatistical models to analyze sparse mosquito density data. The ZINB models included predictors similar to the ZIB model in chapter 2. Model based predicted estimates of SR and mosquito densities were multiplied to obtain EIR estimates. High resolution (250 m by 250 m) temporal (monthly) EIR maps were produced for the study area. The results showed that distance to water bodies and vegetation are the main factors influencing the mosquito density in the study area. In addition, there was strong evidence of spatial and temporal patterns in mosquito density and EIR in the study area. In chapter 4, we used the household assets and characteristics data routinely collected in the KEMRI/CDC HDSS to compare different methods used to calculate household socioeconomic index based on assets as a proxy to household socioeconomic status. We ranked households into quintiles using generated household index and assessed changes in household quintiles over time. The results reveal that multiple correspondence analysis (MCA) explains our data better than ordinary and polychoric principal component analysis. The gap between the poorest and the least poor households increased in the ratio of 1:6 at the end of the study period. Spatial analysis also showed a gradual increase in least poor households in the southern part of the study area as the year progresses. High resolution EIR monthly estimates obtained in chapter 3 were linked to locations of mortality outcome in the study area. The relationship between malaria transmission intensity measured by EIR, all-cause and malaria specific mortality was assessed using Bayesian spatio-temporal geostatistical Cox proportion hazard models. The models included EIR estimates (with their uncertainty), age, household socioeconomic quintiles, ITN use and parameters describing space-time correlation. EIR was included in the model as an errors-in-variable covariate to take into account the prediction uncertainty. The study population was categorized into the following age groups neonates (0-28 days), post-neonates (1-11 months), child (1-4 years), 5-14, 15-29, 30-59 and =60 years. Analysis was carried out in each age group and results were discussed in chapters 5 and 6. The results of these analyses suggest that the effect of malaria transmission on all-cause and malaria-specific mortality is age-dependent. Under-five year old children have the highest risk of dying from malaria or any disease with increase in transmission intensity. No trend is observed in older children and adults =< 59 years old. This re-enforces the need for malaria interventions to selectively target the affected age groups thus making control effective. However, the effects of malaria transmission on all-cause and malaria specific mortality in under-five age groups were similar when compared. This could be attributed to poor specificity of verbal autopsy in identifying malaria deaths in malaria endemic areas. Higher transmission intensity appeared to have a protective effect to elderly population. These suggest gene selection and acquisition of immunity due to long exposure of malaria infection from childhood. Use of ITN has shown a reduction in all-cause mortality in almost all age groups except in child (1-4 year), but the effect is only strong in post-neonates and adults aged 30-59 years olds. Higher household socioeconomic status was also associated with lower all-cause mortality, but surprisingly was not associated with malaria specific mortality in the study area. The results of this work improve our understanding of the relation between malaria transmissions, all-cause and malaria specific mortality in the KEMRI/CDC HDSS. Results from Rufiji DSS suggest also similar trends implying that our results may be used to generalize the transmission-pattern. However, we still need to compare our results with those from other HDSS sites before making a general conclusion. Similarly, these results are important in developing effective malaria control interventions. Another contribution of this work is the development of spatio-temporal models for sparse entomological data which can be used to fit other epidemiological datasets and the estimation of high resolution EIR surfaces.