Bayesian Spatial Modeling of Malaria Incidence in Selected Counties of Western Kenya Using Conditional Autoregressive and Besag-York-Mollie Models

The incidence of malaria varies significantly in heterogeneity and overdispersion between areal units resulting in latent spatial dependence and structured variability. Models that assume independence can give biased parameter estimates and underestimated standard errors. The inability to consider correlated residual structures may confound the true relative risk patterns and compromise inferential validity. As a consequence, spatial statistical modeling enables the proper quantification of dependence structures, stabilize risk patterns, and better predictive accuracy. The study proposed the Bayesian hierarchical spatial modeling techniques through Conditional Autoregressive (CAR) and Besag-York-Mollie (BYM) models. Specifically, the research intended to analyze the spatial distribution and clustering of malaria incidence, estimate both the CAR and BYM models with the data and compare the predictive performance of the two models accurately. This study employed secondary data accessed from the Kenya Malaria Indicator Survey and the Demographic Health Survey. Spatial autocorrelation analysis was conducted to identify patterns of malaria incidence. Markov Chain Monte Carlo (MCMC) methods were used to estimate the parameters of the models. The Deviance Information Criterion (DIC) was utilized to compare the two models and determine the better fit. Model diagnostics indicated statistically significant spatial autocorrelation (Moran's I = 0.4462, Z = 2.5566, p < 0.05), confirming rejection of the null hypothesis of spatial independence and establishing a clustered spatial stochastic process. Information-theoretic criteria yielded DIC values of 79.87 (CAR) and 79.81 (BYM), and Watanabe-Akaike Information Criterion (WAIC) values of 78.94 (CAR) and 78.39 (BYM), while predictive assessment produced Log Marginal Predictive Likelihood (LMPL) values of -57.53 (CAR) and -45.19 (BYM), indicating superior posterior predictive performance for the BYM specification. Bayesian hierarchical spatial modeling was recommended for malaria incidence as it improves inferential precision. The study results facilitated the identification of high-risk clusters, thereby providing a statistical basis for evidence-based public health policy formulation.