Nonlinear area-to-point regression kriging for spatial-temporal mapping of malaria risk

Mapping spatial-temporal variations of malaria risk serves a very useful purpose of improving public health intervention and protection. Smooth disease risk mapping can help to reduce errors and biases due to demographic heterogeneity in predicting malaria risk using the reported number of malaria cases in space and time. This study presents a new statistical model that is expanded from the existing area-to-point (ATP) kriging models in spatial statistics to map spatial-temporal variations of malaria risk in southern Vietnam. The essence of the new model is a Poisson regression ATP model that has fixed effects and random effects. The fixed effects link disease data and environmental data at various measurement and observation scales. The fixed effects are instead approximated by maximum-entropy approximation. This advancement is to minimize the ecological biases when disease data are only available from national routine surveillance at small areas. The random effects which are spatial-temporally auto-correlated are predicted by using simple ATP kriging. The results of mapping malaria risk at district level using data at provincial level are validated using areal cross-validation. Compare to the results from the same case study but using common ATP log-linear model, the new model is superior in terms of minimizing prediction biases. The case study of mapping malaria risk demonstrates the superiority of the new model in mapping disease risk using data at different scales. Moreover, the model allows the uncertainty about the mapping outcome to be quantified.