Model-Based Geostatistics for Prevalence Mapping in Low-Resource Settings Rejoinder

In low-resource settings, prevalence mapping relies on empirical prevalence data from a finite, often spatially sparse, set of surveys of communities within the region of interest, possibly supplemented by remotely sensed images that can act as proxies for environmental risk factors. A standard geostatistical model for data of this kind is a generalized linear mixed model with binomial error distribution, logistic link, and a combination of explanatory variables and a Gaussian spatial stochastic process in the linear predictor. In this article, we first review statistical methods and software associated with this standard model, then consider several methodological extensions whose development has been motivated by the requirements of specific applications. These include: methods for combining randomized survey data with data from non-randomized, and therefore potentially biased, surveys; spatio-temporal extensions; and spatially structured zero-inflation. Throughout, we illustrate the methods with disease mapping applications that have arisen through our involvement with a range of African public health programs.