Disease Mapping with Generative Models
Disease mapping focuses on learning about areal units presenting high relative risk. Disease mapping models for disease counts specify Poisson regressions in relative risks compared with the expected counts. These models typically incorporate spatial random effects to accomplish spatial smoothing. Fitting of these models customarily computes expected disease counts via internal standardization. This places the data on both sides of the model, i.e., the counts are on the left side but they are also used to obtain the expected counts on the right side. As a result, these internally standardized models are incoherent and not generative; probabilistically, they could not produce the observed data. Here, we argue for adopting the direct generative model for disease counts. We model disease incidence instead of relative risks, using a generalized logistic regression. We extract relative risks post model fitting. We also extend the generative model to dynamic settings. We compare the generative models with internally standardized models through simulated datasets and a well-examined lung cancer morbidity data in Ohio. Each model is a spatial smoother and they smooth the data similarly with regard to relative risks. However, the generative models tend to provide tighter credible intervals. Since the generative specification is no more difficult to fit, is coherent, and is at least as good inferentially, we suggest it should be the model of choice for spatial disease mapping.