Abstract:
Disease mapping is the study of the distribution of disease relative risks or
rates in space and time, and normally uses generalized linear mixed models
(GLMMs) which includes fixed effects and spatial, temporal, and spatio-temporal random effects. Model fitting and statistical inference are
commonly accomplished through the empirical Bayes (EB) and fully Bayes
(FB) approaches. The EB approach usually relies on the penalized quasi-likelihood (PQL), while the FB approach, which has increasingly become
more popular in the recent past, usually uses Markov chain Monte Carlo
(McMC) techniques. However, there are many challenges in conventional
use of posterior sampling via McMC for inference. This includes the need
to evaluate convergence of posterior samples, which often requires extensive simulation and can be very time consuming. Spatio-temporal models
used in disease mapping are often very complex and McMC methods may
lead to large Monte Carlo errors if the dimension of the data at hand is
large. To address these challenges, a new strategy based on integrated
nested Laplace approximations (INLA) has recently been recently developed as a promising alternative to the McMC. This technique is now becoming more popular in disease mapping because of its ability to fit fairly
complex space-time models much more quickly than the McMC. In this
paper, we show how to fit different spatio-temporal models for disease
mapping with INLA using the Leroux CAR prior for the spatial component, and we compare it with McMC using Kenya HIV incidence data
during the period 2013-2016.
