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.
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