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.
Highlights
Statistical methods for disease mapping have grown very fast in the last decade
Model fitting and statistical inference are commonly accomplished through the empirical Bayes (EB) and fully Bayes (FB) approaches
Spatio-temporal models used in disease mapping are often very complex and Markov chain Monte Carlo (McMC) methods may lead to large Monte Carlo errors if the dimension of the data at hand is large
Summary
Statistical methods for disease mapping have grown very fast in the last decade. Modern registers provide a lot of information with high quality data recorded for different regions over a period of time (e.g. years). Spatio-temporal models used in disease mapping are often very complex and McMC methods may lead to large Monte Carlo errors and large computation time if the dimension of the data at hand is large [5]. There is a need to strike a balance between the exact inference, model complexity and computing time This is an issue in spatio-temporal disease mapping where the data at hand are usually large and the models are complex. Many latent Gaussian models, which comprises the models described in this paper, have conditional independence properties that lead to sparse precision matrices This is an advantage in INLA since it helps in speeding up the computation providing Bayesian inference without running long and complex McMC algorithms.
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