Author(s)

Benard Tonui^1*, Samuel Mwalili², Anthony Wanjoya²

¹Department of Mathematics & Computer Science, University of Kabianga, Kericho, Kenya.
²Department of Statistics & Actuarial Science, Jomo Kenyatta University of Agriculture & Technology, Juja, Kenya.

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.

HIV, INLA, McMC, Leroux CAR Prior, Disease Mapping, Spatio-Temporal Models

Tonui, B. , Mwalili, S. and Wanjoya, A. (2018) Spatio-Temporal Variation of HIV Infection in Kenya. Open Journal of Statistics, 8, 811-830. doi: 10.4236/ojs.2018.85053.