Bayesian Disease Mapping: A Literature Review With an Application, Using WinBugs Software

Abstract

In this paper we review the improper and proper conditional autoregressive (CAR) models. A set of spatially correlated Gaussian random effects are assumed. The CAR model which contains components from both the uncorrelated heterogeneity (UH) and correlated heterogeneity (CH) models, have been applied to the South African acute pericarditis 2014 data set, where a Poisson model is used. Acute pericarditis is caused by an inflammation of the pericardium in the heart. The data set has been used to examine whether there is a significant difference between the proper conditional autoregressive prior and the intrinsic conditional autoregressive prior for the correlated heterogeneity component in a convolution model. Both the hyperpriors of the precision for the uncorrelated heterogeneity components were modelled by using the Jeffreys’ prior. The sensitivity of the hyperprior has also been investigated. The deaths from this disease in 2014 in South Africa have been considered, where disease maps and the relative risk of acquiring and dying from acute pericarditis have been investigated, as well as the standardised mortality ratio (SMR). The convergence and burn-in period of the models were assessed by the Brook-Gelman-Rubin (BGR) diagnostic. The deviance information criterion (DIC) was used to assess the models.