Bayesian Disease Mapping in The Presence of Under-reporting

Abstract

In real life situations, the values of the response variable, which is the count data is mostly under-reported. In this work, we develop a model to cater for under-reporting in count data. In particular, we allow under-reporting to vary spatially by regions and it is captured by a binomial probability. Poisson distribution is used in modeling the count response under the assumption that over-dispersion does not exist. In the case of under-reporting, it was made to also vary spatially from one unit to the other through a probability captured by a binomial distribution. The spatial variations of the disease were divided into correlated and uncorrelated parts. When a Poisson Regression analysis was used, both the correlated and uncorrelated parts were all found to share a significant relationship with the relative risk for each region with more contribution coming from the uncorrelated part. The model obtained was applied to diabetes data in Ghana. Disease maps for the diseases are also developed for Ghana at administrative (district) level. These maps are critical and informative to policy makers. These maps allow them to target policies and use the already meagre resources well.