Modeling underreported infant mortality data with a random censoring poisson model

Abstract

In poor and socially deprived areas, economic, social and health data are typically underreported. As a consequence, inference using the observed counts for the event of interest will be biased and risks will be underestimated. To overcome this problem, Bailey et al. (2005) propose to consider data from suspected areas as censored information and develop a spatial Bayesian approach for the so-called Censored Poisson model (CPM). However, the CPM assumes that all censored areas are precisely known a priori, which is not a simple task in many practical situations. To account for potential underreporting in an infant mortality dataset, we propose an extension on the CPM by jointly modeling the data generating and the data reporting processes. We assume that observed counts have a Poisson distribution and the underreporting probabilities are associated to an appropriate logistic model. By doing that, we introduce the Random Censoring Poisson model (RCPM) in which the censoring mechanism is treated as random instead of requiring a previous specication of the censored (underreported) areas. Informative priors on the data reporting process are considered. We also propose a MCMC sampling scheme based on the data augmentation technique. By artificially augmenting the data through latent variables, we facilitate the posterior sampling process. To evaluate the proposed model, we run a simulation study in which such a model is compared with the CPM using diferent fixed censoring criteria. Also, we apply the proposed model to map the early neonatal mortality rates in Minas Gerais State, Brazil, where data quality is truly poor in many regions.