Bayesian spatial hierarchical mixture models for excess zeros data: review and application to female lymphatic filariasis cases

Abstract

Many cases of epidemiological data reported has an excessive value of zero. The number of excess zeros can be more than half, even up to 80% of all existing data. This can occur in cases of rare diseases that do not cause significant symptoms at the start of infection. Therefore, the number and the rise of reported cases becomes difficult to detect. This paper proposes several Bayesian methods which are mixture of several distributions, namely binomial, Poisson and zero-inflated Poisson, and discuss the extension of these models to spatial data with excess zeros. Spatial data is implemented with Bayesian hierarchical framework, using Besag-York-Mollié re-parameterization (BYM2) model for spatial random effects, and penalized complexity prior for latent level process in the mixture models of different types of zeros. Bayesian inference uses INLA (Integrated Nested Laplace Approximation) for more accurate and faster results for spatially based hierarchical data. We further review recent implementation of proposed Bayesian mixture models using female lymphatic filariasis cases in 2019 at 27 district city level in West Java, Indonesia, and its elevation as explanatory variable. Mixture models were compared using DIC, and the results obtained indicate that mixture distributions between Binomial-Poisson and Binomial-zero-inflated Poisson type 1 produce suitable models for characteristic of excess zeros data around 67% with high extreme observation values in certain regions.