Bayesian Spatial Joint Model for Disease Mapping of Zero-Inflated Data with R-INLA: A Simulation Study and an Application to Male Breast Cancer in Iran.

Naeimehossadat Asmarian,Najaf Zare,Seyyed Mohammad Taghi Ayatollahi,Zahra Sharafi

doi:10.3390/ijerph16224460

Abstract

Hierarchical Bayesian log-linear models for Poisson-distributed response data, especially Besag, York and Mollié (BYM) model, are widely used for disease mapping. In some cases, due to the high proportion of zero, Bayesian zero-inflated Poisson models are applied for disease mapping. This study proposes a Bayesian spatial joint model of Bernoulli distribution and Poisson distribution to map disease count data with excessive zeros. Here, the spatial random effect is simultaneously considered into both logistic and log-linear models in a Bayesian hierarchical framework. In addition, we focus on the BYM2 model, a re-parameterization of the common BYM model, with penalized complexity priors for the latent level modeling in the joint model and zero-inflated Poisson models with different type of zeros. To avoid model fitting and convergence issues, Bayesian inferences are implemented using the integrated nested Laplace approximation (INLA) method. The models are compared according to the deviance information criterion and the logarithmic scoring. A simulation study with different proportions of zero exhibits INLA ability in running the models and also shows slight differences between the popular BYM and BYM2 models in terms of model choice criteria. In an application, we apply the fitting models on male breast cancer data in Iran at county level in 2014.

Highlights

In recent years, spatial statistical methods and spatial models for smoothing disease rates are widely applied within epidemiology and ecology studies
As to improving Markov chain Monte Carlo (MCMC) algorithms, several MCMC sampling strategies have been suggested; for example, methods based on the Metropolis-adjusted Langevin algorithm (MALA), methods based on Hamiltonian mechanics (HMC) and the single-block strategy [6]
Our focus is on joint model, so we display the result of the joint model as a sample of simulation study results

Summary

Introduction

Spatial statistical methods and spatial models for smoothing disease rates are widely applied within epidemiology and ecology studies. York and Mollié (BYM) model using Markov chain Monte Carlo (MCMC) method is a Bayesian hierarchical model that is widely used in disease mapping (see for example Ebrahimipour et al [2] and Sharafi et al [3]). As to improving MCMC algorithms, several MCMC sampling strategies have been suggested; for example, methods based on the Metropolis-adjusted Langevin algorithm (MALA), methods based on Hamiltonian mechanics (HMC) and the single-block strategy [6]. Despite all these developments, MCMC sampling techniques for LGMs suffer from slow convergence and poor mixing

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