Hierarchical modeling for the analysis of zero-inflated time-series count data observed in multiple locations

Abstract

In this research, we propose statistical methodologies for the analysis of zero-inflated time-series count data observed in multiple locations. In the first part, we propose a two-stage approach for meta-analysis or meta-regression. The first stage uses a generalized linear model with Poisson distribution to estimate location-specific association. The second stage uses multivariate meta-regression and mixed-effects meta-regression to pool the association across locations and to identify the underlying factors that may explain the between-location heterogeneity. The two-stage meta-analysis was applied to analyze the daily time-series suicide data collected from 47 prefectures in Japan for 1972-2015. In the second part, we propose nonparametric Bayesian Poisson hurdle random effects models (nb-PHM) to explore the heterogeneity in the location-specific associations in a fully Bayesian hierarchical modeling framework. The proposed models attempted to address several limitations of the two-stage approach. First, the Poisson hurdle model consists of two parts

a binary part and a positive part. The binary part models the probability that the count outcome is zero or not while the positive part model the non-zero counts. That way, we can have more flexibility to deal with inflated or deflated zeros for the count outcome than the conventional Poisson distribution assumption. The Poisson hurdle model also allows for examining the covariates effect both on the binary part and the positive part, separately. Second, as the time-series data are collected from multiple locations, we consider a hierarchical structure in both parts of the model by specifying location-specific random effects to represent the location-specific association. Moreover, the random effects of both binary and positive parts are modeled jointly to induce between-part correlations. To describe the between-location heterogeneity more flexibly, we assume not only a normal distribution but also a Dirichlet process (DP) mixture of normals for the joint vector of random effects. That way, we can conduct a model-based clustering and identify an underlying subgroup structure if it exists. For the proposed nb-PHM, we consider a fully Bayesian inference through the Markov Chain Monte Carlo sampling to avoid the two-stage approach. The methodology is illustrated through an application to Japan suicide data, Korea tick data, and a simulation study.