Nonparametric Bayesian Poisson hurdle random effects model: an application to temperature–suicide association study

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Abstract In environmental epidemiology, the short-term association between temperature and suicide has been examined by analyzing daily time-series data on suicide and temperature collected from multiple locations. A two-stage meta-analytic approach has been conventionally used. A Poisson regression with splines is fitted for each location in the first stage, and location-specific association parameter estimates are pooled, adjusted, and regressed onto location-specific variables using meta-regressions in the second stage. However, several limitations of the conventional two-stage approaches have been reported. First, the Poisson distribution assumption may be inappropriate because the daily number of suicides is often zero. Second, the normal assumption in the second-stage meta-regression is not sufficiently flexible to describe between-location heterogeneity when subgroups exist. Third, the two-stage approach does not properly account for the statistical uncertainty associated with first-stage estimates. In this study, we propose a nonparametric Bayesian Poisson hurdle random effects model to investigate heterogeneity in the temperature–suicide association across multiple locations. The proposed model consists of two parts, binary and positive, with random coefficients specified to describe heterogeneity. Furthermore, random coefficients combined with location-specific indicators were assumed to follow a Dirichlet process mixture of normals to identify the subgroups. The proposed methodology was validated through a simulation study and applied to data from a nationwide temperature–suicide association study in Japan.