A Poisson Mixed Effects Model for Investigating the Exposure-by-Cohort Interaction: A Gibbs Sampling Approach

A meta-analysis is a useful method for taking the findings of many studies and combining them in the hopes of identifying consistent patterns and sources of disagreement among those findings. While we interpret the average exposure effect, it is necessary to examine the homogeneity of the observed exposure effects across cohort, that is, exposure-by-cohort interaction. If the homogeneity is confirmed, the conclusions concerning exposure effects can be generalized to a broader population. In this paper, a Poisson mixed effects model is used to investigate the cohort effects on the exposure as well as on the baseline risk. The marginal posterior distributions are estimated by a Markov Chain Monte Carlo method, i.e. the Gibbs sampling, to overcome current computational limitations. We illustrate the methods with analyses of data from the Japan Arteriosclerosis Longitudinal Study, in which the effects of smoking on stroke events are examined based on the individual data of 23,860 subjects among 10 cohorts.