Nonparametric estimation of effect heterogeneity in rare events meta-analysis: bivariate, discrete mixture model

Böhning, D.; Martin, S.; Sangnawakij, P.; Jansen, K.; Böhning, W.; Holling, H.

Abstract

Meta-analysis provides an integrated analysis and summary of the effects observed in k independent studies. The conventional analysis proceeds by first calculating a study-specific effect estimate, and then provides further analysis on the basis of the available k independent effect estimates associated with their uncertainty measures. Here we consider a setting where counts of events are available from k independent studies for a treatment and a control group. We suggest to model this situation with a study-specific Poisson regression model, and allow the study-specific parameters of the Poisson model to arise from a nonparametric mixture model. This approach then allows the estimation of the heterogeneity variance of the effect measure of interest in a nonparametric manner. A case study is used to illustrate the methodology throughout the paper.