Mixed-Effects Poisson Regression Models for Meta-Analysis of Follow-Up Studies with Constant or Varying Durations

Pantelis G. Bagos and Georgios Κ. Nikolopoulos

We present a framework for meta-analysis of follow-up studies with constant or varying duration using the binary nature of the data directly. We use a generalized linear mixed model framework with the Poisson likelihood and the log link function. We fit models with fixed and random study effects using Stata for performing meta-analysis of follow-up studies with constant or varying duration. The methods that we present are capable of estimating all the effect measures that are widely used in such studies such as the Risk Ratio, the Risk Difference (in case of studies with constant duration), as well as the Incidence Rate Ratio and the Incidence Rate Difference (for studies of varying duration). The methodology presented here naturally extends previously published methods for meta-analysis of binary data in a generalized linear mixed model framework using the Poisson likelihood. Simulation results suggest that the method is uniformly more powerful compared to summary based methods, in particular when the event rate is low and the number of studies is small. The methods were applied in several already published meta-analyses with very encouraging results. The methods are also directly applicable to individual patients’ data offering advanced options for modeling heterogeneity and confounders.

The Stata program can be found here.


The methods are described in detail here:

Bagos PG, Nikolopoulos GK. Mixed-effects Poisson regression models for meta-analysis of follow-up studies with constant or varying durations. 2009, The International Journal of Biostatistics, 5(1), Article 21 [PDF] [Google Scholar]