Meta-analysis of incidence of rare events

Abstract

This is a review of methods for the meta-analysis of incidence of rare events using summary-level data. It is motivated and illustrated by the dataset used in a published analysis of cardiovascular safety in rosiglitazone trials. This review compares available methods for binary data, considering risk-difference, relative-risk and odds-ratio scales, fixed-effect and random-effects models, and frequentist and Bayesian approaches. Particular issues in this dataset include low incidence rates, the occurrence of studies with no events under one or all treatments, and discrepancy among results achieved using different statistical methodologies. The common method of adding a correction factor to handle zeroes may introduce bias where the incidence of events is small, as in this case. Alternative analyses on the log-odds scale are shown to give similar results, but the choice between them is less important than the potential sources of bias in any meta-analysis arising from limitations in the underlying dataset. It is important to present results carefully, including numerical and graphical summaries on the natural scale of risk when the analysis is on a statistically appropriate scale such as log-odds: the incidence rates should accompany an estimated ratio (of odds or risk) to put the analysis into the proper context. Beyond the statistical methodologies which are the focus of this paper, this dataset highlights the importance of understanding the limitations of the data being combined. Because the rosiglitazone dataset contains clinically heterogeneous trials with low event rates that were not designed or intended to assess cardiovascular outcomes, the findings of any meta-analysis of such trials should be considered hypothesis-generating.