Meta-analysis of safety for low event-rate binomial trials.

This article focuses on meta-analysis of low event-rate binomial trials. We introduce two forms of random effects: (1) 'studies at random' (SR), where we assume no more than independence between studies; and (2) 'effects at random' (ER), which forces the effect size distribution to be independent of the study design. On the basis of the summary estimates of proportions, we present both unweighted and study-size weighted methods, which, under SR, target different population parameters. We demonstrate mechanistically that the popular DerSimonian-Laird (DL) method, as DL actually warned in their paper, should never be used in this setting. We conducted a survey of the major cardiovascular literature on low event-rate studies and found that DL using odds ratios or relative risks to be the clear method of choice. We looked at two high profile examples from diabetes and cancer, respectively, where the choice of weighted versus unweighted methods makes a large difference. A large simulation study supports the accuracy of the coverage of our approximate confidence intervals. We recommend that before looking at their data, users should prespecify which target parameter they intend to estimate (weighted vs. unweighted) but estimate the other as a secondary analysis.