Meta-analysis methods for risk difference: a comparison of different models

Risk difference is a frequently-used effect measure for binary outcomes. In a meta-analysis, commonly-used methods to synthesize risk differences include: 1) the two-step methods that estimate study-specific risk differences first, then followed by the univariate common-effect model, fixed-effects model, or random-effects models; and 2) the one-step methods using bivariate random-effects models to estimate the summary risk difference from study-specific risks. These methods are expected to have similar performance when the number of studies is large and the event rate is not rare. However, studies with zero events are common in meta-analyses, and bias may occur with the conventional two-step methods from excluding zero-event studies or using an artificial continuity correction to zero events. In contrast, zero-event studies can be included and modeled by bivariate random-effects models in a single step. This article compares various methods to estimate risk differences in meta-analyses. Specifically, we present two case studies and three simulation studies to compare the performance of conventional two-step methods and bivariate random-effects models in the presence or absence of zero-event studies. In conclusion, we recommend researchers using bivariate random-effects models to estimate risk differences in meta-analyses, particularly in the presence of zero events.