Accurate confidence intervals for risk difference in meta-analysis with rare events

Meta-analysis provides a useful statistical tool to effectively estimate treatment effect from multiple studies. When the outcome is binary and it is rare (e.g., safety data in clinical trials), the traditionally used methods may have unsatisfactory performance.

We propose using importance sampling to compute confidence intervals for risk difference in meta-analysis with rare events. The proposed intervals are not exact, but they often have the coverage probabilities close to the nominal level. We compare the proposed accurate intervals with the existing intervals from the fixed- or random-effects models and the interval by Tian et al. (2009).

We conduct extensive simulation studies to compare them with regards to coverage probability and average length, when data are simulated under the homogeneity or heterogeneity assumption of study effects.

The proposed accurate interval based on the random-effects model for sample space ordering generally has satisfactory performance under the heterogeneity assumption, while the traditionally used interval based on the fixed-effects model works well when the studies are homogeneous.