ZIBGLMM: Zero-inflated bivariate generalized linear mixed model for meta-analysis with double-zero-event studies

Double-zero-event studies (DZS) pose a challenge for accurately estimating the overall treatment effect in meta-analysis (MA). Current approaches, such as continuity correction or omission of DZS, are commonly employed, yet these ad hoc methods can yield biased conclusions. Although the standard bivariate generalized linear mixed model (BGLMM) can accommodate DZS, it fails to address the potential systemic differences between DZS and other studies. In this article, we propose a zero-inflated bivariate generalized linear mixed model (ZIBGLMM) to tackle this issue. This two-component finite mixture model includes zero inflation for a subpopulation with negligible or extremely low risk. We develop both frequentist and Bayesian versions of ZIBGLMM and examine its performance in estimating risk ratios against the BGLMM and conventional two-stage MA that excludes DZS. Through extensive simulation studies and real-world MA case studies, we demonstrate that ZIBGLMM outperforms the BGLMM and conventional two-stage MA that excludes DZS in estimating the true effect size with substantially less bias and comparable coverage probability.