Copas-Heckman-Type Sensitivity Analysis for Publication Bias in Rare-Event Meta-Analysis Under Generalized Linear Mixed Models.

In systematic reviews and meta-analyses, publication bias (PB) is one of the serious concerns and mainly induced by selective publication of academic literatures. Although many methods have been proposed to address PB, almost all of them are based on the normal-normal (NN) random-effects model, assuming that data are normally distributed at both the within-study and between-study levels. For rare-event meta-analysis where data contain rare occurrences of events, the standard NN random-effects model may perform poorly. Instead, some generalized linear mixed models (GLMMs) which employ the exact distribution for the number of events at the within-study level increase the estimation accuracy and have been widely used in practice. However, limited methods can be applied to address PB in the GLMMs. To address this limitation, we propose a framework of sensitivity analysis for evaluating the impact of PB in the contrast-based GLMMs. The proposed framework is developed based on the famous Copas-Heckman-type sensitivity analysis methods by relating study-specific true effect sizes with the latent Gaussian variable on the study sample sizes for adjusting PB. The proposed methods completely avoid the need for continuity corrections and can be easily implemented using standard software with low computational cost. Simulation studies are conducted to assess the performance of the proposed methods in adjusting PB and compare the results with related existing methods. Several real-world examples are also analyzed to show the broad applicability of our proposal in evaluating the potential impact of PB in meta-analysis of odds ratios and proportions with rare-event outcomes.