A Bayesian Selection Model for Correcting Outcome Reporting Bias With Application to a Meta-analysis on Heart Failure Interventions

Multivariate meta-analysis (MMA) is a powerful tool for jointly estimating multiple outcomes' treatment effects. However, the validity of results from MMA is potentially compromised by outcome reporting bias (ORB), or the tendency for studies to selectively report outcomes. Until recently, ORB has been understudied. Since ORB can lead to biased conclusions, it is crucial to correct the estimates of effect sizes and quantify their uncertainty in the presence of ORB. With this goal, we develop a Bayesian selection model to adjust for ORB in MMA. We further propose a measure for quantifying the impact of ORB on the results from MMA. We evaluate our approaches through a meta-evaluation of 748 bivariate meta-analyses from the Cochrane Database of Systematic Reviews. Our model is motivated by and applied to a meta-analysis of interventions on hospital readmission and quality of life for heart failure patients. In our analysis, the relative risk (RR) of hospital readmission for the intervention group changes from a significant decrease (RR: 0.931, 95% confidence interval [CI]: 0.862-0.993) to a statistically nonsignificant effect (RR: 0.955, 95% CI: 0.876-1.051) after adjusting for ORB. This study demonstrates that failing to account for ORB can lead to different conclusions in a meta-analysis.