Controversy and Debate: Questionable utility of the relative risk in clinical research: Paper 2: Is the Odds Ratio “portable” in meta-analysis? Time to consider bivariate generalized linear mixed model

Objectives: A recent paper by Doi et al. advocated completely replacing the relative risk (RR) with the odds ratio (OR) as the effect measure in clinical trials and meta-analyses with binary outcomes. Besides some practical advantages of RR over OR, Doi et al.’s key assumption that the OR is “portable” in the meta-analysis, that is, study-specific ORs are likely not correlated with baseline risks, was not well justified. Study designs and settings: We summarized Spearman's rank correlation coefficient between study-specific ORs and baseline risks in 40,243 meta-analyses from the Cochrane Database of Systematic Reviews. Results: Study-specific ORs tend to be higher in studies with lower baseline risks of disease for most meta-analyses in Cochrane Database of Systematic Reviews. Using an actual meta-analysis example, we demonstrate that there is a strong negative correlation between OR (RR or RD) with the baseline risk and the conditional effects notably vary with baseline risks. Conclusions: Replacing RR or RD with OR is currently unadvisable in clinical trials and meta-analyses. It is possible that no effect measure is “portable” in a meta-analysis. In addition to the overall (or marginal) effect, we suggest presenting the conditional effect based on the baseline risk using a bivariate generalized linear mixed model.