Accounting for post‐randomization variables in meta‐analysis: A joint meta‐regression approach

Meta‐regression is widely used in systematic reviews to investigate sources of heterogeneity and the association of study‐level covariates with treatment effectiveness. Existing meta‐regression approaches are successful in adjusting for baseline covariates, which include real study‐level covariates (e.g., publication year) that are invariant within a study and aggregated baseline covariates (e.g., mean age) that differ for each participant but are measured before randomization within a study. However, these methods have several limitations in adjusting for post‐randomization variables. Although post‐randomization variables share a handful of similarities with baseline covariates, they differ in several aspects. First, baseline covariates can be aggregated at the study level presumably because they are assumed to be balanced by the randomization, while post‐randomization variables are not balanced across arms within a study and are commonly aggregated at the arm level. Second, post‐randomization variables may interact dynamically with the primary outcome. Third, unlike baseline covariates, post‐randomization variables are themselves often important outcomes under investigation. In light of these differences, we propose a Bayesian joint meta‐regression approach adjusting for post‐randomization variables. The proposed method simultaneously estimates the treatment effect on the primary outcome and on the post‐randomization variables. It takes into consideration both between‐ and within‐study variability in post‐randomization variables. Studies with missing data in either the primary outcome or the post‐randomization variables are included in the joint model to improve estimation. Our method is evaluated by simulations and a real meta‐analysis of major depression disorder treatments.