A causal meta-analysis framework for clinical trials with unequal randomization ratios.

Meta-analysis synthesizes evidence from multiple randomized clinical trials and informs evidence-based practices across various medical domains. Recently, causally interpretable meta-analysis has been proposed and applied to treatment evaluations for target populations, requiring individual participant data (IPD). Standard meta-analysis assumes transportability or exchangeability of a (conditional) relative effect (such as relative risk or odds ratio), which may be violated when the relative effects are correlated with the baseline risks across clinical trials. In addition, the weighted average of some study-specific effect measures such as the (log) odds ratios or the (log) hazard ratios is non-collapsible and does not correspond to any target population. Furthermore, when the randomization ratios between treated versus untreated arms vary across trials, confounding bias may occur. To address these challenges, we propose a causal meta-analysis (CMA) framework using only aggregated data, enabling causally interpretable and accurate estimation for different target populations. The CMA adjusts its weights for treatment effect across various target populations, including the average treatment effect (ATE), the ATE on the treated (ATT) population, the ATE on the control (ATC) population, and the ATE in the overlap (ATO) population. Mathematically, we discover the connection between traditional meta-analysis estimators and CMAs. For example, the Mantel-Haenszel weighted meta-analysis is equivalent to the CMA with ATO.