Causal meta-analysis by integrating multiple observational studies with multivariate outcomes.

Integrating multiple observational studies to make unconfounded causal or descriptive comparisons of group potential outcomes in a large natural population is challenging. Moreover, retrospective cohorts, being convenience samples, are usually unrepresentative of the natural population of interest and have groups with unbalanced covariates. We propose a general covariate-balancing framework based on pseudo-populations that extends established weighting methods to the meta-analysis of multiple retrospective cohorts with multiple groups. Additionally, by maximizing the effective sample sizes of the cohorts, we propose a FLEXible, Optimized, and Realistic (FLEXOR) weighting method appropriate for integrative analyses. We develop new weighted estimators for unconfounded inferences on wide-ranging population-level features and estimands relevant to group comparisons of quantitative, categorical, or multivariate outcomes. Asymptotic properties of these estimators are examined. Through simulation studies and meta-analyses of TCGA datasets, we demonstrate the versatility and reliability of the proposed weighting strategy, especially for the FLEXOR pseudo-population.