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Integrating multiple observational studies to make unconfounded causal ordescriptive comparisons of group potential outcomes in a large naturalpopulation is challenging. Moreover, retrospective cohorts, being conveniencesamples, are usually unrepresentative of the natural population of interest andhave groups with unbalanced covariates. We propose a generalcovariate-balancing framework based on pseudo-populations that extendsestablished weighting methods to the meta-analysis of multiple retrospectivecohorts with multiple groups. Additionally, by maximizing the effective samplesizes of the cohorts, we propose a FLEXible, Optimized, and Realistic (FLEXOR)weighting method appropriate for integrative analyses. We develop new weightedestimators for unconfounded inferences on wide-ranging population-levelfeatures and estimands relevant to group comparisons of quantitative,categorical, or multivariate outcomes. The asymptotic properties of theseestimators are examined, and accurate small-sample procedures are devised forquantifying estimation uncertainty. Through simulation studies andmeta-analyses of TCGA datasets, we discover the differential biomarker patternsof the two major breast cancer subtypes in the United States and demonstratethe versatility and reliability of the proposed weighting strategy, especiallyfor the FLEXOR pseudo-population.

Causal Meta-Analysis by Integrating Multiple Observational Studies with Multivariate Outcomes