  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.
