  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. The asymptotic properties of these
estimators are examined, and accurate small-sample procedures are devised for
quantifying estimation uncertainty. Through simulation studies and
meta-analyses of TCGA datasets, we discover the differential biomarker patterns
of the two major breast cancer subtypes in the United States and demonstrate
the versatility and reliability of the proposed weighting strategy, especially
for the FLEXOR pseudo-population.

Methodology