  While meta-analyzing retrospective cancer patient cohorts, an investigation
of differences in the expressions of target oncogenes across cancer subtypes is
of substantial interest because the results may uncover novel tumorigenesis
mechanisms and improve screening and treatment strategies. Weighting methods
facilitate unconfounded comparisons of multigroup potential outcomes in
multiple observational studies. For example, Guha et al. (2022) introduced
concordant weights, allowing integrative analyses of survival outcomes by
maximizing the effective sample size. However, it remains unclear how to use
this or other weighting approaches to analyze a variety of continuous,
categorical, ordinal, or multivariate outcomes, especially when research
interests prioritize uncommon or unplanned estimands suggested by post hoc
analyses; examples include percentiles and moments of group potential outcomes
and pairwise correlations of multivariate outcomes. This paper proposes a
unified meta-analytical approach accommodating various types of endpoints and
fosters new estimators compatible with most weighting frameworks. Asymptotic
properties of the estimators are investigated under mild assumptions. For
undersampled groups, we devise small-sample procedures for quantifying
estimation uncertainty. We meta-analyze multi-site TCGA breast cancer data,
shedding light on the differential mRNA expression patterns of eight targeted
genes for the subtypes infiltrating ductal carcinoma and infiltrating lobular
carcinoma.
