  Comparative meta-analyses of groups of subjects by integrating multiple
observational studies rely on estimated propensity scores (PSs) to mitigate
covariate imbalances. However, PS estimation grapples with the theoretical and
practical challenges posed by high-dimensional covariates. Motivated by an
integrative analysis of breast cancer patients across seven medical centers,
this paper tackles the challenges associated with integrating multiple
observational datasets. The proposed inferential technique, called Bayesian
Motif Submatrices for Covariates (B-MSC), addresses the curse of dimensionality
by a hybrid of Bayesian and frequentist approaches. B-MSC uses nonparametric
Bayesian "Chinese restaurant" processes to eliminate redundancy in the
high-dimensional covariates and discover latent motifs or lower-dimensional
structure. With these motifs as potential predictors, standard regression
techniques can be utilized to accurately infer the PSs and facilitate
covariate-balanced group comparisons. Simulations and meta-analysis of the
motivating cancer investigation demonstrate the efficacy of the B-MSC approach
to accurately estimate the propensity scores and efficiently address covariate
imbalance when integrating observational health studies with high-dimensional
covariates.
