Domain adaptation enables generalizable and efficient data-driven research. However, existing work has largely focused on domain adaptation for some intrinsically homogeneous target cohort, overlooking inherent heterogeneity within the target, which can exacerbate biases and unfairness in the presence of subgroups with imbalanced sample sizes. We develop a novel domain adaptation framework that addresses a more complicated target dataset that consists of heterogeneous and data-sparse subgroups and lacks gold-standard label observations. Our method simultaneously handles high-dimensionality, covariate shift, and outcome model heterogeneity by combining a model-assisted debiasing step used for covariate shift correction with an adaptive knowledge-guided sparsification procedure used to mitigate the issue of sample disparity. We also introduce a new model selection strategy to avoid negative knowledge transfer in the absence of labels in the target data. Our method is theoretically justified for being robust to nuisance model misspecification and adaptive to heterogeneity between the subgroups. Numerical experiments and two real-world applications, including genetic risk modeling of type 2 diabetes and prediction of mutation-induced protein stability changes, demonstrate the practical advantages of our method.

Surrogate variables play an important role in various fields due to the scarcity or absence of gold-standard labels. We develop a novel approach named SASH for Surrogate-Assisted and data-Shielding High-dimensional integrative regression. It is a semi-supervised approach that efficiently leverages sizable unlabeled samples with error-prone surrogate outcomes from multiple local sites to improve model estimation using the small gold-labeled sample. To facilitate stable and efficient knowledge extraction from the surrogates, our method first obtains a preliminary supervised estimator, and then uses it to assist in training a regularized single-index model (SIM) for the surrogates. Interestingly, through a chain of convex and properly penalized sparse regressions that approximate the SIM loss using bias correction, our method avoids the problem of local minima in the SIM, and fully eliminates the impact of the preliminary estimator's excessive error. In addition, it protects individual-level information through the aggregation of summary statistics from local sites, leveraging a similar idea of bias-corrected approximation. Through simulation studies, we demonstrate that our method outperforms existing approaches. Finally, we apply our method to develop a genetic risk model for type 2 diabetes using large-scale data sets from UK and Mass General Brigham biobanks, where only a small fraction of subjects in one site are labeled through manual chart review.