Transfer Learning for Linear Regression with Mismatched Covariates

Transfer learning is a powerful approach for improving model performance in a study of interest by leveraging data from related auxiliary studies. In this paper, we propose a novel transfer learning method to develop optimal linear predictors for continuous outcomes using datasets with differing sets of predictors. We address two challenges involved in this setting: distributional difference and covariate mismatch. The former refers to variations in data distributions across studies. The latter pertains to discrepancies in the measured covariates across studies, which result in mismatched feature spaces. Because direct data integration is not feasible, we extend the direct sparse regression procedure using covariance from multimodality data (DISCOM) framework with fusion learning to accommodate heterogeneous data sources. We demonstrate the robustness and efficacy of our proposed method through extensive simulation studies and an application to treatment utilization among ICU patients diagnosed with sepsis.