Surrogate variables in electronic health records (EHR) and biobank data play
an important role in biomedical studies due to the scarcity or absence of
chart-reviewed gold standard labels. We develop a novel approach named SASH for
{\bf S}urrogate-{\bf A}ssisted and data-{\bf S}hielding {\bf H}igh-dimensional
integrative regression. It is a semi-supervised approach that efficiently
leverages sizable unlabeled samples with error-prone EHR surrogate outcomes
from multiple local sites, to improve the learning accuracy of the small
gold-labeled data. {To facilitate stable and efficient knowledge extraction
from the surrogates, our method first obtains a preliminary supervised
estimator, and then uses it to assist 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 with
bias-correction, our method avoids the local minima issue of the SIM training,
and fully eliminates the impact of the preliminary estimator's large error. In
addition, it protects individual-level information through
summary-statistics-based data aggregation across the local sites, leveraging a
similar idea of bias-corrected approximation for SIM.} Through simulation
studies, we demonstrate that our method outperforms existing approaches on
finite samples. Finally, we apply our method to develop a high dimensional
genetic risk model for type II diabetes using large-scale data sets from UK and
Mass General Brigham biobanks, where only a small fraction of subjects in one
site has been labeled via chart reviewing