Surrogate Assisted Semi-supervised Inference for High Dimensional Risk Prediction

Risk modeling with electronic health records (EHR) data is challenging due to no direct observations of the disease outcome and the high-dimensional predictors. In this paper, we develop a surrogate assisted semi-supervised learning approach, leveraging small labeled data with annotated outcomes and extensive unlabeled data of outcome surrogates and high-dimensional predictors. We propose to impute the unobserved outcomes by construct-ing a sparse imputation model with outcome surrogates and high-dimensional predictors. We further conduct a one-step bias correction to enable interval estimation for the risk prediction. Our inference procedure is valid even if both the imputation and risk pre-diction models are misspecified. Our novel way of ultilizing unlabelled data enables the high-dimensional statistical inference for the challenging setting with a dense risk predic-tion model. We present an extensive simulation study to demonstrate the superiority of our approach compared to existing supervised methods. We apply the method to genetic risk prediction of type-2 diabetes mellitus using an EHR biobank cohort.