Prior Adaptive Semi-supervised Learning with Application to EHR Phenotyping.

Abstract

Electronic Health Record (EHR) data, a rich source for biomedical research, have been successfully used to gain novel insight into a wide range of diseases. Despite its potential, EHR is currently underutilized for discovery research due to its major limitation in the lack of precise phenotype information. To overcome such difficulties, recent efforts have been devoted to developing supervised algorithms to accurately predict phenotypes based on relatively small training datasets with gold standard labels extracted via chart review. However, supervised methods typically require a sizable training set to yield generalizable algorithms, especially when the number of candidate features, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math>, is large. In this paper, we propose a semi-supervised (SS) EHR phenotyping method that borrows information from both a small, labeled dataset (where both the label <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Y</mi></math> and the feature set <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi></math> are observed) and a much larger, weakly-labeled dataset in which the feature set <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi></math> is accompanied only by a surrogate label <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi></math> that is available to all patients. Under a <i>working</i> prior assumption that <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi></math> is related to <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi></math> only through <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Y</mi></math> and allowing it to hold <i>approximately</i>, we propose a prior adaptive semi-supervised (PASS) estimator that incorporates the prior knowledge by shrinking the estimator towards a direction derived under the prior. We derive asymptotic theory for the proposed estimator and justify its efficiency and robustness to prior information of poor quality. We also demonstrate its superiority over existing estimators under various scenarios via simulation studies and on three real-world EHR phenotyping studies at a large tertiary hospital.