Semi‐supervised approaches to efficient evaluation of model prediction performance

In many modern machine learning applications, the outcome is expensive or time consuming to collect whereas the predictor information is easy to obtain. Semi‐supervised (SS) learning aims at utilizing large amounts of ‘unlabelled’ data along with small amounts of ‘labelled’ data to improve the efficiency of a classical supervised approach. Though numerous SS learning classification and prediction procedures have been proposed in recent years, no methods currently exist to evaluate the prediction performance of a working regression model. In the context of developing phenotyping algorithms derived from electronic medical records, we present an efficient two‐step estimation procedure for evaluating a binary classifier based on various prediction performance measures in the SS setting. In step I, the labelled data are used to obtain a non‐parametrically calibrated estimate of the conditional risk function. In step II, SS estimates of the prediction accuracy parameters are constructed based on the estimated conditional risk function and the unlabelled data. We demonstrate that, under mild regularity conditions, the estimators proposed are consistent and asymptotically normal. Importantly, the asymptotic variance of the SS estimators is always smaller than that of the supervised counterparts under correct model specification. We also correct for potential overfitting bias in the SS estimators in finite samples with cross‐validation and we develop a perturbation resampling procedure to approximate their distributions. Our proposals are evaluated through extensive simulation studies and illustrated with two real electronic medical record studies aiming to develop phenotyping algorithms for rheumatoid arthritis and multiple sclerosis.