Semi-supervised calibration of inferred outcomes for estimating average treatment effects with validated outcomes

Estimating treatment effects with electronic health record data is complicated by the lack of validated outcome measures collected under standard protocols. Typically, outcomes can only be approximated or inferred using putative rules or phenotyping models trained on small subsamples where validated outcomes are available. But biases in the inferred outcomes can introduce biases in downstream treatment effect estimates. To address this issue, we develop a semisupervised method to calibrate inferred outcomes for treatment effect estimation when a subsample is labeled at random with validated outcomes. The calibration ensures that the subsequent treatment effect estimator remains consistent despite errors in the inferred outcomes. This problem can be viewed to be analogous to that of estimating mean outcomes in a longitudinal study subject to monotone missingness, and we demonstrate connections with existing augmented inverse probability weighting estimators. The proposed estimator is multiply robust and locally semiparametric efficient. The finite sample performance is assessed through simulations. We also find that the estimator can achieve efficiency gains in finite samples in the presence of extreme labeling propensity scores owing to an effective normalization of implicit augmentation terms. The method is illustrated through an example analysis evaluating the comparative effectiveness of 2 anti-TNF therapies on disease activity status in patients with rheumatoid arthritis.