A calibration method to stabilize estimation with missing data

The augmented inverse weighting (AIW) estimator is commonly used to estimate the marginal mean of an outcome because of its doubly robust property. However, the AIW estimator can be severely biased if both the propensity score (PS) and the outcome regression (OR) models are misspecified. One possible reason is that misspecification of the PS or OR model yields extreme values in these models, which can have a great influence on the marginal mean estimate. In this article, we propose a calibrated AIW estimator for the marginal mean, which can control the influence of these extreme values and provide a stable marginal mean estimator. The proposed estimator also enjoys the doubly robust property. We also extend this method to handle high-dimensional covariates in PS and OR models. Asymptotic results are also developed. Extensive simulation studies show that the proposed method performs better in most cases than existing approaches by providing a more stable estimate. We apply this method to an AIDS clinical trial study.