Overlap-Weight Estimators with Machine-Learned Plug-Ins and Overlap-Weight Targeted Maximum Likelihood Estimator.

In estimating the average treatment effect (ATE), the plug-in estimator with the efficient influence function and the targeted maximum likelihood estimator (TMLE) are semiparametrically efficient. However, the estimators suffer from the fact that too small/large a propensity score (PS) in the denominators can make the estimators unstable. This is usually overcome by trimming or truncating the data, that is, discarding observations with the PS too small/large or replacing the PS with some lower or upper threshold, which amounts to using a non-smooth weight to move the target parameter away from the ATE. This paper proposes a smooth weight, quadratic in PS instead, which leads to targeting the "overlap-weight (OW) treatment effect" that has several advantages over the ATE. We compare various estimators through simulation and empirical studies, including a trimmed efficient influence-function estimator, TMLE, and their OW versions. We find that the OW versions perform better than the trimmed ones in terms of the absolute bias and root mean squared error, when the ATE is a constant so that all estimators share the same estimand. We also find that "cross-fit" analogous to cross-validation improves the asymptotic variance estimators.