The propensity methodology (Rosenbaum & Rubin, 1983) is widely used in medical research to compare different treatments in designs with a non-randomized treatment allocation. The inverse probability weighted (IPW) estimators are a primary tool for estimating the average treatment effect but the large variance of these estimators is often a significant concern for their reliable use in practice. Inspired by Rao-Blackwellization, this paper proposes a method to smooth an IPW estimator by replacing the weights in the original estimator by their mean over a distribution of the potential treatment assignment. In our simulation study, the smoothed IPW estimator achieves a substantial variance reduction over its original version with only a small increased bias, for example 2-to-7-fold variance reduction for the three IPW estimators in Lunceford & Davidian (2004). In addition, our proposed smoothing can also be applied to the locally efficient and doubly robust estimator for added protection against model misspecification. An implementation in R is provided.

Jianguang “Jason” Liao, PhD