Division of Biostatistics and Bioinformatics, Penn State University, Hershey, Pennsylvania, USA.
Department of Biostatistics, Johns Hopkins University, Baltimore, Maryland, USA.
Biometrics. 2022 Jun;78(2):660-667. doi: 10.1111/biom.13454. Epub 2021 Apr 7.
The propensity methodology is widely used in medical research to compare different treatments in designs with a nonrandomized 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 two-to-sevenfold variance reduction for the three IPW estimators in Lunceford and Davidian [Statistics in Medicine, 23(19), 2937-2960]. 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.
倾向评分方法在医学研究中被广泛应用于比较非随机治疗分配设计中的不同治疗方法。逆概率加权（Inverse Probability Weighting，简称 IPW）估计量是估计平均治疗效果的主要工具，但这些估计量的方差较大，这在实际应用中常常是一个令人关注的问题。受 Rao-Blackwellization 启发，本文提出了一种通过用潜在治疗分配分布中的权重均值替换原始估计量中的权重来平滑 IPW 估计量的方法。在我们的模拟研究中，与原始版本相比，平滑后的 IPW 估计量的方差显著降低，而偏差仅略有增加，例如，Lunceford 和 Davidian [Statistics in Medicine, 23(19), 2937-2960] 中的三个 IPW 估计量的方差降低了两到七倍。此外，我们提出的平滑方法还可以应用于局部有效和双重稳健估计量，以增加对模型误设定的保护。我们提供了一个在 R 中的实现。
