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.

中文翻译：

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使用倾向得分对平均治疗效果的逆概率加权估计量的方差减少

倾向方法广泛用于医学研究，以比较设计中的不同治疗与非随机治疗分配。逆概率加权 (IPW) 估计量是估计平均治疗效果的主要工具，但这些估计量的大方差通常是它们在实践中可靠使用的一个重要问题。受 Rao-Blackwellization 的启发，本文提出了一种平滑 IPW 估计量的方法，方法是将原始估计量中的权重替换为潜在治疗分配分布上的均值。在我们的模拟研究中，平滑的 IPW 估计器在其原始版本的基础上实现了显着的方差减少，而偏差仅增加了一点点，例如，在 Lunceford 和 Davidian [医学统计，23(19)，2937-2960] 中，三个 IPW 估计量的方差减少了 2 到 7 倍。此外，我们提出的平滑也可以应用于局部有效且双重鲁棒的估计器，以增加对模型错误指定的保护。提供了 R 中的实现。