Abstract：
How to analyze data when there is violation of the positivity assumption? Several possible solutions exist in the literature. In this paper, we consider propensity score (PS) methods that are commonly used in observational studies to assess causal treatment effects in the context where the positivity assumption is violated. We focus on and examine four specific alternative solutions to the inverse probability weighting (IPW) trimming and truncation: matching weight (MW), Shannon\'s entropy weight (EW), overlap weight (OW), and beta weight (BW) estimators. We first specify their target population, the population of patients for whom clinical equipoise, that is, where we have sufficient PS overlap. Then, we establish the nexus among the different corresponding weights (and estimators); this allows us to highlight the shared properties and theoretical implications of these estimators. Finally, we introduce their augmented estimators that take advantage of estimating both the propensity score and outcome regression models to enhance the treatment effect estimators in terms of bias and efficiency. We also elucidate the role of the OW estimator as the flagship of all these methods that target the overlap population. Our analytic results demonstrate that OW, MW, and EW are preferable to IPW and some cases of BW when there is a moderate or extreme (stochastic or structural) violation of the positivity assumption. We then evaluate, compare, and confirm the finite-sample performance of the aforementioned estimators via Monte Carlo simulations. Finally, we illustrate these methods using two real-world data examples marked by violations of the positivity assumption.
摘要：
当违反积极性假设时，如何分析数据？文献中存在几种可能的解决方案。在本文中,我们考虑了观察性研究中常用的倾向评分(PS)方法,以在违反阳性假设的情况下评估因果治疗效果.我们专注于并研究了逆概率加权（IPW）修剪和截断的四个特定替代解决方案：匹配权重（MW），香农的熵权(EW)，重叠重量(OW),和β权重(BW)估计器。我们首先确定他们的目标人群，临床平衡的患者群体，也就是说,我们有足够的PS重叠。然后，我们建立了不同的相应权重（和估计器）之间的联系；这使得我们能够强调这些估计器的共同性质和理论意义。最后,我们引入了他们的增广估计器,该估计器利用倾向评分和结果回归模型来提高治疗效果估计器的偏倚和效率.我们还阐明了OW估计器作为所有这些针对重叠人群的方法的旗舰的作用。我们的分析结果表明，MW,当存在适度或极端(随机或结构)违反积极性假设时，EW优于IPW和某些BW情况。然后我们评估，比较,并通过蒙特卡罗模拟证实上述估计器的有限样本性能。最后,我们使用两个以违反积极性假设为标志的真实世界数据示例来说明这些方法。
