Inverse probability weighted Cox models can be used to estimate marginal hazard ratios under different point treatments in observational studies. To obtain variance estimates, the robust sandwich variance estimator is often recommended to account for the induced correlation among weighted observations. However, this estimator does not incorporate the uncertainty in estimating the weights and tends to overestimate the variance, leading to inefficient inference. Here we propose a new variance estimator that combines the estimation procedures for the hazard ratio and weights using stacked estimating equations, with additional adjustments for the sum of terms that are not independently and identically distributed in a Cox partial likelihood score equation. We prove analytically that the robust sandwich variance estimator is conservative and establish the asymptotic equivalence between the proposed variance estimator and one obtained through linearization by Hajage et al. in 2018. In addition, we extend our proposed variance estimator to accommodate clustered data. We compare the finite sample performance of the proposed method with alternative methods through simulation studies. We illustrate these different variance methods in both independent and clustered data settings, using a bariatric surgery dataset and a multiple readmission dataset, respectively. To facilitate implementation of the proposed method, we have developed an $\mathsf{R}$ package ipwCoxCSV.

中文翻译：

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逆概率加权 Cox 模型中的方差估计

逆概率加权 Cox 模型可用于估计观察性研究中不同点处理下的边际风险比。为了获得方差估计，通常建议使用稳健的夹心方差估计来解释加权观测之间的诱导相关性。然而，这个估计器在估计权重时没有考虑不确定性，并且倾向于高估方差，导致推理效率低下。在这里，我们提出了一个新的方差估计器，它结合了使用堆叠估计方程的风险比和权重的估计程序，并对在 Cox 偏似然得分方程中不是独立和相同分布的项的总和进行了额外的调整。等。在 2018 年。此外，我们扩展了我们提出的方差估计器以适应聚类数据。我们通过模拟研究将所提出方法的有限样本性能与替代方法进行了比较。我们分别使用减肥手术数据集和多次再入院数据集在独立和集群数据设置中说明了这些不同的方差方法。为了促进所提出的方法的实施，我们开发了一个$\mathsf{电阻}$包ipwCoxCSV。