Recently it has become common for applied works to combine commonly used survival analysis modeling methods, such as the multivariable Cox model, and propensity score weighting with the intention of forming a doubly robust estimator that is unbiased in large samples when either the Cox model or the propensity score model is correctly specified. This combination does not, in general, produce a doubly robust estimator, even after regression standardization, when there is truly a causal effect. We demonstrate via simulation this lack of double robustness for the semiparametric Cox model, the Weibull proportional hazards model, and a simple proportional hazards flexible parametric model, with both the latter models fit via maximum likelihood. We provide a novel proof that the combination of propensity score weighting and a proportional hazards survival model, fit either via full or partial likelihood, is consistent under the null of no causal effect of the exposure on the outcome under particular censoring mechanisms if either the propensity score or the outcome model is correctly specified and contains all confounders. Given our results suggesting that double robustness only exists under the null, we outline two simple alternative estimators that are doubly robust for the survival difference at a given time point (in the above sense), provided the censoring mechanism can be correctly modeled, and one doubly robust method of estimation for the full survival curve. We provide R code to use these estimators for estimation and inference in the supplementary materials.

翻译：近期，应用研究中常将生存分析常用建模方法（如多变量Cox模型）与倾向性评分加权相结合，旨在构建一种双重稳健估计量——当Cox模型或倾向性评分模型之一被正确设定时，该估计量在大样本下无偏。然而，当存在真实因果效应时，这种组合通常（即使经过回归标准化后）无法生成双重稳健估计量。我们通过模拟研究证明了，对于半参数Cox模型、威布尔比例风险模型及简单比例风险灵活参数模型（后两者通过最大似然法拟合），均存在双重稳健性缺失。我们提出了一项新颖证明：在特定删失机制下，若倾向性评分或结局模型之一被正确设定且包含所有混杂因素，则倾向性评分加权与比例风险生存模型（通过全似然或部分似然拟合）的组合在暴露对结局无因果效应的原假设下具有一致性。鉴于结果表明双重稳健性仅存在于原假设下，我们给出了两种替代估计量——在能正确建模删失机制的前提下，这两种估计量对给定时间点的生存差异（按上述意义而言）具有双重稳健性；同时提供一种对完整生存曲线具有双重稳健性的估计方法。我们在补充材料中附上了用于估计与推断的R代码。