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 of an exposure effect hazard ratio 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 supporting information.

翻译：近期，应用研究中常将常用生存分析建模方法（如多变量Cox模型和倾向性评分加权）相结合，旨在构建暴露效应风险比的双稳健估计量——即当Cox模型或倾向性评分模型之一被正确设定时，该估计量在大样本中无偏。然而，当存在真实因果效应时，这种组合通常无法产生双稳健估计量，即便经过回归标准化处理。我们通过模拟证明了半参数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（后两者均通过极大似然拟合）缺乏双稳健性。我们提出了一项新证明：当暴露对结局无因果效应的零假设成立，且满足特定删失机制时，若倾向性评分或结局模型之一被正确设定并包含所有混杂因素，则通过完全或部分似然拟合的倾向性评分加权与比例风险生存模型组合具有一致性。鉴于结果表明双稳健性仅在零假设下存在，我们提出两种简单的替代估计量（在给定时间点对生存差异具备上述意义上的双稳健性，前提是删失机制可被正确建模），以及一种针对完整生存曲线的双稳健估计方法。我们于辅助信息中提供了使用这些估计量进行估计与推断的R代码。