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Recently it has become common for applied works to combine commonly usedsurvival analysis modeling methods, such as the multivariable Cox model, andpropensity score weighting with the intention of forming a doubly robustestimator that is unbiased in large samples when either the Cox model or thepropensity score model is correctly specified. This combination does not, ingeneral, produce a doubly robust estimator, even after regressionstandardization, when there is truly a causal effect. We demonstrate viasimulation this lack of double robustness for the semiparametric Cox model, theWeibull proportional hazards model, and a simple proportional hazards flexibleparametric model, with both the latter models fit via maximum likelihood. Weprovide a novel proof that the combination of propensity score weighting and aproportional hazards survival model, fit either via full or partial likelihood,is consistent under the null of no causal effect of the exposure on the outcomeunder particular censoring mechanisms if either the propensity score or theoutcome model is correctly specified and contains all confounders. Given ourresults suggesting that double robustness only exists under the null, weoutline two simple alternative estimators that are doubly robust for thesurvival difference at a given time point (in the above sense), provided thecensoring mechanism can be correctly modeled, and one doubly robust method ofestimation for the full survival curve. We provide R code to use theseestimators for estimation and inference in the supplementary materials.

Propensity score weighting plus an adjusted proportional hazards model does not equal doubly robust away from the null