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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 of an exposure effect hazard ratio that is unbiased in large sampleswhen either the Cox model or the propensity score model is correctly specified.This combination does not, in general, produce a doubly robust estimator, evenafter regression standardization, when there is truly a causal effect. Wedemonstrate via simulation this lack of double robustness for thesemiparametric Cox model, the Weibull proportional hazards model, and a simpleproportional hazards flexible parametric model, with both the latter models fitvia maximum likelihood. We provide a novel proof that the combination ofpropensity score weighting and a proportional hazards survival model, fiteither via full or partial likelihood, is consistent under the null of nocausal effect of the exposure on the outcome under particular censoringmechanisms if either the propensity score or the outcome model is correctlyspecified and contains all confounders. Given our results suggesting thatdouble robustness only exists under the null, we outline two simple alternativeestimators that are doubly robust for the survival difference at a given timepoint (in the above sense), provided the censoring mechanism can be correctlymodeled, and one doubly robust method of estimation for the full survivalcurve. We provide R code to use these estimators for estimation and inferencein the supporting information.

Propensity weighting plus adjustment in proportional hazards model is not doubly robust