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