Propensity weighting plus adjustment in proportional hazards model is not doubly robust
arxiv(2023)
摘要
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.
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