🤖 AI Summary
Combining inverse probability weighting (IPW) with multivariable Cox regression is commonly—but incorrectly—regarded as doubly robust; rigorous analysis shows it achieves consistency only under the null causal effect assumption and lacks double robustness in general, even with regression standardization.
Method: We propose the first doubly robust estimation framework for both pointwise survival probability differences and the full survival curve, introducing two novel doubly robust estimators for survival differences and one for the survival curve. All estimators remain consistent when either the outcome model (e.g., Cox, Weibull, or flexible parametric proportional hazards models) or the treatment assignment model is correctly specified.
Results: We establish theoretical consistency and asymptotic normality, validate finite-sample performance and failure modes via extensive simulations, and demonstrate superior robustness and efficiency over conventional IPW–Cox approaches. A comprehensive R package is provided, enabling estimation, inference, and practical implementation.
📝 Abstract
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 2 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.
