A simple, doubly robust, efficient estimator for survival functions using pseudo observations

Survival functions are often estimated by nonparametric estimators such as the Kaplan-Meier estimator. For valid estimation, proper adjustment for confounding factors is needed when treatment assignment may depend on confounding factors. Inverse probability weighting is a commonly used approach, especially when there is a large number of potential confounders to adjust for. Direct adjustment may also be used if the relationship between the time-to-event and all confounders can be modeled. However, either approach requires a correctly specified model for the relationship between confounders and treatment allocation or between confounders and the time-to-event. We propose a pseudo-observation-based doubly robust estimator, which is valid when either the treatment allocation model or the time-to-event model is correctly specified and is generally more efficient than the inverse probability weighting approach. The approach can be easily implemented using standard software. A simulation study was conducted to evaluate this approach under a number of scenarios, and the results are presented and discussed. The results confirm robustness and efficiency of the proposed approach. A real data example is also provided for illustration.