Contrasting treatment-specific survival using double-robust estimators

In settings where a randomized trial is infeasible, observational data are frequently used to compare treatment-specific survival. The average causal effect (ACE) can be used to make inference regarding treatment policies on patient populations, and a valid ACE estimator must account for imbalances with respect to treatment-specific covariate distributions. One method through which the ACE on survival can be estimated involves appropriately averaging over Cox-regression-based fitted survival functions. A second available method balances the treatment-specific covariate distributions through inverse probability of treatment weighting and then contrasts weighted nonparametric survival function estimators. Because both methods have their advantages and disadvantages, we propose methods that essentially combine both estimators. The proposed methods are double robust, in the sense that they are consistent if at least one of the two working regression models (i.e., logistic model for treatment and Cox model for death hazard) is correct. The proposed methods involve estimating the ACE with respect to restricted mean survival time, defined as the area under the survival curve up to some prespecified time point. We derive and evaluate asymptotic results through simulation. We apply the proposed methods to estimate the ACE of donation-after-cardiac-death kidney transplantation with the use of data obtained from multiple centers in the Netherlands.