One-step TMLE for targeting cause-specific absolute risks and survival curves

This paper considers one-step targeted maximum likelihood estimation method for general competing risks and survival analysis settings where event times take place on the positive real line R+ and are subject to right-censoring. Our interest is overall in the effects of baseline treatment decisions, static, dynamic or stochastic, possibly confounded by pre-treatment covariates. We point out two overall contributions of our work. First, our method can be used to obtain simultaneous inference across all absolute risks in competing risks settings. Second, we present a practical result for achieving inference for the full survival curve, or a full absolute risk curve, across time by targeting over a fine enough grid of points. The one-step procedure is based on a one-dimensional universal least favorable submodel for each cause-specific hazard that can be implemented in recursive steps along a corresponding universal least favorable submodel. We present a theorem for conditions to achieve weak convergence of the estimator for an infinite-dimensional target parameter. Our empirical study demonstrates the use of the methods.