One-step Targeted Maximum Likelihood for Time-to-event Outcomes

Current Targeted Maximum Likelihood Estimation (TMLE) methods used to analyze time-to-event data estimate the survival probability for each time point separately, which result in estimates that are not necessarily monotone. In this paper, we present an extension of TMLE for observational time-to-event data, the one-step Targeted Maximum Likelihood Estimator for the treatment-rule specific survival curve. We construct a one-dimensional universal least favorable submodel that targets the entire survival curve, and thereby requires minimal extra fitting with data to achieve its goal of solving the efficient influence curve equation. Through the use of a simulation study, we will show that this method improves on previously proposed methods in both robustness and efficiency, and at the same time respects the monotone decreasing nature of the survival curve.