Multiply Robust Estimation of Conditional Survival Probability with Time-Varying Covariates

It is often of interest to study the association between covariates and the incidence of a time-to-event outcome, but a common challenge is right-censoring and time-varying covariates measured on a fixed discrete time scale that may explain the censoring afterwards. For example, in vaccine trials, it is of interest to study the association between immune response levels after administering the vaccine and the incidence of the endpoint, but there is loss to follow-up or administrative censoring, and the immune response levels measured at multiple visits may be predictive of the censoring. Existing methods rely on stringent parametric assumptions, only estimate a marginal survival probability, or do not fully use the discrete-time structure of post-treatment covariates. In this paper, we propose a nonparametric estimator of the survival probability conditional on covariates with time-varying covariates. We show that the estimator is multiply robust: it is consistent if, within each time window between adjacent visits, at least one of the time-to-event distribution and the censoring distribution is consistently estimated. We demonstrate the superior performance of this estimator in a numerical simulation, and apply the method to a COVID-19 vaccine efficacy trial.