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

It is often of interest to study the association between covariates and the cumulative incidence of a time-to-event outcome, but a common challenge is right-censoring. When time-varying covariates are measured on a fixed discrete time scale, it is desirable to account for these more up-to-date covariates when addressing censoring. For example, in vaccine trials, it is of interest to study the association between immune response levels after administering the vaccine and the cumulative incidence of the endpoint, while accounting for loss to follow-up explained by immune response levels measured at multiple post-vaccination visits. Existing methods rely on stringent parametric assumptions, do not account for informative censoring due to time-varying covariates when time is continuous, 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 continuous-time survival probability conditional on covariates, accounting for censoring due to time-varying covariates measured on a fixed discrete time scale. 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.