It is often of interest to study the association between covariates and the cumulative incidence of a right-censored time-to-event outcome. When time-varying covariates are measured on a fixed discrete time scale, it is desirable to account for more up-to-date covariates that may inform future censoring. Existing methods rely on stringent parametric assumptions, do not account for informative censoring due to time-varying covariates for continuous time, estimate a marginal survival probability, or do not fully use the discrete-time structure of time-varying covariates. We propose a nonparametric and sequentially doubly robust estimator of the continuous-time survival probability conditional on covariates in this setting. We also show that, in the special case of estimating the marginal survival probability, our estimator is asymptotically efficient. We demonstrate the superior performance of our estimator in a simulation experiment, and apply the method to a COVID-19 vaccine efficacy trial.

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