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 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. 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 sequentially doubly robust: it is consistent if, within each time window between adjacent visits, the censoring distribution is consistently estimated, or both the time-to-event distribution and a conditional mean probability are consistently estimated. 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.

翻译：研究协变量与右删失事件时间结局的累积发生率之间的关联常具重要意义。当以固定离散时间尺度测量时变协变量时，需在应对删失时考虑这些更新的协变量信息。例如在疫苗试验中，研究者关注接种疫苗后免疫应答水平与终点事件累积发生率间的关联，同时需处理由多次接种后访视测量的免疫应答水平导致的失访问题。现有方法或依赖严苛的参数假设，或在连续时间框架下未考虑由时变协变量引发的信息性删失，或仅估计边际生存概率，亦或未充分利用治疗后协变量的离散时间结构。本文提出一种基于连续时间生存概率的非参数估计方法，该概率以协变量为条件，同时控制固定离散时间尺度测量的时变协变量引起的删失。我们证明该估计量具有序贯双重稳健性：若在相邻访视间的时间窗内，删失分布被一致估计，或时间事件分布与条件均值概率均被一致估计，则该估计量保持一致性。进一步证明，在估计边际生存概率的特殊情形下，该估计量具有渐近有效性。通过模拟实验验证了所提估计量的优越性能，并将其应用于一项COVID-19疫苗效力试验。