In the presence of right-censored data with covariates, the conditional Kaplan-Meier estimator (also known as the Beran estimator) consistently estimates the conditional survival function of the random follow-up for the event of interest. However, a necessary condition is the unambiguous knowledge of whether each individual is censored or not, which may be incomplete in practice. We therefore propose a study of the Beran estimator when the censoring indicators are generic random variables and discuss necessary conditions for the efficiency of the Beran estimator. From this, we provide a new estimator for the conditional survival function with missing not at random (MNAR) censoring indicators based on a conditional copula model for the missingness mechanism. In addition to the theoretical results, we illustrate how the estimators work for small samples through a simulation study and show their practical applicability by analyzing synthetic and real data.

翻译：在存在协变量的右删失数据中，条件Kaplan-Meier估计量（也称Beran估计量）能够一致地估计感兴趣事件随机随访时间的条件生存函数。然而，其必要条件是每个个体是否被删失的明确信息，这在实践中可能不完整。为此，我们研究了删失指示变量为一般随机变量时Beran估计量的性质，并讨论了其有效性的必要条件。在此基础上，基于缺失机制的Copula模型，我们提出了一种针对缺失非随机（MNAR）删失指示变量的条件生存函数新估计量。除理论结果外，我们通过模拟研究展示了该估计量在小样本下的表现，并通过分析合成数据与真实数据证明了其实用价值。