Our objective is to construct well-calibrated prediction sets for a time-to-event outcome subject to right-censoring with guaranteed coverage. Inspired by modern conformal inference, our approach avoids the need for a well-specified parametric or semiparametric survival model. Unlike existing conformal methods for survival data, which assume Type-I censoring with fully observed censoring times, we consider the more common right-censoring setting in which only the censoring time or only the event time is observed, whichever comes first. Under a standard conditional independence censoring condition, we propose and analyze several lower prediction bounds for the survival time of a future observation, including inverse-probability-of-censoring weighting, and its augmented version based on the semiparametric efficient influence function for the relevant marginal quantile of the outcome accounting for dependent censoring. We formally establish asymptotic coverage guarantees of the proposed methods, and demonstrate both theoretically and through empirical experiments, that the augmented approach substantially improves efficiency over all other proposed methods. Specifically, its coverage error bound is doubly robust, and therefore of second order, thus ensuring that it is asymptotically negligible relative to the coverage error of the other methods.

翻译：本文旨在为存在右删失的事件时间结局构建具有保证覆盖率的校准预测集。受现代共形推断启发，我们的方法无需指定正确的参数化或半参数化生存模型。与现有针对生存数据的共形方法（假设I型删失且完全观测到删失时间）不同，我们考虑更常见的右删失设置，即仅能观测到删失时间或事件时间（以先发生者为准）。在标准条件独立删失假设下，我们提出并分析了几种针对未来观测生存时间的下界预测方法，包括逆删失概率加权及其基于半参数有效影响函数的增强版本（该函数针对考虑相依删失的相关边际分位数构建）。我们正式建立了所提方法的渐近覆盖保证，并通过理论推导与实证实验证明：相比其他方法，增强方法在效率上具有显著提升。具体而言，其覆盖误差边界具有双重稳健性（因此属于二阶量级），从而确保其覆盖误差相对于其他方法在渐近上可忽略不计。