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：本文旨在为受右删失影响的时间-事件结局构建具有保障覆盖率的良好校准预测集。受现代保形推断思想的启发，我们的方法避免了对参数化或半参数化生存模型的强假设。与现有生存数据保形方法（通常假设Ⅰ型删失且删失时间完全可观测）不同，我们考虑了更常见的右删失场景：仅观测到删失时间或事件时间中的较早发生者。在标准条件独立删失假设下，我们提出并分析了针对未来观测生存时间的若干下预测界方法，包括逆删失概率加权法及其增强版本——该增强方法基于考虑相依删失的结局相关边际分位数半参数有效影响函数。我们严格建立了所提方法的渐近覆盖率保证，并通过理论证明与实证实验表明：增强方法在效率上显著优于其他所有提议方法。具体而言，其覆盖率误差界具有双重稳健性，属于二阶误差，从而确保其渐近可忽略性优于其他方法的覆盖率误差。