This paper presents a framework for causal inference in the presence of censored data,where the failure time is marked by a continuous variable referred to as a mark.The mark is observed after treatment and is not meaningful when the failure time is censored. In addition, due to the continuous nature of the marks, observations at each given mark are sparse. These facts make the identification and estimation of causality a challenging task. To address these issues, we define a new mark-specific treatment effect within the potential outcomes framework and characterize its identifying conditions. We then propose a local smoothing estimator for the causal effects and establish its asymptotic properties. We further develop testing methods to evaluate whether the treatment has an effect on the failure time when controlling the values of the mark at certain points or within a defined interval, and develop a Gaussian approximation method to obtain the critical values. We evaluate our method using simulation studies as well as a real dataset from the Antibody Mediated Prevention trials.

翻译：本文提出了一种在删失数据存在情况下进行因果推断的框架，其中失效时间由一个称为标记的连续变量标记。标记在治疗后被观测到，且当失效时间被删失时无意义。此外，由于标记的连续性，每个给定标记下的观测数据稀疏。这些事实使得因果关系的识别与估计成为一项具有挑战性的任务。为解决这些问题，我们在潜在结果框架内定义了一种新的标记特异性处理效应，并刻画了其可识别条件。随后，我们提出了一种用于因果效应的局部平滑估计量，并建立了其渐近性质。我们进一步开发了检验方法，以评估当在特定点或定义区间内控制标记取值时，处理是否对失效时间产生影响，并采用高斯逼近方法获取临界值。我们通过仿真研究以及来自抗体介导预防试验的真实数据集评估了该方法。