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.

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