Causal inference for censored data with continuous marks

This paper presents a framework for causal inference in the presence of censored data, where the failure time is marked by a continuous variable known as a mark. The mark can be viewed as an extension of the failure cause in the classical competing risks model where the cause of failure is replaced by a continuous mark only observed at uncensored failure times. Due to the continuous nature of the marks, observations at each specific mark are sparse, making the identification and estimation of causality a challenging task. To address this issue, we define a new mark-specific treatment effect within the potential outcomes framework and characterize its identifying conditions. We then propose a local smoothing causal estimand and establish its asymptotic properties. We evaluate our method using simulation studies as well as a real dataset from the Antibody Mediated Prevention trials.