Causal inference for censored data with continuous marks

TL;DR

This paper introduces a new framework and estimator for causal inference with censored data and continuous marks, addressing identification challenges and providing testing methods, validated through simulations and real data.

Contribution

It defines a mark-specific treatment effect, proposes a local smoothing estimator, and develops testing procedures for causal effects in censored data with continuous marks.

Findings

The estimator has desirable asymptotic properties.

Testing methods effectively evaluate treatment effects.

Simulation and real data validate the proposed approach.

Abstract

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.