Establishing the Parallels and Differences Between Right-Censored and Missing Covariates

TL;DR

This paper explores the relationship between right-censored and missing covariates in survival analysis, proposing new estimators and analyzing their properties through simulations and real data application.

Contribution

It establishes theoretical connections between right-censored and missing covariates, introduces a new estimator for informative censoring, and evaluates estimator performance.

Findings

Connections between censored and missing covariates are clarified.

A new estimator for informative covariate censoring is proposed.

Simulation confirms theoretical properties and robustness.

Abstract

While right-censored time-to-event outcomes have been studied for decades, handling time-to-event covariates, also known as right-censored covariates, is now of growing interest. So far, the literature has treated right-censored covariates as distinct from missing covariates, overlooking the potential applicability of estimators to both scenarios. We bridge this gap by establishing connections between right-censored and missing covariates under various assumptions about censoring and missingness, allowing us to identify parallels and differences to determine when estimators can be used in both contexts. These connections reveal adaptations to five estimators for right-censored covariates in the unexplored area of informative covariate right-censoring and to formulate a new estimator for this setting, where the event time depends on the censoring time. We establish the asymptotic properties of the six estimators, evaluate their robustness under incorrect distributional assumptions, and establish their comparative efficiency. We conducted a simulation study to confirm our theoretical results, and then applied all estimators to a Huntington disease observational study to analyze cognitive impairments as a function of time to clinical diagnosis.