Survival Estimation for Missing not at Random Censoring Indicators based on Copula Models

TL;DR

This paper introduces a new estimator for conditional survival functions in the presence of MNAR censoring indicators, using copula models, and demonstrates its effectiveness through simulations and real data analysis.

Contribution

It develops a novel estimator for MNAR censoring using copula models, extending the Beran estimator to incomplete censoring information.

Findings

Estimator performs well in small sample simulations

Method is applicable to synthetic and real datasets

Provides theoretical conditions for estimator efficiency

Abstract

In the presence of right-censored data with covariates, the conditional Kaplan-Meier estimator (also known as the Beran estimator) consistently estimates the conditional survival function of the random follow-up for the event of interest. However, a necessary condition is the unambiguous knowledge of whether each individual is censored or not, which may be incomplete in practice. We therefore propose a study of the Beran estimator when the censoring indicators are generic random variables and discuss necessary conditions for the efficiency of the Beran estimator. From this, we provide a new estimator for the conditional survival function with missing not at random (MNAR) censoring indicators based on a conditional copula model for the missingness mechanism. In addition to the theoretical results, we illustrate how the estimators work for small samples through a simulation study and show their practical applicability by analyzing synthetic and real data.