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In the presence of right-censored data with covariates, the conditionalKaplan-Meier estimator (also known as the Beran estimator) consistentlyestimates the conditional survival function of the random follow-up for theevent of interest. However, a necessary condition is the unambiguous knowledgeof whether each individual is censored or not, which may be incomplete inpractice. We therefore propose a study of the Beran estimator when thecensoring indicators are generic random variables and discuss necessaryconditions for the efficiency of the Beran estimator. From this, we provide anew estimator for the conditional survival function with missing not at random(MNAR) censoring indicators based on a conditional copula model for themissingness mechanism. In addition to the theoretical results, we illustratehow the estimators work for small samples through a simulation study and showtheir practical applicability by analyzing synthetic and real data.

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