Some insight on censored cost estimators

Censored survival data analysis has been studied for many years. Yet, the analysis of censored mark variables, such as medical cost, quality-adjusted lifetime, and repeated events, faces a unique challenge that makes standard survival analysis techniques invalid. Because of the 'informative' censorship imbedded in censored mark variables, the use of the Kaplan-Meier (Journal of the American Statistical Association 1958; 53:457-481) estimator, as an example, will produce biased estimates. Innovative estimators have been developed in the past decade in order to handle this issue. Even though consistent estimators have been proposed, the formulations and interpretations of some estimators are less intuitive to practitioners. On the other hand, more intuitive estimators have been proposed, but their mathematical properties have not been established. In this paper, we prove the analytic identity between some estimators (a statistically motivated estimator and an intuitive estimator) for censored cost data. Efron (1967) made similar investigation for censored survival data (between the Kaplan-Meier estimator and the redistribute-to-the-right algorithm). Therefore, we view our study as an extension of Efron's work to informatively censored data so that our findings could be applied to other marked variables.