Is ignorance bliss: Fixed vs. random censoring

Abstract

While censored data is sufficiently common to have generated an enormous field of applied statistical research, the basic model for such data is also sufficiently non-standard to provide ample surprises to the statistical theorist, especially one who is too quick to assume regularity conditions. Here we show that estimators of the survival quantile function based on assuming additional information about the censoring distribution behave more poorly than estimators (like the inverse of Kaplan–Meier) that discard this information. This phenomenon will be explored with special emphasis on the Powell estimator, which assumes that all censoring times are observed.