A Model for Informative Censoring

In the usual model for censored survival analysis, observations are of the form X = min(T, C), where T and C are nonnegative random variables representing lifetime and censoring time, respectively. Under the usual assumption of independence of T and C, the Kaplan-Meier estimator (KME) is the appropriate estimator of S(t) = Pr(T > t). The KME can lead to substantial overestimates of survival probabilities if the event of censoring indicates an unfavorable prognosis for future survival. We consider an alternative model in which censoring only occurs in a subpopulation defined by the frailty distribution. A self-consistent estimator of the survival function appropriate to the model is obtained.