ESTIMATION OF SURVIVAL FUNCTION BASED ON MODELING OF CENSORING PATTERN

The Kaplan-Meier estimator(KM-estimator)is an important tool in the analysis of right censored data. It is a non-parametric estimator of an unknown survival function of a lifetime random variable. The purpose of this paper is to obtain a semi-parametric estimator of the survival function. In many practical data, there are several patterns of censoring, for example, censoring is apt to occur for the larger observable time. Such a pattern can be expressed by a function defined by conditional probability of censoring under condition that the observable time is given. We call the function censoring pattern function, and assume a parametric form for it. The survival function estimator derived in this paper is semi-parametric in the sense that the parametric form is assumed only for the censoring pattern function. The estimator is a generalization of the KM-estimator, and the estimated variance derived in this paper is a generalization of the Greenwood's formula. We investigate asymptotic properties of the semi-parametric estimator and show that it is asymptotically more efficient than the KM-estimator. We also show that its mean absolute error is smaller than that of the KM-estimator by a simulation study.