Semiparametric Censorship Models Research Articles

Asymptotic representation of presmoothed Kaplan–Meier integrals with covariates in a semiparametric censorship model

Presmoothed Kaplan–Meier integrals have been proposed as suitable estimators in semiparametric censorship models. They are based on a modification of Kaplan–Meier weights which replaces the censoring indicators by some smooth (parametric) fit to the conditional probability of uncensoring, leading to estimators with smaller variance. In this paper an asymptotic representation of these estimators as a sum of i.i.d. random variables is established. The situation in which covariates are present is considered; therefore, the present paper extends previous results in Dikta et al. (2005) to the setting with covariates. As a consequence, a CLT for presmoothed Kaplan–Meier integrals with covariates is obtained. Application to censored regression is given. The finite sample performance of the estimator is investigated through simulations.

Nonparametric estimation of the conditional distribution function in a semiparametric censorship model

In this paper we propose a new nonparametric estimator of the conditional distribution function under a semiparametric censorship model. We establish an asymptotic representation of the estimator as a sum of iid random variables, balanced by some kernel weights. This representation is used for obtaining large sample results such as the rate of uniform convergence of the estimator, or its limit distributional law. We prove that the new estimator outperforms the conditional Kaplan–Meier estimator for censored data, in the sense that it exhibits lower asymptotic variance. Illustration through real data analysis is provided.

Semiparametric censorship model with covariates

In real applications, we may be confronted with the problem of informative censoring. Koziol-Green model is commonly used to model the possible information contained in the informative censoring. However the proportionality assumption cast by Koziol-Green model (see (1.2) below) is "too restrictive in that it limits the scope of the Cox model in practice" (Subramanian, 2000). In this paper, we try to relax the proportionality condition of Koziol-Green model by modeling the censorship semiparametrically. It is shown that our suggested semiparametric censoring model is an applicable extension of the Koziol-Green model. Through a close connection with the logistic regression, our model assumptions are readily to be checked in practice. We also propose estimation for both the regression parameter and the cumulative baseline hazard function which can incorporate the additional information contained in the semiparametric censorship model. Simulations and the analysis of a real dataset confirm the applicability of the suggested model and estimation.