[show abstract][hide abstract] ABSTRACT: In survival analysis, the classical Koziol–Green model under random censorship is commonly used for informative censoring. We propose in this paper an extension of this model in which we derive a nonparametric estimator for the distribution function of a survival time under two types of informative censoring. For the first type of informative censoring, we assume that the censoring time depends on the survival time through the expression of their joint distribution by an Archimedean copula. For the second type of informative censoring, we assume that the marginal distribution of the censoring time is a function of the marginal distribution of the survival time where this function is found through a section of a known copula function on the observed lifetime and the censoring indicator. We prove in this paper the uniform consistency of the new estimator and show the weak convergence of the associated process. Afterwards, we give some finite sample simulation results and illustrate this estimator on a real-life data set.
Journal of Nonparametric Statistics 06/2011; 23(2):439-453. · 0.53 Impact Factor
[show abstract][hide abstract] ABSTRACT: In this chapter, we consider a non-parametric testing procedure for an extension of the Koziol-Green model under two types
of informative censoring. For the first type of informative censoring, we allow the censoring time to depend on the lifetime
through an Archimedean copula function. For the second type, we generalize the relationship between the marginal distributions
of the censoring time and lifetime by means of another copula function on the observed time and censoring indicator. In addition,
we describe a bootstrap procedure to approximate the null distribution of the test statistics and illustrate it on a practical
data set on survival with malignant melanoma.
[show abstract][hide abstract] ABSTRACT: In this paper we consider the conditional Koziol–Green model of Braekers and Veraverbeke [2008. A conditional Koziol–Green model under dependent censoring. Statist. Probab. Lett., accepted for publication] in which they generalized the Koziol–Green model of Veraverbeke and Cadarso Suárez [2000. Estimation of the conditional distribution in a conditional Koziol–Green model. Test 9, 97–122] by assuming that the association between a censoring time and a time until an event is described by a known Archimedean copula function. They got in this way, an informative censoring model with two different types of informative censoring. Braekers and Veraverbeke [2008. A conditional Koziol–Green model under dependent censoring. Statist. Probab. Lett., accepted for publication] derived in this model a non-parametric Koziol–Green estimator for the conditional distribution function of the time until an event, for which they showed the uniform consistency and the asymptotic normality. In this paper we extend their results and prove the weak convergence of the process associated to this estimator. Furthermore we show that the conditional Koziol–Green estimator is asymptotically more efficient in this model than the general copula-graphic estimator of Braekers and Veraverbeke [2005. A copula-graphic estimator for the conditional survival function under dependent censoring. Canad. J. Statist. 33, 429–447]. As last result, we construct an asymptotic confidence band for the conditional Koziol–Green estimator. Through a simulation study, we investigate the small sample properties of this asymptotic confidence band. Afterwards we apply this estimator and its confidence band on a practical data set.
Journal of Statistical Planning and Inference. 01/2009;
[show abstract][hide abstract] ABSTRACT: In this paper, we extend the Koziol-Green random censorship model (Koziol and Green (1976)) by assuming that the association between the observable random variables is described by a copula family that depends on an unknown parameter θ. We propose a pseudo-likelihood estimator for θ and show its consistency and asymptotic normality. In addition, we prove the weak convergence of the process associated to the extended Koziol-Green estimator. Through a simulation study, we investigate the finite sample performance of this estimator and finally apply it to a practical data set on survival with malignant melanoma.
Communications in Statistics—Theory and Methods. 12/2008; 40(7).