[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.
[Show abstract][Hide abstract] ABSTRACT: Aim: Criteria for future accreditation of breast cancer centres in Belgium will be mainly based on the case load per surgeon or per centre. We would like to argue that the prospective collection of relevant data and the analysis of treatment related outcome derived from these data is feasible and should be the ultimate criterion for quality assessment and thus for accreditation since outcome is a more direct measurement of quality.
Methods: Data were prospectively collected on 715 invasive non metastatic breast cancers between 2002 and 2007 treated according to standard, best-evidence protocols in the setting of a large district hospital. Univariate and multivariate survival analysis were performed and compared to national and international databases.
Results: 5 year disease-free survival (DFS) and overall survival (OS) in our series were respectively 77 and 84%. In the multivariate analysis of DFS, only her-2-neu status (her-2-neu positivity being associated with a poor prognosis) and age (older age being a worse prognostic factor) were statistically significant prognostic factors. For OS, her-2-neu, age, and positive nodes were statistically significant prognostic factors. The outcome is comparable to other data sets.
Conclusion: Centres dedicated to the care of women with breast cancer have the moral duty to produce outcome based results of their treatment. This report shows that such a collection of data is feasible and can be imposed as a prerequisite for accreditation. We also argue that outcome based data of treatment are a more solid base for quality assurance than case load.
[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.
Copula Theory and Its Applications, 12/2009: pages 279-288;
[Show abstract][Hide abstract] ABSTRACT: In survival analysis, it is common to assume that the lifetime and the censoring time are independent. However in various data sets, we notice that this is not a correct situation and that the censoring time is informative for the estimation of the distribution of the lifetime. Koziol and Green develop a first informative censoring model in which they assume that the survival function of the censoring time is a power of the survival function of the lifetime. This model is afterwards generalized by Veraverbeke and Cardarso-Suarez (2000) to the fixed design regression setting. A second informative censoring model is developed by Zhang and Klein. They assume that the association between the lifetime and the censoring time is given by a known copula function. This model is further investigated by Rivest and Wells in the case of an Archimedean copula and by Braekers and Veraverbeke (2005) in a fixed design regression. In this paper, we combine both models. We assume on the one hand, a Archimedean copula for the association between the lifetime and the censoring time, and on the other hand that the conditional survival function of the censoring time is a function of the conditional survival function of the lifetime. In this model we find a nonparametric estimator for the conditional distribution function of the lifetime. As results, we prove an almost sure representation, uniform consistency and weak convergence for this estimator. Furthermore we construct an asymptotic confidence band for this estimator and compare it with the estimator of Braekers and Veraverbeke (2005).
[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 03/2009; 139(3-139):930-943. DOI:10.1016/j.jspi.2008.06.001 · 0.68 Impact Factor
[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.
Communication in Statistics- Theory and Methods 12/2008; 40(7-7). DOI:10.1080/03610920903564750 · 0.27 Impact Factor