Flexible Modeling in the Koziol-Green Model by a Copula Function

Abstract

In survival analysis, the classical Koziol-Green random censorship model is commonly used to describe informative censoring. Hereby, it is assumed that the distribution of the censoring time is a power of the distribution of the survival time. In this article, we extend this model by assuming a general function between these distributions. We determine this function from a relationship between the observable random variables which is described by a copula family that depends on an unknown parameter θ. For this setting, we develop a semi-parametric estimator for the distribution of the survival time in which we propose a pseudo-likelihood estimator for the copula parameter θ. As results, we show first the consistency and asymptotic normality of the estimator for θ. Afterwards, we prove the weak convergence of the process associated to the semi-parametric distribution estimator. Furthermore, we investigate the finite sample performance of these estimators through a simulation study and finally apply it to a practical data set on survival with malignant melanoma.

Keywords:

• Asymptotic representation
• Consistency
• Copula
• Pseudo-likelihood
• Random censorship
• Simulation
• Weak convergence

Mathematics Subject Classification:

• Primary 62N02
• Secondary 62G20, 62G05

6. Acknowledgment

Both authors gratefully acknowledge financial support from IAP research network P6/03 of the Belgian Government (Belgian Science Policy).