2011/06/21_Roel Braekers (University of Hasselt, Belgium)

Extending the Classical Koziol-Green model for informative censoring

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2011/06/21 – 12:30 h | Roel Braekers, University of Hasselt (Belgium).

Abstract

In survival analysis, we are interested in the time until an event. However, due to different practical reasons, we often do not fully observe this time. There is a second independent random variable, a censoring time, which obscures the observation process and we only observe the smallest of both times and an indicator variable that indicates which variable is the smallest.

The classical approach to model the distribution function for the time until an event while assuming that the censoring time is informative for the time until an event is by the Koziol-Green model. In this model it is assumed that the survival function of the censoring time is a power of the survival function of the time until an event.

In this talk, we will generalize this model and assume a parametric function, depending on a parameter Θ, to describe the relationship between the time until an event and the censoring time. Hereby we show that this assumption is equivalent to specifying a slide of a copula function for the observed lifetime and the censoring indicator. Based on this equivalence, we propose a pseudo maximum likelihood function to estimate the parameter Θ.

As results, we show the consistency and asymptotic normality of the parameter Θ. Furthermore we derive the weak convergence of the semi-parametric estimator for the distribution function of the time until an event. In a simulation study, we investigate the finite sample performance of these estimators and we apply this model to a practical data set.

References:
R. Braekers, A. Gaddah (2011), Flexible modeling in the Koziol-Green model by a copula function, Communications in Statistics: Theory and Methods, 40, 1218-1235.