Extending the Archimedean Copula Methodology to Model Multivariate Survival Data Grouped in Clusters of Variable Size

• Activity Number: 229
• Type: Contributed
• Date/Time: Monday, August 4, 2014 : 2:00 PM to 3:50 PM
• Sponsor: International Indian Statistical Association
• Author(s): Roel Braekers*+ and Leen Prenen and Luc Duchateau
• Companies: Hasselt University and Hasselt University and Ghent University
• Keywords: Multivariate survival data ; Copula function ; Clustering ; Variable size ; Consistency ; Asymptotic Normality

Abstract

For clustered survival data, two models are commonly used that take the association between the lifetimes into account: frailty and copula models. Frailty models assume that the hazard function of each individual is independent, conditionally on a common frailty term. Copula models assume that the joint survival function of individuals within a cluster is given by a copula function, evaluated in the marginal survival functions. A major disadvantage of copula models over frailty models is that the size of the clusters must be small and equal to set up manageable estimation procedures. We describe in this talk a copula model for variable size clustered survival data. Hereby we focus on the class of Archimedean copula functions with completely monotone generators and exploit their Laplace transform-expression. We develop one- and two-stage procedures to estimate the association parameter. As results, we show the consistency and asymptotic normality of this estimator. We perform a simulation study to investigate the finite sample properties and illustrate this copula model on a real life data set on the time until first insemination for cows that are clustered within herds.