Title: Parametric estimation of the association parameters in hierarchical survival data by nested Archimedean copula functions
Authors: Mirza Nazmul Hasan - Hasselt University (Belgium) [presenting]
Roel Braekers - Hasselt University (Belgium)
Abstract: There has been a growing interest in modeling hierarchical clustered multivariate survival data, which are possibly censored and/or missing. This type of data arise when a sample consists of clusters and each cluster has several, correlated sub-clusters contains various, dependent survival times, such that two layers of dependence occurs into the data-set. In the analysis of such survival times, two approaches are commonly used when we want to take the association between the survival times within a cluster and/or sub-cluster into account. A first approach is through frailty models while a second approach is by using copula models. A frailty model is a conditional model which assumes that different individuals within the same cluster are independent, conditionally on a common frailty term. In contrast, a copula model assumes that the joint survival function can be described by a copula function evaluated in the marginal survival functions of different individuals within a cluster. We use nested Archimedean copula functions to describe the dependency between different event times and investigate a one stage parametric estimation procedure for the association parameters of the models for hierarchical survival data, where both the clusters and sub-clusters are allowed to be moderate to large and varying in size. We perform a simulation study to check the finite sample properties of the estimators and also illustrate the method on a real life data-set.