Title: Modelling unbalanced hierarchical survival data using nested Archimedean copula functions
Authors: Roel Braekers - Hasselt University (Belgium) [presenting]
Abstract: A copula model for hierarchically nested clustered survival times is introduced in which the different clusters and sub-clusters are possibly unbalanced. Due to the right censoring, we do not fully observe each outcome variable. This, together with the hierarchical structure of the data, makes it difficult to set-up a full likelihood function for a general copula model. To circumvent this problem, we focus hereto on the class of hierarchical nested Archimedean copula functions and use the properties of this copula family to simplify the full likelihood function. For the marginal survival time, we consider a semi-parametric Cox's regression model. Since maximizing the likelihood function for all parameters is computational difficult, we consider a two-stage estimation procedure in which we first estimate the marginal parameters and afterwards estimate the association parameters. As result, we obtained the asymptotic consistency and normality of the association parameters. Next we compare the finite sample behaviour of the different estimators through a simulation study. Furthermore we illustrate this copula model on a practical real life data example.