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Title: Using nested Archimedean copulas to investigate the correlation structure in udder infection times Authors:  Roel Braekers - Hasselt University (Belgium) [presenting]
Abstract: The imposed correlation structure on clustered multivariate time to event data, is in most cases taken as of a simple nature. In the shared frailty model, for example, all pairwise correlations between event times in a cluster are taken the same. When modelling the infection times for the four udder quarters clustered within a cow, more complex correlation structures are needed that will also give more insight into the infection process. We choose a copula approach to study more complex correlation structures in clustered infection times. We are able to model the marginal distributions separately from the association parameters, leaving them unaffected by the imposed association structure between the clustered event times. We use both Archimedean and nested Archimedean copula functions to model the associations. After introducing the different copula models, we compare them using likelihood ratio tests and explore the association structures by conditional probabilities. Afterwards we use simulations to validate the size and power of the different likelihood ratio tests used to discriminate between the copula models. Furthermore, we simulate from different copula families to look at the robustness of the association estimates when the association structure is misspecified.