Title: Investigation and interpretation of the correlation structure in udder infection times by nested Archimedean copulas
Authors: Roel Braekers - Hasselt University (Belgium) [presenting]
Leen Prenen - Hasselt University (Belgium)
Luc Duchateau - Universiteit Gent (Belgium)
Abstract: The correlation structure which is often imposed on clustered multivariate time to event data, is in most cases of a simple nature. For example, in the shared frailty model, all pairwise correlations between event times in a cluster are taken the same. In modelling the infection times of the four udder quarters clustered within a cow, more complex correlation structures are possibly required. And if, such more complex correlation structures give more insight into the infection process and its spread over the different udder quarters of the cow. We choose a copula approach to study more complex correlation structures in clustered infection times. Hereby, 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.