Modelling clustered survival data through Archimedean copulas

Abstract

Survival data are often grouped in clusters. One way to model the association between the individuals in a cluster, is through copula models. However, up to now, the use of copula models was restricted to small and equal cluster sizes. We extended the copula methodology to accommodate for clusters that have large and varying size, using the broad class of Archimedean copulas. In the second part of the thesis, we examined techniques to model survival data that exhibit multiple levels of clustering, i.e. clusters within clusters. We did this for the specific example of the time to infection of the four parts of the cow udder. When taking a closer look at a cow udder, we see that the distance between the two parts in front (resp., at the rear) is smaller than the distance between the front and rear pairs. This means that infection might spread easier from one front part to another front part, than it would spread from front to rear. We compared a set of models that are biologically relevant in this context. Although we detected a significant difference in association between the subclusters and within subclusters, since the global level of association high, it is important to know for a dairy holder that noninfected udder quarters are highly at risk whenever one of the udder quarters of a cow is already infected. Nevertheless, this four-dimensional data example is a valuable starting point to extend the models to more complex data structures.