Factor copula models for right-censored clustered survival data

Abstract

The vast majority of the random phenomena studied by applied statisticians are governed by complex dependence structures. Neglecting these associations in the statistical analysis often gives rise to misleading and biased results. This is precisely what makes multivariate data analysis so important. In multivariate survival analysis, for example, particularly when dealing with clustered survival data, the interest lies in modelling the multiple lifetimes (time until an event happens) of individuals grouped in clusters. The lifetimes of individuals inside a cluster are known to be associated to each other through a complicated dependence structure, the intracluster dependence. On top of this, survival data are often right-censored, a condition where a subject survives up to a certain point in time, but the exact moment of occurrence of the event of interest is not observed. These features make the study of right-censored clustered survival data non-trivial. In general, there are two types of models that are commonly used to model these forms of data: frailty models and copula models. In frailty models, we assume that the different lifetimes in a cluster are independent of each other, conditional on a common random term, the frailty term. Although frailty models are widely used to model clustered survival data, they have some deficiencies: the number of frailty distributions which are implemented is limited. Furthermore, the interpretation of the frailty parameter is not straightforward since it expresses the heterogeneity between clusters, rather than the association between lifetimes in a cluster. On the other hand, the interpretation of the parameters in copula models is easier since these models are, by their form, adapted to make a clear distinction between the marginal behaviour of a lifetime and the association between different lifetimes. Moreover, an extensive number of parametric copula families is available and already implemented in several statistical software packages. However, up to now, copula models have not been used to their full potential in clustered survival data modelling. Their usage was restricted to settings where either the size of the clusters is fixed, or the number of copula families implemented is limited. Considering these shortcomings of the current methodologies, this thesis aims to make a contribution towards the modelling of clustered survival data by copula models. In this sense, we propose a new class of models based on the flexible factor copula models that can handle right-censored clustered survival data grouped in variable sized clusters and allows the use of any copula family to model intracluster dependence. Additionally, we provide the computational routines for implementations of our methods. We show, with a real data application and simulation studies, that the newly proposed methods have solid finite sample properties, straightforward interpretation and are not computationally expensive.