Goodness-of-fit methods for multivariate survival data

Specialeforsvar ved Jeppe Ekstrand Halkjær Madsen

Titel: Goodness-of-fit methods for multivariate survival data

Abstract: This thesis covers goodness-of-fit methods for multivariate survival data (i.e. survival data with dependent observations). Frailty models and copula models are presented as ways of modelling this kind of data, and it is shown how parameters in these models can be estimated. It is shown that they are different ways of describing models that are more or less the same. Frailty models and copula models do, however, differ in their ways of describing the different properties of the models. Special attention is given to time-dependent measures of dependence between observations, and two ways of measuring tail-dependence for censored data are introduced. Methods that utilize the different properties of the models are applied to Danish twin data to illustrate the methods, and to find out what model fits the twin data best. Especially the cross hazard ratio is useful, both for plots to find out what kind of dependence there is in the data and for tests to determine what model best fits the data. No model gets clearly rejected by formal tests, but the PVF frailty model seems to be the only model that truly captures the dependence over time in the data 

Vejledere: Susanne Ditlevsen,
                   Torben Martinussen, SUND
Censor:      Anders Gorst-Rasmussen, Novo Nordisk