Survival modelling with frailty

In the survival analysis literature, the standard model for data analysis is the semi-parametric Proportional Hazard (PH) model of Cox (1972). MacKenzie (1996) introduced the Generalised Time Dependent Logistic (GTDL) family of non-PH parametric survival models, which compete with Cox’s PH model. This thesis develops the GTDL model side-by-side with the PH Weibull model. In many datasets, some attributes that might be deemed relevant may not be available. The effect of the unmeasured covariates can be quantified in a variety of ways. The technique employed here is to incorporate a random effect, called frailty, into both the Weibull and GTDL models. Further model generalisation is effected by including covariates in the frailty dispersion parameters, thus leading to structured dispersion models (Lee and Nelder, 2001). The PH Piecewise Exponential model is also developed and it is seen to not accommodate frailty. These models are used to analyse a large breast cancer registry dataset. The goodness of fit of each model is evaluated by use of a modified χ2 statistic. A comparison is also drawn between the survival predictions of the Cox model and the Nottingham Prognostic Index, which is the model used by physicians to predict survival from breast cancer. Multivariate Weibull and GTDL models, which are capable of handling more than one survival component simultaneously, are also developed.