Frailty models in survival analysis

Abstract

This dissertation is about frailty models in survival analysis. Survival analysis deals with lifetime data, which measure the time to a well-defined event of interest. Traditional survival models assume homogeneity within the population, meaning that all individuals have the same risk of death. Traditional models include both the Kaplan Meier and Nelson-Aalen approaches, as well as the Cox proportional hazards model; however, these do not account for association and unobserved heterogeneity in the population. The concept of frailty provides a suitable way to introduce random effects in the model to deal with the limitations of the traditional models. A frailty model is a random effects model for time variables, where the random effect, or frailty, has a multiplicative effect on the hazard function. This study explores the application of shared and unshared frailty models on survival data of patients who underwent aortic valve replacements, and investigates the degree of heterogeneity of the model predictors using shared and unshared approaches. An investigation into the semi-parametric techniques used to model frailty is also carried out, wherein alternative estimation strategies such as the expectation-maximisation (EM) algorithm and the penalised partial likelihood (PPL) method are required.