Return to search

Non-parametric competing risks with multivariate frailty models

This research focuses on two theories: (i) competing risks and (ii) random eect (frailty) models. The theory of competing risks provides a structure for inference in problems where cases are subject to several types of failure. Random eects in competing risk models consist of two underlying distributions: the conditional distribution of the response variables, given the random eect, depending on the explanatory variables each with a failure type specic random eect; and the distribution of the random eect. In this situation, the distribution of interest is the unconditional distribution of the response variable, which may or may not have a tractable form. The parametric competing risk model, in which it is assumed that the failure times are coming from a known distribution, is widely used such as Weibull, Gamma and other distributions. The Gamma distribution has been widely used as a frailty distribution, perhaps due to its simplicity since it has a closed form expression of the unconditional hazard function. However, it is unrealistic to believe that a few parametric models are suitable for all types of failure time. This research focuses on a distribution free of the multivariate frailty models. Another approach used to overcome this problem is using nite mixture of parametric frailty especially those who have a closed form of unconditional survival function. In addition, the advantages and disadvantages of a parametric competing risk models with multivariate parametric and/or non-parametric frailty (correlated random eects) are investigated. In this research, four main models are proposed: rst, an application of a new computation and analysis of a multivariate frailty with competing risk model using Cholesky decomposition of the Lognormal frailty. Second, a correlated Inverse Gaussian frailty in the presence of competing risks model. Third, a non-parametric multivariate frailty with parametric competing risk model is proposed. Finally, a simulation study of nite mixture of Inverse Gaussian frailty showed the ability of this model to t dierent frailty distribution. One main issue in multivariate analysis is the time it needs to t the model. The proposed non-parametric model showed a signicant time decrease in estimating the model parameters (about 80% less time compared the Log-Normal frailty with nested loops). A real data of recurrence of breast cancer is used as the applications of these models.
Date January 2013
CreatorsMasuadi, E.
PublisherOxford Brookes University
Source SetsEthos UK
Detected LanguageEnglish
TypeElectronic Thesis or Dissertation

Page generated in 0.0015 seconds