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.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:588488 |
| Date | January 2013 |
| Creators | Masuadi, E. |
| Publisher | Oxford Brookes University |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://radar.brookes.ac.uk/radar/items/e828e4da-de08-2f34-37b0-8cc3bbaf7150/1 |
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