| Summary: | Thesis (M.A.S.)--Memorial University of Newfoundland, 2002. Mathematics and Statistics Bibliography: leaves 79-80 Cure rate estimation is one of the most important issues in clinical trials and cure rate models are the main models. In the past decade, the standard cure rate model has been discussed and used. However, this model involves several drawbacks. Chen, Ibrahim and Sinha (1999) considered Bayesian methods for right-censored survival data for populations with a surviving (cure) fraction. In that paper, the authors proposed the cure rate model under the Weibull distribution which is quite different from the standard cure rate model. This proposed cure rate model overcomes the drawbacks of the standard cure rate model. However, it is not clear from their work whether their proposed cure rate models can be extended to other distributions. In this practicum, we shall extend those proposed cure rate models in Chen et al (1999) to the following distributions: log-logistic, Gompertz, and Gamma. Prior elicitations will also be discussed in detail, and classes of noninformative and informative prior distributions will be proposed. Furthermore, several theoretical properties of the proposed priors and resulting posteriors will be derived. -- At the end of this practicum, a melanoma clinical trial is used to illustrate applications of the log-logistic, Gompertz and Gamma distributions to the proposed cure rate models for Bayesian analysis. -- KEY WORDS: Cure rate model; Historical data; Current data; Posterior distribution; Gamma distribution; Log-logistic distribution; Gompertz distribution.
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