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Title: | Some Flexible Families of Mixture Cure Frailty Models and Associated Inference |
Authors: | He, Mu |
Advisor: | Balakrishnan, Narayanaswamy |
Department: | Mathematics and Statistics |
Keywords: | Survival analysis;PH;AFT;Mixture cure frailty model |
Publication Date: | 2021 |
Abstract: | In survival analysis or time-to-event analysis, one of the primary goals of analysis is to predict the occurrence of an event of interest for subjects within the study. Even though survival analysis methods were originally developed and used in medical re- search, those methods are also commonly used nowadays in other areas as well, such as in predicting the default of a loan and in estimating of the failure of a system. To include covariates in the analysis, the most widely used models are the propor- tional hazard model developed by Cox (1972) and the accelerated failure time model developed by Buckley and James (1979). The proportional hazard (PH) model as- sumes subjects from different groups have their hazard functions proportionally, while the accelerated failure time (AFT) model assumes the effect of covariates is to accel- erate or decelerate the occurrence of event of interest. In some survival analyses, not all subjects in the study will experience the event. Such a group of individuals is referred to `cured' group. To analyze a data set with a cured fraction, Boag (1948) and Berkson and Gage (1952) discussed a mixture cure model. Since then, the cure model and associated inferential methods have been widely stud- ied in the literature. It has also been recognized that subjects in the study are often correlated within clusters or groups; for example, patients in a hospital would have similar conditions and environment. For this reason, Vaupel et al. (1979) proposed a frailty model to model the correlation among subjects within clusters and conse- quently the presence of heterogeneity in the data set. Hougaard (1989), McGilchrist and Aisbett (1991), and Klein (1992) all subsequently developed parametric frailty models. Balakrishnan and Peng (2006) proposed a Generalized Gamma frailty model, which includes many common frailty models, and discussed model fitting and model selection based on it. To combine the key components and distinct features of the mixture cure model and the frailty model, a mixture cure frailty model is discussed here for modelling correlated survival data when not all the subjects under study would experience the occurrence of the event of interest. Longini and Halloran (1996) and Price and Manatunga (2001) developed several parametric survival models and employed the Likelihood Ratio Test (LRT) to perform a model discrimination among cure, frailty and mixture cure frailty models. In this thesis, we first describe the components of a mixture cure frailty model, wherein the flexibility of the frailty distributions and lifetime survival functions are discussed. Both proportional hazard and accelerated failure time models are considered for the distribution of lifetimes of susceptible (or non-cured) individuals. Correlated ran- dom effect is modelled by using a Generalized Gamma frailty term, and an EM-like algorithm is developed for the estimation of model parameters. Some Monte Carlo simulation studies and real-life data sets are used to illustrate the models as well as the associated inferential methods. |
URI: | http://hdl.handle.net/11375/26258 |
Appears in Collections: | Open Access Dissertations and Theses |
Files in This Item:
File | Description | Size | Format | |
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He_Mu_20210227_PhD.pdf | PhD thesis | 379.11 kB | Adobe PDF | View/Open |
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