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. / Thesis / Doctor of Philosophy (PhD)
| Identifer | oai:union.ndltd.org:mcmaster.ca/oai:macsphere.mcmaster.ca:11375/26258 |
| Date | January 2021 |
| Creators | He, Mu |
| Contributors | Balakrishnan, Narayanaswamy, Mathematics and Statistics |
| Source Sets | McMaster University |
| Language | English |
| Detected Language | English |
| Type | Thesis |
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