Skip navigation
  • Home
  • Browse
    • Communities
      & Collections
    • Browse Items by:
    • Publication Date
    • Author
    • Title
    • Subject
    • Department
  • Sign on to:
    • My MacSphere
    • Receive email
      updates
    • Edit Profile


McMaster University Home Page
  1. MacSphere
  2. Open Access Dissertations and Theses Community
  3. Open Access Dissertations and Theses
Please use this identifier to cite or link to this item: http://hdl.handle.net/11375/23906
Full metadata record
DC FieldValueLanguage
dc.contributor.advisorBalakrishnan, Narayanaswamy-
dc.contributor.authorFENG, TIAN-
dc.date.accessioned2019-02-15T14:18:05Z-
dc.date.available2019-02-15T14:18:05Z-
dc.date.issued2019-
dc.identifier.urihttp://hdl.handle.net/11375/23906-
dc.description.abstractCure rate models, introduced by Boag (1949), are very commonly used while modelling lifetime data involving long time survivors. Applications of cure rate models can be seen in biomedical science, industrial reliability, finance, manufacturing, demography and criminology. In this thesis, cure rate models are discussed under a competing cause scenario, with the assumption of proportional odds (PO) lifetime distributions for the susceptibles, and statistical inferential methods are then developed based on right-censored data. In Chapter 2, a flexible cure rate model is discussed by assuming the number of competing causes for the event of interest following the Conway-Maxwell (COM) Poisson distribution, and their corresponding lifetimes of non-cured or susceptible individuals can be described by PO model. This provides a natural extension of the work of Gu et al. (2011) who had considered a geometric number of competing causes. Under right censoring, maximum likelihood estimators (MLEs) are obtained by the use of expectation-maximization (EM) algorithm. An extensive Monte Carlo simulation study is carried out for various scenarios, and model discrimination between some well-known cure models like geometric, Poisson and Bernoulli is also examined. The goodness-of-fit and model diagnostics of the model are also discussed. A cutaneous melanoma dataset example is used to illustrate the models as well as the inferential methods. Next, in Chapter 3, the destructive cure rate models, introduced by Rodrigues et al. (2011), are discussed under the PO assumption. Here, the initial number of competing causes is modelled by a weighted Poisson distribution with special focus on exponentially weighted Poisson, length-biased Poisson and negative binomial distributions. Then, a damage distribution is introduced for the number of initial causes which do not get destroyed. An EM-type algorithm for computing the MLEs is developed. An extensive simulation study is carried out for various scenarios, and model discrimination between the three weighted Poisson distributions is also examined. All the models and methods of estimation are evaluated through a simulation study. A cutaneous melanoma dataset example is used to illustrate the models as well as the inferential methods. In Chapter 4, frailty cure rate models are discussed under a gamma frailty wherein the initial number of competing causes is described by a Conway-Maxwell (COM) Poisson distribution in which the lifetimes of non-cured individuals can be described by PO model. The detailed steps of the EM algorithm are then developed for this model and an extensive simulation study is carried out to evaluate the performance of the proposed model and the estimation method. A cutaneous melanoma dataset as well as a simulated data are used for illustrative purposes. Finally, Chapter 5 outlines the work carried out in the thesis and also suggests some problems of further research interest.en_US
dc.language.isoenen_US
dc.subjectCure rate modelsen_US
dc.subjectMixture modelen_US
dc.subjectLong-term survivorsen_US
dc.subjectCOM-Poisson distributionen_US
dc.subjectWeighted Poisson distributionen_US
dc.subjectEM algorithmen_US
dc.subjectRight censoringen_US
dc.subjectNon-informative censoringen_US
dc.subjectProfile likelihooden_US
dc.subjectAsymptotic variances and covariancesen_US
dc.subjectMaximum likelihood estimationen_US
dc.subjectLikelihood-ratio testen_US
dc.subjectExponential distributionen_US
dc.subjectProportional odds modelen_US
dc.subjectWeibull distributionen_US
dc.subjectLog-logistic distributionen_US
dc.subjectGamma distributionen_US
dc.subjectMixture of chi-squareen_US
dc.subjectAkaike Information Criterion (AIC)en_US
dc.subjectBayesian Information Criterion (BIC)en_US
dc.subjectModel discriminationen_US
dc.subjectMonte Carlo simulationsen_US
dc.subjectGoodness-of-fit testen_US
dc.subjectCutaneous melanomaen_US
dc.titleCURE RATE AND DESTRUCTIVE CURE RATE MODELS UNDER PROPORTIONAL ODDS LIFETIME DISTRIBUTIONSen_US
dc.typeThesisen_US
dc.contributor.departmentMathematics and Statisticsen_US
dc.description.degreetypeThesisen_US
dc.description.degreeDoctor of Philosophy (PhD)en_US
Appears in Collections:Open Access Dissertations and Theses

Files in This Item:
File Description SizeFormat 
Feng_Tian_201902_PhD.pdf
Open Access
1.02 MBAdobe PDFView/Open
Show simple item record Statistics


Items in MacSphere are protected by copyright, with all rights reserved, unless otherwise indicated.

Sherman Centre for Digital Scholarship     McMaster University Libraries
©2022 McMaster University, 1280 Main Street West, Hamilton, Ontario L8S 4L8 | 905-525-9140 | Contact Us | Terms of Use & Privacy Policy | Feedback

Report Accessibility Issue