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Aspects of competing risks survival analysis
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Bond, Simon James (2004) Aspects of competing risks survival analysis. PhD thesis, University of Warwick.
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Official URL: http://webcat.warwick.ac.uk/record=b1753330~S1
Abstract
This thesis is focused on the topic of competing risks survival analysis. The first
chapter provides an introduction and motivation with a brief literature review. Chapter 2
considers the fundamental functional of all competing risks data: the crude incidence
function. This function is considered in the light of the counting process framework
which provides powerful mathematics to calculate confidence bands in an analytical
form, rather than bootstrapping or simulation.
Chapter 3 takes the Peterson bounds and considers what happens in the event
of covariate information. Fortunately, these bounds do become tighter in some cases.
Chapter 4 considers what can be inferred about the effect of covariates in the case
of competing risks. The conclusion is that there exist bounds on any covariate-time
transformation. These two preceding chapters are illustrated with a data set in chapter 5.
Chapter 6 considers the result of Heckman and Honore (1989) and investigates
the question of their generalisation. It reaches the conclusion that the simple assumption
of a univariate covariate-time transformation is not enough to provide identifiability.
More practical questions of modeling dependent competing risks data through
the use of frailty models to induce dependence is considered in chapter 7. A practical
and implementable model is illustrated.
A diversion is taken into more abstract probability theory in chapter 8 which
considers the Bayesian non-parametric tool: P61ya trees. The novel framework of this
tool is explained and some results are obtained concerning the limiting random density
function and the issues which arise when trying to integrate with a realised P61ya
distribution as the integrating measure.
Chapter 9 applies the theory of chapters 7 and 8 to a competing risks data set
of a prostate cancer clinical trial. This has several continuous baseline covariates and
gives the opportunity to use a frailty model discussed in chapter 7 where the unknown
frailty distribution is modeled using a P61ya tree which is considered in chapter 8.
An overview of the thesis is provided in chapter 10 and directions for future
research are considered here.
Item Type: | Thesis (PhD) | ||||
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Subjects: | Q Science > QA Mathematics R Medicine > R Medicine (General) |
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Library of Congress Subject Headings (LCSH): | Survival analysis (Biometry), Competing risks | ||||
Official Date: | March 2004 | ||||
Dates: |
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Institution: | University of Warwick | ||||
Theses Department: | Department of Statistics | ||||
Thesis Type: | PhD | ||||
Publication Status: | Unpublished | ||||
Supervisor(s)/Advisor: | Shaw, Ewart | ||||
Sponsors: | Engineering and Physical Sciences Research Council; Knowle Hill School Fund | ||||
Extent: | xviii, 240 leaves | ||||
Language: | eng |
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