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Survival models for censored point processes
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Cowling, Benjamin John (2003) Survival models for censored point processes. PhD thesis, University of Warwick.
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WRAP_thesis_Cowling_2003.pdf - Submitted Version Download (9Mb) | Preview |
Official URL: http://webcat.warwick.ac.uk/record=b1665095~S1
Abstract
In studies of recurrent events, there can be a lot of information about a cohort over
a period of time, but it may not be possible to extract as much information from
the data as would be liked. This thesis considers data on individuals experiencing
recurrent events, before and after they are randomised to treatment. The prerandomisation
outcome is a period count, while the post-randomisation outcome
is a survival time. Standard survival analysis may treat the pre-randomisation
period count as a covariate, but it is proposed that point process models will give
a more precise estimate of the treatment effect.
A joint model is presented, based on a Poisson process with individual frailty. The
pre-randomisation seizure counts are distributed as Poisson variables with rate
depending on explanatory variables as well as a random frailty. The model for the
post-randomisation survival times is the exponential distribution with the same
individual seizure rate, modified by a multiplicative treatment effect. A conjugate
mixing distribution (frailty) is used, and alternative mixing distributions are also
discussed.
The model is motivated by and illustrated on individual patient data from five
randomised trials of two treatments for epilepsy. The data are presented, and the
standard analyses are contrasted with the results of the joint model.
This thesis also considers the relative efficiency of the joint model compared to
other survival models. Finally, some extensions to the model are considered, including
a more general non-conjugate mixing distribution, and alternative ways
of including explanatory variables in the joint model.
Item Type: | Thesis (PhD) |
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Subjects: | Q Science > QA Mathematics |
Library of Congress Subject Headings (LCSH): | Statistics, Poisson processes, Point processes, Epilepsy |
Official Date: | November 2003 |
Institution: | University of Warwick |
Theses Department: | Department of Statistics |
Thesis Type: | PhD |
Publication Status: | Unpublished |
Supervisor(s)/Advisor: | Hutton, Jane (Statistician) ; Shaw, Ewart |
Sponsors: | Engineering and Physical Sciences Research Council (EPSRC) |
Extent: | xvi, 221 leaves |
Language: | eng |
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