Rogers, Jennifer Kaye (2011) Statistical models for censored point processes with cure fractions. PhD thesis, University of Warwick.

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Abstract

We consider the analysis of data from the MRC Multicentre Trial for Early Epilepsy and Single Seizures (MESS), which was undertaken to assess the differences between two policies: immediate, or deferred treatment for patients in early epilepsy. In studies of recurrent events, like epileptic seizures, there is typically lots of information about individuals’ seizure patterns over a period of time, which is often not fully utilised in analysis. We develop methodology that allows pre-randomisation seizure counts and post-randomisation times to first seizure, and from first to second seizure, to be jointly modelled, assuming that these outcomes are predicted by (unobserved) seizure rates. The joint model was found to be superior to standard survival methods. The model had more power to detect statistically significant covariate effects not found by standard survival analysis, however, interesting characteristics within the data, not present in the model were also highlighted. The simple joint model was extended to acknowledge these characteristics. The results suggested that the identically distributed assumption for the survival times may not be accurate. Instead we adjusted the model to allow for changes in seizure rate both at randomisation and following a seizure postrandomisation. There is evidence to suggest that there may be a substantial subset of the MESS sample containing individuals who we would not expect to experience seizures post-randomisation. If survival data has a proportion that are immune to the event of interest, a model that ignores this may give misleading results. We considered a cure rate model that allows the separation of individuals who will never experience seizure recurrence and those who are at risk of future seizures. We can then formulate probabilistic models for the 'at risk' individuals. These modifications to the simple joint model have been considered both in isolation and together in a full model.

Item Type:	Thesis or Dissertation (PhD)
Subjects:	Q Science > QA Mathematics
Library of Congress Subject Headings (LCSH):	Epilepsy -- Treatment -- Mathematical models, Survival analysis (Biometry)
Date:	January 2011
Institution:	University of Warwick
Theses Department:	Department of Statistics
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Hutton, Jane L.
Sponsors:	Engineering and Physical Sciences Research Council (EPSRC)
Extent:	xv, 193 leaves : charts
Language:	eng
URI:	http://wrap.warwick.ac.uk/id/eprint/35595

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