Models for prognostic variables in matched groups with censored data
This thesis is organised and presented in nine chapters. The first chapter, the introduction, is in two broad sections and begins by discussing the origins of matched data and the reasons for matching. The general problems of censored data are mentioned and brief descriptions of the past attempts to analyse matched censored data are given, together with their shortcomings. The second section de-fines the notation used and presents the background to the failure time distributions and the types of censoring considered. Chapter 2 is concerned with the analysis of data from the proportional hazards model. The two existing methods are reviewed then a new solution, the integrated method, is proposed and the theory developed. These methods are com-pared in the following chapter, Chapter 3. Chapter 4 concentrates on data arising from the normal theory accelerated failure model. The previous solution is discussed and the results are derived for a new solution based upon the EM algorithm. This is extended to allow for right and interval censored data. The existing solution and the new solution are compared in Chapter 5. Chapter 6 provides analyses of some data sets to compare the results arising from the new methods and the existing solutions, in a practical framework. Chapter 7 discusses the relative merits of the new methods as compared with the previous solutions in the analysis of matched censored data and concludes with an outline of other areas in this field which require further research and the way in which the problems might be tackled. Chapter 8 comprises four appendices whilst Chapter 9 lists the references cited in the text.