Title:

A study of two practical problems in clinical trials methodology

In this thesis, two problems which commonly arise in the context of clinical trials, but which are often dealt with inappropriately are considered. The thesis consists of two parts, one corresponding to each of the problems considered. Part I (Chapters 24 inclusive) considers the problem of how to handle incomplete multivariate data, while Part II (Chapters 57 inclusive) looks at some methods for comparing groups which have an a priori ordering. Chapter 1 provides a general introduction to clinical trials methodology, describing some of the basic concepts involved, for example randomisation and blinding. In addition, some recent developments, for instance metaanalysis, are outlined. The chapter ends with an informal review of the last two years' issues of two leading medical statistics journals, namely "Statistics in Medicine" and "Controlled Clinical Trials", in order to highlight some of the topics of current interest. Chapter 2 introduces the problem of handling incomplete data. The basic terminology for describing missing data mechanisms is given, with special emphasis being given to the ideas of "Missing at Random" as described in Rubin(1976). The chapter ends with a review of some of the commoner methods of analysis used. Some of the potential problems which can arise when using these methods are outlined. In Chapter 3, the ideas of maximum likelihood estimation in the presence of incomplete data are developed. After describing some existing likelihoodmaximisation techniques for handling single groups in isolation, these ideas are then extended to the multiplegroup problem. Methods are developed for fitting models where several groups are constrained to have a common covariance matrix, but are allowed to have different means. This allows emulation of the likelihood ratio testing procedures usually only applicable if the data are complete. In Chapter 4, the techniques of the previous two chapters are applied to three real examples. Some of the work of Section 4.1 has appeared previously in Murray and Findlay(1988). The main results of chapters 24 are summarised. Emphasised is the fact that inappropriate handling of even a relatively small amount of incomplete data can have a substantial effect on the results obtained. Chapter 5 marks the beginning of Part II of the thesis. The ideas of orderrestricted inference are introduced, and some potential areas of application are outlined. After a review of some of the existing literature, it becomes clear that there exist certain common clinical trials scenarios where no appropriate testing procedures are available. Notably, there is no procedure available for testing for differences between ordered groups of Normally distributed data while incorporating covariate information. After devising a suitable testing technique for such problems, eight different tests are defined which incorporate differing degrees of information and assvimptions about the data under study, in terms of distributional assumptions, covariate information and prior group ordering information. In Chapter 6 the aim is to compare the performance of the eight tests defined in Chapter 5 under a variety of conditions, after evaluating and optimising the specifications of one relatively recent test (Marcus and Genizi (1987)). The performance of the eight tests are assessed : (a) as the group separation is varied, (b) as the covariate/response correlation is varied, and (c) as the error distribution is made other than Normal. The conclusions drawn are that while the incorporation of covariates and ordering information is always worthwhile, the assumption of Normality does not greatly affect the sensitivity of the analyses performed. It is noted that there could be some difficulties in gaining acceptance by clinicians for the more complicated procedures described, and that, in practical terms, gaining statistical sensitivity could well be at the cost of losing credibility. In Chapter 7, ordered testing procedures are applied to some published data sets, and the results thus obtained are compared to those which were published. Finally, Chapter 8 outlines the conclusions for the thesis as a whole, stressing the important implications as regards clinical research. Some ideas for future research in the topics covered are proposed.
