The two-stage procedure had been used as a standard method to analyse cross-over trials for many years before its major deficiency was found. The inflated type I error rate of the two-stage procedure indicates that there have been more trials which have produced false positive results than originally believed. Because of the 24 years gap between the introduction of the method and the publishing of its deficiency, it is conceivable that the impact of the change in the perception about the validity of the two-stage procedure might not have taken effect overnight. The objective of this thesis is to examine the impact of the change in the perception about the validity of the two-stage procedure on four different aspects of medical statistics. The areas of medical statistics include both applications of, and references to, the analysis of cross-over trials to give a full picture of the use of the two-stage procedure. Methods used are citation analysis for all scientific journals, systematic review for medical journals, comprehensive review for general medical statistics books and questionnaire survey for the pharmaceutical industry. The results have been inconclusive in terms of the estimation of how prevalently the two-stage procedure has been used. However, the four studies demonstrated that the analysis of cross-over trials is often associated with the two-stage procedure while the deficiency of the two-stage procedure has not been generally acknowledged. It can be concluded that further understanding of Use of the two-stage procedure for analysis of cross-over trials in four aspects of medical statistics the two-stage procedure and better references in the analysis of cross-over trials are needed in all four areas of medical statistics.

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This thesis investigates the application of classical and contemporary statistical methods in medical research attempting to bridge the gap between statistics and clinical medicine. The importance of using simple and advanced statistical methods in constructing and assessing risk models in medicine will be demonstrated by empirical studies related to vascular complications: namely abdominal aortic aneurysm and diabetic retinopathy. First, data preprocessing and preliminary statistical analysis are examined and their application is investigated using data on abdominal aortic aneurysm. We illustrate that when dealing with missing data, the co-operation between statisticians and clinicians is necessary. Also, we show advantages and disadvantages of exploratory analysis. Second, we describe and compare classification models for AAA selective screening. Tow logistic regression models are proposed. We also show that it is important to assess the performance of classifiers by cross-validation and bootstrapping. We also examine models that include other definitions of abnormality, weighted classification and multiple class models. Third, we consider the application of graphical models. We look at different types of graphical models that can be used for classification and for identifying the underlying data structure. The use of Naïve Bayes classifier (NBC) is shown and subsequently we illustrate the Occam’s window model selection in a statistical package for Mixed Interactions Modelling (MIM). The EM-algorithm and multiple imputation method are used to deal with inconsistent entries in the dataset. Finally, modelling mixture of Normal components is investigated by graphical modelling and compared with an alternative minimisation procedure. Finally, we examine risk factors of diabetic sight threating retinopathy (STR). We show the complexity of data preparation and preliminary analysis as well as the importance of using the clinicians’ opinion on selecting appropriate variables. Blood pressure measurements have been examined as predictors of STR. The fundamental role of imputation and its influence on the conclusions of the study are demonstrated. From this study, we conclude that the application of statistics in medicine is an optimisation procedure where both the statistical and the clinical validity need to be taken into account. Also, the combination of simple and advanced methods should be used as it provides additional information. Data, software and time limitations should be considered before and during statistical analysis and appropriate modifications might be implemented to avoid compromising the quality of the study. Finally, medical research should be regarded for statisticians and clinicians as part of a learning process.