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Title: Optimal group sequential tests
Author: Eales, John D.
ISNI:       0000 0001 3436 8725
Awarding Body: University of Bath
Current Institution: University of Bath
Date of Award: 1991
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Sequential procedures were originally designed for use in an industrial context. However the flexibility and efficiency of sequential methods made them attractive to those involved in medical experimentation. The earliest sequential designs for clinical trials were fully sequential, that is they required an analysis to be conducted after every patient response. More recently the emphasis has been on group sequential designs, where analyses are carried out after groups of patient responses. One of the distinguishing features of sequential procedures is that the required sample size is a random variable. For fixed group sizes, a given maximum number of analyses and given error constraints, group sequential tests can be designed which minimize a given function of expected sample size. We term such procedures optimal group sequential tests. In this thesis we introduce a computationally efficient and numerically stable method for the computation of optimal group sequential tests. Although we approach this problem from a frequentist perspective, our method makes use of both Bayesian decision theory and dynamic programming. In Chapters 3 and 4 we consider computing optimal one-sided and two-sided tests respectively. The two-sided tests permit the rejection of the null hypothesis, H0, at any analysis, but they only allow H0 to be accepted at the final analysis. In Chapter 5 we consider computing optimal wedge tests which, like two-sided tests, test Hq against a two-sided alternative, but, unlike two-sided tests, allow H0 to be accepted or rejected at each analysis. In Chapter 6 we consider some of the Bayesian and Bayes decision theoretic procedures proposed in the literature. Finally, in Chapter 7, we look at a number of ideas for future research as well as some relevant topics which have not been considered elsewhere in the thesis.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: Statistics