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Title: Multivariate global testing and adaptive designs
Author: Minas, Giorgos
Awarding Body: University of Warwick
Current Institution: University of Warwick
Date of Award: 2013
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Global tests are a key research endpoint in multivariate studies. They provide an omnibus assessment of the overall effects across the multivariate outcomes. This global evaluation is clearly of high practical value in the field of neuroimaging, which has become increasingly important in recent years. Existing global testing methodologies, however, fail to accommodate the demands of neuroimaging studies that have typically small sample sizes and highly correlated local outcomes. In this thesis a novel class of multivariate global tests is developed. The proposed tests are based on a formal framework for using prior information and accumulated data to learn the effect direction. This framework is used to construct test statistics that target the estimated effect direction, rather than the whole multivariate space, for detecting global effects. Adaptive designs are employed to allow for sequential modifications of the test statistics, based on accumulated data, without inflating the type I error. A major focus in our methodology is power performance. The proposed tests are shown to be optimal in terms of predictive power. Furthermore, a power characterisation allowing us to explain the behaviour of our tests and perform simple power analysis is derived. An extensive power analysis, including comparisons to alternative global tests, is performed. Applications to neuroimaging studies are illustrated through two real examples. Our results show that the developed methodology can be particularly useful in cases where the sample sizes are small and prior information about the effect direction is available.
Supervisor: Not available Sponsor: Engineering and Physical Sciences Research Council (EPSRC) (EP/F034210/1)
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: QA Mathematics