Minas, Giorgos, Aston, John A. D. and Stallard, Nigel (2014) Adaptive multivariate global testing. Journal of the American Statistical Association, Volume 109 (Number 506). doi:10.1080/01621459.2013.870905

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Abstract

We present a methodology for dealing with recent challenges in testing global hypotheses using multivariate observations. The proposed tests target situations, often arising in emerging applications of neuroimaging, where the sample size n is relatively small compared with the observations’ dimension K. We employ adaptive designs allowing for sequential modifications of the test statistics adapting to accumulated data. The adaptations are optimal in the sense of maximizing the predictive power of the test at each interim analysis while still controlling the type I error. Optimality is obtained by a general result applicable to typical adaptive design settings. Further, we prove that the potentially high-dimensional design space of the tests can be reduced to a low-dimensional projection space enabling us to perform simpler power analysis studies, including comparisons to alternative tests. We illustrate the substantial improvement in efficiency that the proposed tests can make over standard tests, especially in the case of n smaller or slightly larger than K. The methods are also studied empirically using both simulated data and data from an EEG study, where the use of prior knowledge substantially increases the power of the test.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics R Medicine > RC Internal medicine > RC0321 Neuroscience. Biological psychiatry. Neuropsychiatry
Divisions:	Faculty of Medicine > Warwick Medical School > Health Sciences Faculty of Science > Statistics Faculty of Science > Centre for Systems Biology Faculty of Medicine > Warwick Medical School
Library of Congress Subject Headings (LCSH):	Diagnostic imaging, Neurology -- Research , Statistics
Journal or Publication Title:	Journal of the American Statistical Association
Publisher:	American Statistical Association
ISSN:	0162-1459
Official Date:	2014
Dates:	Date Event 2014 Published 13 June 2014 Available 19 December 2013 Accepted 1 April 2013 Submitted
Date of first compliant deposit:	28 July 2016
Volume:	Volume 109
Number:	Number 506
DOI:	10.1080/01621459.2013.870905
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Open Access
Funder:	Engineering and Physical Sciences Research Council (EPSRC)
Grant number:	EP/K021672/1 (EPSRC)

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