Adaptive Multivariate Global Testing

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' dim...

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Bibliographic Details
Published in:Journal of the American Statistical Association 2014-06, Vol.109 (506), p.613-623
Main Authors: Minas, Giorgos, Aston, John A.D., Stallard, Nigel
Format: Article
Language:English
Subjects:
Abandoned mines
Adaptation
Adaptive design
Biometrics
Clinical trials
data analysis
Design analysis
Design evaluation
electroencephalography
equations
Hypothesis testing
Mathematical vectors
Matrices
Multivariate analysis
Multivariate test
Neuroimaging
Power analysis
Power functions
Sample size
Simulations
Statistics
Theater design
Theory and Methods
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Summary: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. Supplementary materials for this article are available online.
ISSN:1537-274X
0162-1459
1537-274X
DOI:10.1080/01621459.2013.870905