title: Non-parametric combination and related permutation tests for neuroimaging.
abstract: In this work, we show how permutation methods can be applied to combination analyses such as those that include multiple imaging modalities, multiple data acquisitions of the same modality, or simply multiple hypotheses on the same data. Using the well-known definition of union-intersection tests and closed testing procedures, we use synchronized permutations to correct for such multiplicity of tests, allowing flexibility to integrate imaging data with different spatial resolutions, surface and/or volume-based representations of the brain, including non-imaging data. For the problem of joint inference, we propose and evaluate a modification of the recently introduced non-parametric combination (NPC) methodology, such that instead of a two-phase algorithm and large data storage requirements, the inference can be performed in a single phase, with reasonable computational demands. The method compares favorably to classical multivariate tests (such as MANCOVA), even when the latter is assessed using permutations. We also evaluate, in the context of permutation tests, various combining methods that have been proposed in the past decades, and identify those that provide the best control over error rate and power across a range of situations. We show that one of these, the method of Tippett, provides a link between correction for the multiplicity of tests and their combination. Finally, we discuss how the correction can solve certain problems of multiple comparisons in one-way ANOVA designs, and how the combination is distinguished from conjunctions, even though both can be assessed using permutation tests. We also provide a common algorithm that accommodates combination and correction.
authors: Oxford Centre for Functional MRI of the Brain, University of Oxford, Oxford, United Kingdom.
authors: Anderson M
authors: http://orcid.org/0000-0002-4169-9781
authors: AM
authors: Winkler
authors: Oxford Centre for Functional MRI of the Brain, University of Oxford, Oxford, United Kingdom.
authors: Matthew A
authors: MA
authors: Webster
authors: Clinical Research and Imaging Centre, University of Bristol, Bristol, United Kingdom.
authors: Jonathan C
authors: JC
authors: Brooks
authors: Oxford Centre for Functional MRI of the Brain, University of Oxford, Oxford, United Kingdom.
authors: Irene
authors: I
authors: Tracey
authors: Oxford Centre for Functional MRI of the Brain, University of Oxford, Oxford, United Kingdom.
authors: Stephen M
authors: SM
authors: Smith
authors: Oxford Centre for Functional MRI of the Brain, University of Oxford, Oxford, United Kingdom.|Department of Statistics & Warwick Manufacturing Group, University of Warwick, Coventry, United Kingdom.
authors: Thomas E
authors: TE
authors: Nichols
mesh_terms: D000465:Algorithms; D002540:Cerebral Cortex / Q000502:physiology* / Q000503:physiopathology; D006801:Humans; D007091:Image Processing, Computer-Assisted / Q000379:methods*; D008279:Magnetic Resonance Imaging / Q000379:methods; D059906:Neuroimaging / Q000379:methods*; D010147:Pain Measurement / Q000379:methods; D018709:Statistics, Nonparametric
keywords: conjunctions; general linear model; multiple testing; non-parametric combination; permutation tests