Non‐parametric combination and related permutation tests for neuroimaging

TLDR

The study introduces a single‑phase non‑parametric combination method using permutation tests to jointly analyze multiple imaging modalities, data acquisitions, or hypotheses while reducing computational demands. The authors employ synchronized permutations with union‑intersection and closed testing procedures to correct for multiple tests, evaluate various combining methods for optimal error control, and provide a unified algorithm that accommodates diverse data types. The proposed method outperforms classical multivariate tests such as MANCOVA, with Tippett’s combination offering superior error control, and it resolves multiple‑comparison problems in ANOVA while distinguishing combination from conjunction. Hum Brain Mapp 37:1486‑1511, 2016; © 2016 Wiley Periodicals, Inc.

Abstract

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. Hum Brain Mapp 37:1486‐1511, 2016 . © 2016 Wiley Periodicals, Inc.