A Test for Confounding in Coupling of Multimodal Neuroimaging Data

Multimodal neuroimaging studies often involve comparisons between brain maps. Recently, statistical methods have been proposed to quantify and assess spatial correspondence between two modalities. The simple permutation-based inter-modal correspondence (SPICE) test evaluates whether within-subject correspondence exceeds chance, where the null distribution is constructed by permuting subject labels for one modality. Despite its easy implementation and minimal spatial assumptions, the critical assumption underlying permutation analysis, that subjects are exchangeable under the null, may be violated when covariates such as age, sex, or disease status systematically alter brain map distributions. This violation can produce results analogous to Simpson's paradox, where apparent population-level correspondence reflects between-group differences rather than genuine within-subject coupling. We propose a formal U-statistic-based test for such covariate effects, enabling both diagnostic evaluation of assumption violations and scientific discovery. Using synthetic and semi-synthetic neuroimaging data, we demonstrate well-controlled Type I error and high statistical power. We apply our method to test for confounding effects due to age and sex using real data from two pairs of imaging modalities in the Philadelphia Neurodevelopmental Cohort. Our framework increases the rigor and interpretability of intermodal coupling analyses, with broad implications for neuroimaging studies in heterogeneous populations, especially in developmental, aging, and disease-focused research.