Abstract
In this paper, we present a new blockwise permutation test approach based on the moments of the test statistic. The method is of importance to neuroimaging studies. In order to preserve the exchangeability condition required in permutation tests, we divide the entire set of data into certain exchangeability blocks. In addition, computationally efficient moments-based permutation tests are performed by approximating the permutation distribution of the test statistic with the Pearson distribution series. This involves the calculation of the first four moments of the permutation distribution within each block and then over the entire set of data. The accuracy and efficiency of the proposed method are demonstrated through simulated experiment on the magnetic resonance imaging (MRI) brain data, specifically the multi-site voxel-based morphometry analysis from structural MRI (sMRI).
Highlights
Hypothesis testing has been widely used in neuroimaging data analysis, such as morphometry analysis [1,2,3,4,5], brain activation detection and inference [6,7,8,9,10], and functional integration and connectivity [11]
We assume that the test statistic T can be expressed as a weighted v-statistic [5, 23] of degree d as following: where x = (x1,x2,...,xn )T is a dataset with n observations, w is an index function, and h is a symmetric data function that is invariant under permutation of (i1,..., id )
We apply our blockwise permutation method to a simulated multi-site structural MRI (sMRI) data set for voxel-based morphometry (VBM)
Summary
Hypothesis testing has been widely used in neuroimaging data analysis, such as morphometry analysis [1,2,3,4,5], brain activation detection and inference [6,7,8,9,10], and functional integration and connectivity [11]. In order to deal with small sample size neuroimaging data with unknown distribution, nonparametric permutation tests are employed [4, 7]. Permutation tests construct the distribution of a test statistic by resampling data without replacement. In the two-sample hypothesis testing case, data exchangeability means the distributions of two group data are identical under the null hypothesis [14, 15]. We propose and develop a novel moments-based blockwise permutation test method. The first four moments of the entire set of data are computed by combining the first four moments from all blocks through an efficient representation With this computationally efficient moments-based blockwise permutation tests scheme, we maintain the flexibility of permutation tests, preserve the exchangeability condition, and reduce the computational cost dramatically. We apply the proposed method to neuroimaging data for voxel-based morphometry from simulated multisite sMRI, compensating for the undesirable spatial effects/artifacts with more sensitive and robust imaging data analyses
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