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#### LISA: a new threshold-free and non-parametric statistical inference method for fMRI data

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##### Citation

Lohmann, G., Stelzer, J., Mueller, K., Kumar, V., Grodd, W., Buschmann, T., et al. (2017).
*LISA: a new threshold-free and non-parametric statistical inference method for fMRI data*.
Poster presented at 23rd Annual Meeting of the Organization for Human Brain Mapping (OHBM 2017), Vancouver, BC, Canada.

Cite as: https://hdl.handle.net/21.11116/0000-0000-C455-3

##### Abstract

Introduction:
Statistical inference in fMRI data analysis remains a challenging problem. Current techniques were mostly developed for 3T data, but are often unsatisfactory in terms of spatial acuity and sensitivity when applied to ultrahigh field data (>=7T). Furthermore, a recent publication by Eklund et al. [1] has highlighted problems with inflated false positive rates which can be alleviated by using very stringent initial cluster-forming thresholds (p < 0.001), but possibly at the expense of inflated false negative rates. Here we propose a new method to address these problems. It is called "LISA" because it is inspired by hot spot analysis of geographical information systems where hot spots are identified using so-called Local Indicators of Spatial Association (LISA) [2]. With LISA, every voxel receives a hot spot score which serves as a new test statistic and may be seen as a compromise between cluster-level and voxel-level inference.
Methods:
If operated at the second (group) level, the algorithm LISA expects as input a set of contrast maps obtained from a first level GLM analysis. First a voxelwise t-test is applied yielding a map in which each voxel has a z-value uncorrected for multiple comparisons. We now apply a bilateral filter to this map which suppresses noise while preserving spatial acuity [3]. The parameters of this filter were determined using simulated data and were kept constant for all experiments reported below. The filtered map highlights hot spots of activation which LISA aims to detect. Statistical inference is performed by controlling the false discovery rate (FDR). Note that the classical FDR algorithm [4] assumes that all data points are independent and under the null hypothesis z-values follow a standard Gaussian distribution. Both assumptions may be violated here. Therefore, we use a different FDR procedure which is based on a two-component model [5] in which we estimate the null distribution using random permutations of the contrast maps. The LISA algorithm can also be used at the first level (single subject analysis) in which case it expects as input a preprocessed fMRI data set and the experimental design information. To ensure exchangeability, the null distribution is obtained using random permutations of labels [6,7]. Otherwise, the algorithm works as described above.
Results:
We subjected LISA to a battery of tests.
Test 1: We analysed 127 data sets of the "Beijing" sample of [1], using the same experimental designs and preprocessing regimes as in [1] (6mm spatial smoothing). In each of the four designs (B1,B2,E1,E2) , we randomly drew 100 samples consisting of 40 data sets and obtained the following family-wise error rates: 3/100 (B1), 0/100 (B2), 0/100 (E1), 2/100 (E2).
Test 2: Simulated data. Comparison with FSL-TFCE [9], see fig.1.
Test 3: fMRI data of the "emotion task" of the Human Connectome Project (HCP) [8]. We randomly selected 10 sets of 20 data sets each and compared the LISA results with results obtained by FSL-TFCE [9], see fig.2 (top).
Test 4: Single subject data acquired at a 9.4T human whole-body scanner (Siemens) using a custom-built 31-channel receive coil array. Gradient Echo EPI, 30 slices, Grappa 4, 6/8 partial fourier, PSF-based distortion correction, resolution 0.8mm isotropic, 30 slices, 405 volumes, TR/TE=1580/22ms, FOV 171mm, working memory task, 8+8 trials (2back/0back), fig.2 (bottom)
Conclusions:
Lisa corrects for FDR, but under the Eklund test it produced even more conservative results than expected if corrected for the familywise error. LISA appears to be less conservative than FSL-TFCE, and shows a high spatial precision and sensitivity when applied to data acquired at an ultra-high field scanner. Applying an edge-preserving filter at a late stage in the analysis chain rather than during preprocessing.