Efficient Blockwise Permutation Tests Preserving Exchangeability

Authors

  • Chunxiao Zhou Mark O. Hatfield Clinical Research Center, National Institutes of Health, Bethesda, MD, USA
  • Chris E. Zwilling Department of Psychology, University of Illinois at Urbana-Champaign, Champaign, IL, USA
  • Vince D. Calhoun Dept. of ECE, The University of New Mexico, and The Mind Research Network and LBERI, Albuquerque, NM, USA
  • Michelle Y. Wang Department of Statistics, Department of Bioengineering, University of Illinois at Urbana-Champaign, Champaign, IL, USA

DOI:

https://doi.org/10.6000/1929-6029.2014.03.02.8

Keywords:

Efficient nonparametric test, moments, Pearson distribution series, structural MRI, voxel-based morphometry

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).

Author Biographies

Chunxiao Zhou, Mark O. Hatfield Clinical Research Center, National Institutes of Health, Bethesda, MD, USA

Mark O. Hatfield Clinical Research Center

Chris E. Zwilling, Department of Psychology, University of Illinois at Urbana-Champaign, Champaign, IL, USA

Department of Psychology,

Vince D. Calhoun, Dept. of ECE, The University of New Mexico, and The Mind Research Network and LBERI, Albuquerque, NM, USA

The Mind Research Network and LBERI

Michelle Y. Wang, Department of Statistics, Department of Bioengineering, University of Illinois at Urbana-Champaign, Champaign, IL, USA

Departments of Statistics, Psychology, and Bioengineering

References

Ashburner J, Csernansky JG, Davatzikos C, Fox NC, Frisoni GB, Thompson PM. Computer-assisted Imaging to Assess Brain Structure in Healthy and Diseased Brains. Lancet Neurol 2003; 2(2): 79-88. http://dx.doi.org/10.1016/S1474-4422(03)00304-1 DOI: https://doi.org/10.1016/S1474-4422(03)00304-1

Ashburner J. VBM Tutorial 2010. http://www.fil.ion.ucl.ac.uk

Gaonkar B, Pohl K, Davatzikos C. Pattern Based Morphometry. Medical Imaging Computing and Computer Assisted Intervention. 2011: p. 459-466. DOI: https://doi.org/10.1007/978-3-642-23629-7_56

Pantazis D, Leahy RM, Nichols TE, Styner M. Statistical Surface-based Morphometry using A Non-parametric Approach. IEEE International Symposium on Biomedical Imaging; 2004: p. 1283-1286. http://www.stat.wisc.edu/ ~mchung/softwares/pvalue/permutation.tstat.hippocampus.pdf

Zhou C, Wang H, Wang YM. Efficient Moments-based Permutation Tests. Advances in Neural Information Processing Systems; 2009: p. 2277-2285. http://papers.nips.cc/paper/3858-efficient-moments-based-permutation-tests.pdf

Friston KJ, Holmes AP, Worsley KJ, Poline JP, Frith CD, Frackowiak RSJ. Statistical Parametric Maps in Functional Imaging: A General Linear Approach. Hum Brain Mapp 1995; 2: 189-210. http://dx.doi.org/10.1002/hbm.460020402 DOI: https://doi.org/10.1002/hbm.460020402

Holmes AP, Blair RC, Watson JDG, Ford I. Nonparametric Analysis of Statistic Images from Functional Mapping Experiments. J Cereb Blood Flow Metab 1996; 16: 7–22. http://dx.doi.org/10.1097/00004647-199601000-00002 DOI: https://doi.org/10.1097/00004647-199601000-00002

Nichols TE, Holmes AP. Nonparametric Permutation Tests for Functional Neuroimaging: A primer with Examples. Hum Brain Mapp 2001; 15: 1-25. http://dx.doi.org/10.1002/hbm.1058 DOI: https://doi.org/10.1002/hbm.1058

Sandrone S, Bacigaluppi M, Galloni MR, Cappa SF, Moro A, Catani M, Filippi M, Monti MM, Perani D, Martino G. Weighing Brain Activity with the Balance: Angelo Mosso's Original Manuscripts Come to Light. Brain 2014; 137: 621-33. http://dx.doi.org/10.1093/brain/awt091 DOI: https://doi.org/10.1093/brain/awt091

Worsley KJ, Evans AC, Marrett S, Neelin P. A Three-dimensional Statistical Analysis for CBF Activation Studies in Human Brain. J Cereb Blood Flow Metab 1992; 12: 900–918. http://dx.doi.org/10.1038/jcbfm.1992.127 DOI: https://doi.org/10.1038/jcbfm.1992.127

Wang YM, Xia J. Unified Framework for Robust Estimation of Brain Networks from fMRI using Temporal and Spatial Correlation Analyses. IEEE Trans on Med Imaging 2009; 28(8): 1296-1307. http://dx.doi.org/10.1109/TMI.2009.2014863 DOI: https://doi.org/10.1109/TMI.2009.2014863

Ashburner J, Friston KJ. Voxel-based Morphometry – the Methods. Neuroimage 2000; 11(6): 805-821. http://dx.doi.org/10.1006/nimg.2000.0582 DOI: https://doi.org/10.1006/nimg.2000.0582

Zhou C, Wang YM. Hybrid Permutation Test with Application to Surface Shape Analysis. Stat Sin 2008; 18(4): 1553-1568. http://www3.stat.sinica.edu.tw/statistica/oldpdf/A18n417.pdf

Good P. Permutation, Parametric and Bootstrap Tests of Hypotheses. 3rd ed. New York: Springer, 2005.

Edgington E. Randomization Tests. 3rd ed. Boca Raton: CRC 1995.

Fox NC, Schott JM. Imaging Cerebral Atrophy: Normal Ageing to Alzheimer’s Disease. Lancet 2004; 363: 32-394. http://dx.doi.org/10.1016/S0140-6736(04)15441-X DOI: https://doi.org/10.1016/S0140-6736(04)15441-X

Fu L, Fonov V, Pike GB, Evans AC, Collins DL. Automated Analysis of Multi Site MRI Phantom Data for the NIHPD Project. Medical Imaging Computing and Computer Assisted Intervention; 2006: p. 144-151. DOI: https://doi.org/10.1007/11866763_18

Jones RW, Witte RJ. Signal Intensity Artifacts in Clinical MR Imaging. Radiographics 2000; 20: 893–901. http://dx.doi.org/10.1148/radiographics.20.3.g00ma19893 DOI: https://doi.org/10.1148/radiographics.20.3.g00ma19893

Jovicich J, Czanner S, Greve D, Haley E, Kouwe AVD, Gollub R, Kennedy D, Schmitt F, Brown G, Macfall J, Fischl B, Dale A. Reliability in Multi-site Structural MRI Studies: Effects of Gradient Non-linearity Correction on Phantom and Human Data. NeuroImage 2006; 30: 436–443. http://dx.doi.org/10.1016/j.neuroimage.2005.09.046 DOI: https://doi.org/10.1016/j.neuroimage.2005.09.046

Hubert L. Assignment methods in combinatorial data analysis. New York: Marcel Dekker 1987.

Mielke PW, Berry KJ. Permutation Methods: A Distance Function Approach. New York: Springer 2001. http://dx.doi.org/10.1007/978-1-4757-3449-2 DOI: https://doi.org/10.1007/978-1-4757-3449-2

Hahn J, Shapiro SS. Statistical Models in Engineering. New York: John Wiley & Sons 1967.

Serfling RJ. Approximation Theorems of Mathematical Statistics. New York: Wiley 1980. http://dx.doi.org/10.1002/9780470316481 DOI: https://doi.org/10.1002/9780470316481

Benjamini Y, Hochberg Y. Controlling the False Discovery Rate: A Practical and Powerful Approach to Multiple Testing. J R Stat Soc Series B Stat Methodol 1995; 57: 289-300. http://engr.case.edu/ray_soumya/mlrg/controlling_fdr_benjamini95.pdf DOI: https://doi.org/10.1111/j.2517-6161.1995.tb02031.x

Storey JD. A Direct Approach to False Discovery Rates. J R Stat Soc Series B Stat Methodol 2002; 64: 479-498. http://dx.doi.org/10.1111/1467-9868.00346 DOI: https://doi.org/10.1111/1467-9868.00346

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Published

2014-04-30

How to Cite

Zhou, C., Zwilling, C. E., Calhoun, V. D., & Wang, M. Y. (2014). Efficient Blockwise Permutation Tests Preserving Exchangeability. International Journal of Statistics in Medical Research, 3(2), 134–144. https://doi.org/10.6000/1929-6029.2014.03.02.8

Issue

Vol. 3 No. 2 (2014)

Section

General Articles

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Copyright (c) 2014 Chunxiao Zhou, Chris E. Zwilling, Vince D. Calhoun, Michelle Y. Wang

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