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International Journal of Biomedical Imaging
Volume 2009, Article ID 723912, 11 pages
http://dx.doi.org/10.1155/2009/723912
Research Article

Robust and Unbiased Variance of GLM Coefficients for Misspecified Autocorrelation and Hemodynamic Response Models in fMRI

University of Amsterdam, Roetersstraat 15, 1018 WB Amsterdam, The Netherlands

Received 3 December 2008; Revised 3 April 2009; Accepted 21 June 2009

Academic Editor: Yue Wang

Copyright © 2009 Lourens Waldorp. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. G. Sarty, Brain Activity Maps from fMRI Time Series Data, Oxford University Press, Oxford, UK, 2006.
  2. A. Dale and R. Buckner, “Selective averaging of rapidly presented individual trials using fMRI,” Human Brain Mapping, vol. 5, no. 5, pp. 329–340, 1997. View at Publisher · View at Google Scholar
  3. K. Friston, C. Frith, R. Turner, and R. Frackowiak, “Characterizing evoked hemodynamics with fMRI,” NeuroImage, vol. 2, no. 2, pp. 157–165, 1995. View at Publisher · View at Google Scholar
  4. K. Friston, O. Josephs, E. Zarahn, A. Holmes, S. Rouquette, and J.-B. Poline, “To smooth or not to smooth? Bias and efficiency in fMRI time-series analysis,” NeuroImage, vol. 12, no. 2, pp. 196–208, 2000. View at Publisher · View at Google Scholar · View at PubMed
  5. L. Waldorp, H. Huizenga, and R. Grasman, “The Wald test and Cramér-Rao bound for misspecified models in electromagnetic source analysis,” IEEE Transactions on Signal Processing, vol. 53, no. 9, pp. 3427–3435, 2005. View at Publisher · View at Google Scholar · View at MathSciNet
  6. K. Friston, A. Holmes, J.-B. Poline et al., “Analysis of fMRI time-series revisited,” NeuroImage, vol. 2, no. 1, pp. 45–53, 1995. View at Publisher · View at Google Scholar · View at PubMed
  7. J. Marchini and S. Smith, “On bias in the estimation of autocorrelations for fMRI voxel time-series analysis,” NeuroImage, vol. 18, no. 1, pp. 83–90, 2003. View at Publisher · View at Google Scholar
  8. K. J. Worsley, C. Liao, J. Aston et al., “A general statistical analysis for fMRI data,” NeuroImage, vol. 15, no. 1, pp. 1–15, 2002. View at Publisher · View at Google Scholar · View at PubMed
  9. J. Locascio, P. Jennings, C. Moore, and S. Corkin, “Time series analysis in the time domain and resampling methods for studies of functional magnetic resonance brain imaging,” Human Brain Mapping, vol. 5, no. 3, pp. 168–193, 1997. View at Publisher · View at Google Scholar
  10. E. Zarahn, G. Aguirre, and M. D'Esposito, “Empirical analyses of BOLD fMRI statistics: I spatially unsmoothed data collected under null-hypothesis conditions,” NeuroImage, vol. 5, no. 3, pp. 179–197, 1997. View at Publisher · View at Google Scholar
  11. J. Marchini and B. Ripley, “A new statistical approach to detecting significant activation in functional MRI,” NeuroImage, vol. 12, no. 4, pp. 366–380, 2000. View at Publisher · View at Google Scholar · View at PubMed
  12. M. Woolrich, B. Ripley, M. Brady, and S. Smith, “Temporal autocorrelation in univariate linear modeling of FMRI data,” NeuroImage, vol. 14, no. 6, pp. 1370–1386, 2001. View at Publisher · View at Google Scholar · View at PubMed
  13. E. Bullmore, C. Long, J. Suckling et al., “Colored noise and computational inference in neurophysiological (fMRI) time series analysis: resampling methods in time and wavelet domains,” Human Brain Mapping, vol. 12, no. 2, pp. 61–78, 2001. View at Publisher · View at Google Scholar
  14. T. Ferguson, A Course in Large Sample Theory, Chapman & Hall, Suffolk, UK, 1996.
  15. R. Henson, “Analysis of fMRI timeseries: linear time-invariant models, event-related fMRI and optimal experimental design,” in Human Brain Function, R. S. Frackowiak, J. T. Ashburner, W. D. Penny et al., Eds., chapter 10, Academic Press, New York, NY, USA, 2nd edition, 2004. View at Google Scholar
  16. K. Friston, A. Mechelli, R. Turner, and C. Price, “Nonlinear responses in fMRI: the balloon model, Volterra kernels, and other hemodynamics,” NeuroImage, vol. 12, no. 4, pp. 466–477, 2000. View at Publisher · View at Google Scholar · View at PubMed
  17. G. Glover, “Deconvolution of impulse response in event-related BOLD fMRI,” NeuroImage, vol. 9, no. 4, pp. 416–429, 1999. View at Publisher · View at Google Scholar
  18. K. Worsley, “Statistical analysis of activation images,” in Functional MRI: An Introduction to Methods, P. Jezzard, P. Matthews, and S. Smith, Eds., chapter 14, pp. 251–270, Oxford University Press, Oxford, UK, 2001. View at Google Scholar
  19. K. Friston, P. Fletcher, O. Josephs, A. Holmes, M. Rugg, and R. Turner, “Event-related fMRI: characterizing differential responses,” NeuroImage, vol. 7, no. 1, pp. 30–40, 1998. View at Publisher · View at Google Scholar · View at PubMed
  20. S. Huettel, A. Song, and G. Mccarthy, Functional Magnetic Resonance Imaging, Sinauer Associates, New York, NY, USA, 2004.
  21. C. Liao, K. Worsley, J.-B. Poline, J. Aston, G. Duncan, and A. Evans, “Estimating the delay of the fMRI response,” NeuroImage, vol. 16, no. 3, pp. 593–606, 2002. View at Publisher · View at Google Scholar
  22. R. Henson, C. Price, M. Rugg, R. Turner, and K. Friston, “Detecting latency differences in event-related BOLD responses: application to words versus non-words and initial versus repeated face presentations,” NeuroImage, vol. 15, no. 1, pp. 83–97, 2002. View at Publisher · View at Google Scholar · View at PubMed
  23. H. White, “Using least squares to approximate unknown regression functions,” International Economic Review, vol. 21, no. 1, pp. 149–170, 1980. View at Google Scholar
  24. K.-Y. Liang and S. Zeger, “Longitudinal data analysis using generalized linear models,” Biometrika, vol. 73, no. 1, pp. 13–22, 1986. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  25. J. MacKinnon and H. White, “Some heteroskedasticity-consistent covariance matrix estimators with improved finite sample properties,” Journal of Econometrics, vol. 29, no. 3, pp. 305–325, 1985. View at Google Scholar
  26. H. Huizenga and P. Molenaa, “Estimating and testing the sources of evoked potentials in the brain,” Multivariate Behavioral Research, vol. 29, no. 3, pp. 237–267, 1994. View at Google Scholar
  27. T. Gautama and M. Van Hulle, “Estimating the global order of the fMRI noise model,” NeuroImage, vol. 26, no. 4, pp. 1211–1217, 2005. View at Publisher · View at Google Scholar · View at PubMed
  28. Y.-G. Wang and X. Lin, “Effects of variance-function misspecification in analysis of longitudinal data,” Biometrics, vol. 61, no. 2, pp. 413–421, 2005. View at Publisher · View at Google Scholar · View at PubMed · View at MathSciNet
  29. M. Crowder, “On the use of a working correlation matrix in using generalised linear models for repeated measures,” Biometrika, vol. 82, no. 2, pp. 407–410, 1995. View at Publisher · View at Google Scholar
  30. K. Worsley and K. Friston, “Analysis of fMRI time-series revisited—again,” NeuroImage, vol. 2, no. 3, pp. 173–181, 1995. View at Publisher · View at Google Scholar · View at PubMed
  31. R. S. Frackowiak, J. T. Ashburner, W. D. Penny et al., Human Brain Function, Academic Press, New York, NY, USA, 2004.
  32. G. Seber and C. Wild, Nonlinear Regression, John Wiley & Sons, Toronto, Canada, 1989.
  33. A. Wink and J. Roerdink, “BOLD noise assumptions in fMRI,” International Journal of Biomedical Imaging, vol. 2006, Article ID 12014, 11 pages, 2006. View at Publisher · View at Google Scholar
  34. M. Priestly, Spectral Analysis and Time Series, vol. 1, Academic Press, New York, NY, USA, 1981.
  35. T. Amemiya, Advanced Econometrics, Basil Blackwell, Oxford, UK, 1985.
  36. S. Smith and T. Nichols, “Threshold-free cluster enhancement: addressing problems of smoothing, threshold dependence and localisation in cluster inference,” NeuroImage, vol. 44, no. 1, pp. 83–98, 2009. View at Publisher · View at Google Scholar · View at PubMed
  37. W. Weeda, L. Waldorp, I. Christoffels, and H. Huizenga, “Activated region fitting: a robust high power method for fMRI analysis using parameterized regions of activation,” Human Brain Mapping, vol. 30, pp. 2595–2605, 2009. View at Google Scholar
  38. C. Beckmann, M. Jenkinson, and S. Smith, “General multilevel linear modeling for group analysis in FMRI,” NeuroImage, vol. 20, no. 2, pp. 1052–1063, 2003. View at Publisher · View at Google Scholar · View at PubMed
  39. M. Bilodeau and D. Brenner, Theory of Multivariate Statistics, Springer, New York, NY, USA, 1999.