Ridge penalized logistical and ordinal partial least squares regression for predicting stroke deficit from infarct topography

ABSTRACT

Improving the ability to assess potential stroke deficit may aid the selection of patients most likely to benefit from acute stroke therapies. Methods based only on ‘at risk’ volumes or initial neurological condition do predict eventual outcome but not perfectly. Given the close relationship between anatomy and function in the brain, we propose the use of a modified version of partial least squares (PLS) regression to examine how well stroke outcome covary with infarct location. The modified version of PLS incorporates penalized regression and can handle either binary or ordinal data. This version is known as partial least squares with penalized logistic regression (PLS-PLR) and has been adapted from its original use for high-dimensional microarray data. We have adapted this algorithm for use in imaging data and demonstrate the use of this algorithm in a set of patients with aphasia (high level language disorder) following stroke.

Improving the ability to assess potential stroke deficit may aid the selection of patients most likely to benefit from acute stroke therapies. Methods based only on ‘at risk’ volumes or initial neurological condition do predict eventual outcome but not perfectly. Given the close relationship between anatomy and function in the brain, we propose the use of a modified version of partial least squares (PLS) regression to examine how well stroke outcome covary with infarct location. The modified version of PLS incorporates penalized regression and can handle either binary or ordinal data. This version is known as partial least squares with penalized logistic regression (PLS-PLR) and has been adapted from its original use for high-dimensional microarray data. We have adapted this algorithm for use in imaging data and demonstrate the use of this algorithm in a set of patients with aphasia (high level language disorder) following stroke.

Cite this paper

nullChen, J. , Phan, T. and Reutens, D. (2010) Ridge penalized logistical and ordinal partial least squares regression for predicting stroke deficit from infarct topography.*Journal of Biomedical Science and Engineering*, **3**, 568-575. doi: 10.4236/jbise.2010.36079.

nullChen, J. , Phan, T. and Reutens, D. (2010) Ridge penalized logistical and ordinal partial least squares regression for predicting stroke deficit from infarct topography.

References

[1] Barber, P.A., Darby, D.G., Desmond, P.M., Yang, Q., Gerraty, R.P., Jolley, D., Donnan, G.A., Tress, B.M. and Davis, S.M. (1998) Prediction of stroke outcome with echoplanar perfusion- and diffusion-weighted MRI. Neurology, 51(2), 418-426.

[2] Wardlaw, J.M., Keir, S.L., Bastin, M.E., Armitage, P.A. and Rana, A.K. (2002) Is diffusion imaging appearance an independent predictor of outcome after ischemic stroke? Neurology, 59(9), 1381-1387.

[3] Kertesz, A. (1979) Aphasia and associated disorder: Taxonomy, localization and recovery. Grune & Stratton, Inc., New York.

[4] Dronkers N.F. (1996) A new brain region for coordinating speech articulation. Nature, 384, 159-161.

[5] Bates, E. Wilson, S.M. Saygin, A.P. Dick, F. Sereno, M.I. Knight, R.T. and Dronkers, N.F. (2003) Voxel-based lesion-symptom mapping. Nature Neuroscience, 6(5), 448-450.

[6] Frank, I. and Friedman, J. (1993) A statistic review of some chemometrics regression tools, with discussion, Technometrics, 35(2), 109-148.

[7] Wold, H. (1975) Soft modelling by latent variables: Non- linear iterative partial least squares (NIPALS) approach. In: Gani, M.S.B., Ed., Perspectives in Probability and Statistics, Academic Press, London, 117-142.

[8] Naes, T. and Martens, H. (1985) Comparison of prediction methods for multicollinearity data. Communication Statist Assoc, 60, 234-246.

[9] Bookstein, F.L. (1994) Partial least squares: A dose- response model for measurement in the behavioral and brain sciences. Psycoloquy, 5(23), least squares (1).

[10] McIntoch, A.R., Bookstein, F.L., Haxby, J.C. and Grady, C.L. (1996) Spatial pattern analysis of functional brain images using partial least squares. Neuroimage, 3(3), 143-157.

[11] Leibovitch, F.S., et al. (1999) Brain SPECT imaging and left hemispatial neglect covaried using partial least squares: the sunnybrook stroke study. Human Brain Mapping, 7(4), 244-253.

[12] Fort, G. and Lambert-Lacroix, S. (2005) Classification using partial least squares with penalized logistic regres- sion. Bioinformatics, 21(7), 1104-1111.

[13] Shen, L. and Tan, E.C. (2005) PLS and SVD based pena- lized logistic regression for cancer classification using microarray data. Proceedings of the 3rd Asia-Pacific Bioinformatics Conference, Singapore, 17-21 January 2005, 219-228.

[14] Huang, X.H., Pan, W., Han, X.Q., Chen, Y.J., Miller, L.W. and Hall, J. (2005) Borrowing information from relevant microarray studies for sample classification using weighted partial least squares. Computational Biology and Chemistry, 29(3), 204-211.

[15] Marx, B.D. (1996) Iterative reweighted least squares estimation for generalized linear regression. Techno- metrics, 38(4), 374-381.

[16] Phan, T.G., Chen, J., Donnan, G., Srikanth, V., Wood, A. and Reutens, D.C. (2009) Development of a new tool to correlate stroke outcome with infarct topography: A proof- of-concept study. NeuroImage, 49(1), 127-133.

[17] Draper, N.R. and Smith, H. (1998) Applied Regression Analysis, 3rd Edition, Wiley, New York.

[18] Kutner, M.H., Neter, J., Nachtsheim, C.J. and Li, W. (2004) Applied linear statistical models, 5th Edition. McGraw- Hill Irwin, Boston.

[19] Hoerl, A.E. and Kennard, R.W. (1970) Ridge regression: Biased estimation for nonorthogonal problems. Techno- metrics, 12(1), 55-67.

[20] Le Cessie, S. and van Houwelingen, J.C. (1992) Ridge estimators in logistic regression, Applied Statistics, 41(1), 191-201.

[21] Kass, R. and Raftery, A. (1995) Bayes factor. Journal of the American Statistical Association, 90(430), 773-795.

[22] Talairach, J. and Tournoux, P. (1988) Co-planar stereo- tactic atlas of the human brain. Thieme Medical Publi- shers, New York.

[23] Woods, R.P., Grafton, S.T., Watson, J.D., Sicotte, N.L. and Mazziotta, J.C. (1998) Automated image registration: II. Intersubject validation of linear and nonlinear models. Journal of Computer Assisted Tomography, 22(1), 153- 165.

[24] Wold, S., Martens, H. and Wold, H. (1983) The multi- variate calibration problem in chemistry solved by the PLS method. In: Ruhe, A. and Kagstrom, B. Eds., Proceedings of the Conference on Matrix Pencils, Pite Havsbad, 22-24 March 1983, 286-293.

[25] Geladi, P. and Kowalski, B.P. (1986) Partial least-squares regression: A tutorial. Analytica Chimica Acta, 185(1), 1-17.

[26] Abdi, H. (2003) Partial least squares (PLS) regression. In Bryman, A. Futing, T. and Lewis-Beck, M. Eds., Ency- clopedia of Social Sciences Research Methods, London.

[1] Barber, P.A., Darby, D.G., Desmond, P.M., Yang, Q., Gerraty, R.P., Jolley, D., Donnan, G.A., Tress, B.M. and Davis, S.M. (1998) Prediction of stroke outcome with echoplanar perfusion- and diffusion-weighted MRI. Neurology, 51(2), 418-426.

[2] Wardlaw, J.M., Keir, S.L., Bastin, M.E., Armitage, P.A. and Rana, A.K. (2002) Is diffusion imaging appearance an independent predictor of outcome after ischemic stroke? Neurology, 59(9), 1381-1387.

[3] Kertesz, A. (1979) Aphasia and associated disorder: Taxonomy, localization and recovery. Grune & Stratton, Inc., New York.

[4] Dronkers N.F. (1996) A new brain region for coordinating speech articulation. Nature, 384, 159-161.

[5] Bates, E. Wilson, S.M. Saygin, A.P. Dick, F. Sereno, M.I. Knight, R.T. and Dronkers, N.F. (2003) Voxel-based lesion-symptom mapping. Nature Neuroscience, 6(5), 448-450.

[6] Frank, I. and Friedman, J. (1993) A statistic review of some chemometrics regression tools, with discussion, Technometrics, 35(2), 109-148.

[7] Wold, H. (1975) Soft modelling by latent variables: Non- linear iterative partial least squares (NIPALS) approach. In: Gani, M.S.B., Ed., Perspectives in Probability and Statistics, Academic Press, London, 117-142.

[8] Naes, T. and Martens, H. (1985) Comparison of prediction methods for multicollinearity data. Communication Statist Assoc, 60, 234-246.

[9] Bookstein, F.L. (1994) Partial least squares: A dose- response model for measurement in the behavioral and brain sciences. Psycoloquy, 5(23), least squares (1).

[10] McIntoch, A.R., Bookstein, F.L., Haxby, J.C. and Grady, C.L. (1996) Spatial pattern analysis of functional brain images using partial least squares. Neuroimage, 3(3), 143-157.

[11] Leibovitch, F.S., et al. (1999) Brain SPECT imaging and left hemispatial neglect covaried using partial least squares: the sunnybrook stroke study. Human Brain Mapping, 7(4), 244-253.

[12] Fort, G. and Lambert-Lacroix, S. (2005) Classification using partial least squares with penalized logistic regres- sion. Bioinformatics, 21(7), 1104-1111.

[13] Shen, L. and Tan, E.C. (2005) PLS and SVD based pena- lized logistic regression for cancer classification using microarray data. Proceedings of the 3rd Asia-Pacific Bioinformatics Conference, Singapore, 17-21 January 2005, 219-228.

[14] Huang, X.H., Pan, W., Han, X.Q., Chen, Y.J., Miller, L.W. and Hall, J. (2005) Borrowing information from relevant microarray studies for sample classification using weighted partial least squares. Computational Biology and Chemistry, 29(3), 204-211.

[15] Marx, B.D. (1996) Iterative reweighted least squares estimation for generalized linear regression. Techno- metrics, 38(4), 374-381.

[16] Phan, T.G., Chen, J., Donnan, G., Srikanth, V., Wood, A. and Reutens, D.C. (2009) Development of a new tool to correlate stroke outcome with infarct topography: A proof- of-concept study. NeuroImage, 49(1), 127-133.

[17] Draper, N.R. and Smith, H. (1998) Applied Regression Analysis, 3rd Edition, Wiley, New York.

[18] Kutner, M.H., Neter, J., Nachtsheim, C.J. and Li, W. (2004) Applied linear statistical models, 5th Edition. McGraw- Hill Irwin, Boston.

[19] Hoerl, A.E. and Kennard, R.W. (1970) Ridge regression: Biased estimation for nonorthogonal problems. Techno- metrics, 12(1), 55-67.

[20] Le Cessie, S. and van Houwelingen, J.C. (1992) Ridge estimators in logistic regression, Applied Statistics, 41(1), 191-201.

[21] Kass, R. and Raftery, A. (1995) Bayes factor. Journal of the American Statistical Association, 90(430), 773-795.

[22] Talairach, J. and Tournoux, P. (1988) Co-planar stereo- tactic atlas of the human brain. Thieme Medical Publi- shers, New York.

[23] Woods, R.P., Grafton, S.T., Watson, J.D., Sicotte, N.L. and Mazziotta, J.C. (1998) Automated image registration: II. Intersubject validation of linear and nonlinear models. Journal of Computer Assisted Tomography, 22(1), 153- 165.

[24] Wold, S., Martens, H. and Wold, H. (1983) The multi- variate calibration problem in chemistry solved by the PLS method. In: Ruhe, A. and Kagstrom, B. Eds., Proceedings of the Conference on Matrix Pencils, Pite Havsbad, 22-24 March 1983, 286-293.

[25] Geladi, P. and Kowalski, B.P. (1986) Partial least-squares regression: A tutorial. Analytica Chimica Acta, 185(1), 1-17.

[26] Abdi, H. (2003) Partial least squares (PLS) regression. In Bryman, A. Futing, T. and Lewis-Beck, M. Eds., Ency- clopedia of Social Sciences Research Methods, London.