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Diffusion Tensor Magnetic Resonance Imaging in the Analysis of Neurodegenerative Diseases

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Published on: July 28, 2013

Intrinsic Regression Models for Positive-Definite Matrices With Applications to Diffusion Tensor Imaging.

Hongtu Zhu¹, Yasheng Chen, Joseph G Ibrahim

¹H. Zhu is Associate Professor of Biostatistics ( hzhu@bios.unc.edu ), J. G. Ibrahim is Alumni Distinguished Professor of Biostatistics ( ibrahim@bios.unc.edu ), and Y. Li is Ph.D. Student ( liyimei@email.unc.edu ), Department of Biostatistics and Biomedical Research Imaging Center, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599-7420. Y. Chen is Research Fellow ( yasheng.chen@med.unc.edu ) and W. Lin is Professor of Radiology ( weili.lin@med.unc.edu ), Department of Radiology, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599. C. Hall is Professor of Neurology, Department of Neurology, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599 ( hallc@neurology.unc.edu ).

Journal of the American Statistical Association

|February 23, 2010

Summary

This study introduces an intrinsic regression model for analyzing positive-definite matrices in medical imaging, accounting for covariates like age and gender. The novel semiparametric approach enhances statistical analysis in Riemannian manifolds.

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Area of Science:

Statistics
Medical Imaging
Differential Geometry

Background:

Positive-definite matrices are crucial in medical imaging but do not form a vector space.
Classical multivariate regression is often inadequate for analyzing such data.
Understanding associations between medical imaging data and covariates like age and gender is vital.

Purpose of the Study:

To develop an intrinsic regression model for analyzing positive-definite matrices on Riemannian manifolds.
To establish a method for linking Euclidean covariates (age, gender) to matrix responses.
To enable robust statistical analysis in medical imaging applications.

Main Methods:

Developed a semiparametric intrinsic regression model with a link function.
Created an estimation procedure for parameter estimates and their limiting distributions.
Utilized score statistics and a resampling method for hypothesis testing.

Main Results:

The proposed model effectively analyzes positive-definite matrices in relation to covariates.
The estimation procedure provides reliable parameter estimates.
The developed test procedure controls the family-wise error rate in simulations.

Conclusions:

The intrinsic regression model offers a statistically sound approach for medical imaging data analysis.
The methodology is applicable to detecting diagnostic effects, such as on white matter integrity in HIV studies.
This work advances the statistical analysis of complex matrix-valued data in scientific research.