The Annals of Applied Statistics

A lag functional linear model for prediction of magnetization transfer ratio in multiple sclerosis lesions

Gina-Maria Pomann, Ana-Maria Staicu, Edgar J. Lobaton, Amanda F. Mejia, Blake E. Dewey, Daniel S. Reich, Elizabeth M. Sweeney, and Russell T. Shinohara

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We propose a lag functional linear model to predict a response using multiple functional predictors observed at discrete grids with noise. Two procedures are proposed to estimate the regression parameter functions: (1) an approach that ensures smoothness for each value of time using generalized cross-validation; and (2) a global smoothing approach using a restricted maximum likelihood framework. Numerical studies are presented to analyze predictive accuracy in many realistic scenarios. The methods are employed to estimate a magnetic resonance imaging (MRI)-based measure of tissue damage (the magnetization transfer ratio, or MTR) in multiple sclerosis (MS) lesions, a disease that causes damage to the myelin sheaths around axons in the central nervous system. Our method of estimation of MTR within lesions is useful retrospectively in research applications where MTR was not acquired, as well as in clinical practice settings where acquiring MTR is not currently part of the standard of care. The model facilitates the use of commonly acquired imaging modalities to estimate MTR within lesions, and outperforms cross-sectional models that do not account for temporal patterns of lesion development and repair.

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Ann. Appl. Stat., Volume 10, Number 4 (2016), 2325-2348.

Received: May 2016
First available in Project Euclid: 5 January 2017

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Zentralblatt MATH identifier

Functional data analysis functional linear model magnetization transfer ratio image analysis


Pomann, Gina-Maria; Staicu, Ana-Maria; Lobaton, Edgar J.; Mejia, Amanda F.; Dewey, Blake E.; Reich, Daniel S.; Sweeney, Elizabeth M.; Shinohara, Russell T. A lag functional linear model for prediction of magnetization transfer ratio in multiple sclerosis lesions. Ann. Appl. Stat. 10 (2016), no. 4, 2325--2348. doi:10.1214/16-AOAS981.

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Supplemental materials

  • Algorithms and additional results. In this file, we include a sample sourcecode for estimation of the HFLM model, implementation details of the PW and GB approaches, figures for the simulated dense and sparse data, and additional results.