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, Russell T. Shinohara

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)2325-2348
Number of pages24
JournalAnnals of Applied Statistics
Issue number4
StatePublished - Dec 2016


  • Functional data analysis
  • Functional linear model
  • Image analysis
  • Magnetization transfer ratio

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Statistics, Probability and Uncertainty


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