title: Weighted averaging in spectroscopic studies improves statistical power.
abstract: OBJECTIVE
  In vivo MRS is often characterized by a spectral signal-to-noise ratio (SNR) that varies highly between experiments. A common design for spectroscopic studies is to compare the ratio of two spectral peak amplitudes between groups, e.g. individual PCr/γ-ATP ratios in31P-MRS. The uncertainty on this ratio is often neglected. We wished to explore this assumption.
  
  
  BACKGROUND
  The canonical theory for the propagation of uncertainty on the ratio of two spectral peaks and its incorporation in the Frequentist hypothesis testing framework by weighted averaging is presented.
  
  
  METHODS
  Two retrospective re-analyses of studies comparing spectral peak ratios and one prospective simulation were performed using both the weighted and unweighted methods.
  
  
  RESULTS
  It was found that propagating uncertainty correctly improved statistical power in all cases considered, which could be used to reduce the number of subjects required to perform an MR study.
  
  
  CONCLUSIONS
  The variability of in vivo spectroscopy data is often accounted for by requiring it to meet an SNR threshold. A theoretically sound propagation of the variable uncertainty caused by quantifying spectra of differing SNR is therefore likely to improve the power of in vivo spectroscopy studies. Magn Reson Med 78:2082-2094, 2017. © 2017 The Authors Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.
authors.affiliation: Department of Physiology, Anatomy & Genetics, University of Oxford, Oxford, UK.|Department of Physics, Clarendon Laboratory, University of Oxford, Oxford, UK.
authors.forename: Jack J
authors.identifier: http://orcid.org/0000-0002-6258-1299
authors.initials: JJ
authors.lastname: Miller
authors.affiliation: Department of Physiology, Anatomy & Genetics, University of Oxford, Oxford, UK.
authors.forename: Lowri
authors.initials: L
authors.lastname: Cochlin
authors.affiliation: Department of Physiology, Anatomy & Genetics, University of Oxford, Oxford, UK.
authors.forename: Kieran
authors.initials: K
authors.lastname: Clarke
authors.affiliation: Department of Physiology, Anatomy & Genetics, University of Oxford, Oxford, UK.
authors.forename: Damian J
authors.initials: DJ
authors.lastname: Tyler
mesh_terms: D000465:Algorithms; D000818:Animals; D003198:Computer Simulation; D003920:Diabetes Mellitus / Q000000981:diagnostic imaging; D006801:Humans; D007091:Image Processing, Computer-Assisted; D009682:Magnetic Resonance Spectroscopy; D015233:Models, Statistical; D057054:Molecular Imaging; D009010:Monte Carlo Method; D010758:Phosphorus / Q000737:chemistry; D011446:Prospective Studies; D051381:Rats; D011918:Rats, Inbred SHR; D015203:Reproducibility of Results; D012189:Retrospective Studies; D012680:Sensitivity and Specificity; D059629:Signal-To-Noise Ratio
chemical_list: D010758:Phosphorus
keywords: 13C spectroscopy; 31P spectroscopy; biostatistics; hyperpolarized 13C; magnetic resonance spectroscopy; phosphorus MRS; uncertainty analysis