Abstract
PurposeIn 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 in 31P‐MRS. The uncertainty on this ratio is often neglected. We wished to explore this assumption.TheoryThe 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.MethodsTwo retrospective re‐analyses of studies comparing spectral peak ratios and one prospective simulation were performed using both the weighted and unweighted methods.ResultsIt 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.ConclusionThe 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.
Highlights
In vivo magnetic resonance spectroscopy (MRS) studies aim to determine an underlying biological difference between groups of subjects by comparing quantities of interest that are computed from spectra acquired from multiple individuals
The estimated mean 6 standard deviation phosphocreatine to ATP (PCr/ATP) ratio of T2DM patients at rest was found to be 1:74760:268 using equal weight, or 1:73060:249 propagating uncertainty, corresponding to a reduction in r on the order of $7%, and a change in the mean of less than 1%; Cv reduced from 15.3 to 14.4%
The analysis approach proposed here effectively allows for the reduction of measurement uncertainty in the estimation of variation of the population being studied, leading to a reduction in the estimated variance of simulated PCr/ATP data, and yielded gains in two representative, and very distinct, biological examples
Summary
In vivo magnetic resonance spectroscopy (MRS) studies aim to determine an underlying biological difference between groups of subjects by comparing quantities of interest that are computed from spectra acquired from multiple individuals. MRS studies are typically characterized by a highly variable signal-to-noise ratio between individuals and over time, resulting in acquired data that is of variable quality. It is often the case that this intrinsic variability of spectral data is taken into account by imposing a quality minimum on the acquired spectra; for example, by requiring the signal-to-noise ratio of an acquired spectrum to be above an arbitrary threshold, and subject only the population of data that are ‘good enough’ to further analysis (10). The analysis proposed allowed the same conclusion to be drawn with greater certainty, or, alternatively, would necessitate fewer subjects in each group be scanned in order to perform a study of identical statistical power.
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