'Pscore' - A Novel Percentile-Based Metric to Accurately Assess Individual Deviations in Non-Gaussian Distributions of Quantitative MRI Metrics

Abstract

Background: Quantitative MRI metrics could be used in personalized medicine to assess individuals against normative distributions. Conventional Zscore analysis is inadequate in the presence of non-Gaussian distributions. Therefore, if quantitative MRI metrics deviate from normality, an alternative is needed.

Purpose: To confirm non-Gaussianity of diffusion MRI (dMRI) metrics on a publicly available dataset, and to propose a novel percentile-based method, 'Pscore' to address this issue.

Study type: Retrospective cohort.

Population: 961 healthy young-adults (age:22-35 years, Females:53%) from the Human Connectome Project.

Field strength/sequence: 3-T, spin-echo diffusion echo-planar imaging, T1-weighted: MPRAGE.

Assessment: The dMRI data were preprocessed using the TORTOISE pipeline. Forty-eight regions of interest (ROIs) from the JHU-atlas were redrawn on a study-specific diffusion tensor (DT) template and average values were computed from various DT and mean apparent propagator (MAP) metrics. For each ROI, percentile ranks across participants were computed to generate 'Pscores'- which normalized the difference between the median and a participant's value with the corresponding difference between the median and the 5^th/95^th percentile values.

Statistical tests: ROI-wise distributions were assessed using Log transformations, Zscore, and the 'Pscore' methods. The percentages of extreme values above-95^th and below-5^th percentile boundaries (${\text{PEV}}_{<5}(\%)$,${\text{PEV}}_{<5}(\%)$) were also assessed in the overall white matter. Bootstrapping was performed to test the reliability of Pscores in small samples (n=100) using 100 iterations.

Results: The dMRI metric distributions were systematically non-Gaussian, including positively skewed (e.g., mean and radial distributions $\left({PEV}_{>95}\ne 5\%,{PEV}_{<5}\ne 5\%\right)$ whereas 'Pscore' distributions were symmetric and balanced $\left({PEV}_{>95}={PEV}_{<5}=5\%\right)$; even for small bootstrapped samples (average $\overline{PE{V}_{>95}}=\overline{PE{V}_{<5}}=5\pm 0\%\left(SD\right)$).

Data conclusion: The inherent skewness observed for dMRI metrics may preclude the use of conventional Zscore analysis. The proposed 'Pscore' method may help estimating individual deviations more accurately in skewed normative data, even from small datasets.

Keywords: Diffusion MRI; Extreme Values; Individual Deviations; Normative Distribution; Skewness; Zscores.