Revisiting Subject-Specific Analyses in Neuroimaging Data Using “Z-Score” Methods

To the Editor:

Recently the Journal of Neurotrauma published an article entitled “White Matter Organization and Cortical Thickness Differ Among Active Duty Service Members With Chronic Mild, Moderate, and Severe Traumatic Brain Injury” by Gimbel and colleagues. The article presents data suggesting that diffusion magnetic resonance imaging metrics of fractional anisotropy (FA) are more sensitive to the spectrum of traumatic brain injury (TBI) when certain subject-specific analyses are utilized in place of standardized group approaches. Specifically, the abstract states that: “In contrast, DTI FA ‘pothole’ analyses identified widely distributed areas of decreased FA throughout the white matter in both the chronic mild TBI and chronic moderate-to-severe TBI groups.” The study’s Methods Section references several other articles that have similarly used the “pothole” method to report increased sensitivity to TBI-related changes. ^{1 –3}

The Gimbel study correctly recognizes a key statistical challenge in TBI imaging research. Specifically, TBI has classically been associated with spatially heterogeneous lesions, but frequentist approaches for detecting group differences on the voxel-wise or even region-of-interest level ignore this disease characteristic. Subject-specific analyses address this critical issue. However, previous studies have clearly demonstrated that there are several statistical biases associated with the “pothole” method. ^4,5 This principally results from a widely-held statistical misconception that transforming a comparative (most typically “patients”) group’s data from a reference (most typically “healthy controls”) group’s mean and standard deviation results in a “z-score” and associated normal distribution.

In reality, this transformation results in a beta distribution for the reference group and a t-distribution for the comparison group when data from the entire reference group are used to calculate the first two statistical moments of the distribution. ⁴ Importantly, both the beta and t-distribution converge to a z-distribution as the reference group’s N grows larger. This results from the statistical assumption that the reference sample’s statistical moments more accurately represent underlying population parameters at larger N. However, false positives predominate in the “pothole” method when the reference sample size is small and comparisons are many (i.e., voxel-wise transformations in imaging data). This results from a simultaneous underestimation of the reference group’s “potholes” from the beta distribution and an overestimation of the comparison group’s “potholes” from the t-distribution, which require corrections to the transformed data to better approximate a true z-score and eliminate these biases. ⁴ Similarly, other spatial biases are present when the number of “potholes” is summarized on a voxel-wise level rather than across the entire brain. ⁶ Both of these biases are likely present in the Gimbel et al. 2024 study.

The current authors write this Letter to the Editor to remind both ourselves and the community of the very same statistical misconception that we made over a decade ago and is still widely taught in most statistical scientific classes today.