Spatial distribution bias in subject-specific abnormalities analyses

The neuroimaging community has seen a renewed interest in algorithms that provide a location-independent summary of subject-specific abnormalities (SSA) to assess individual lesion load. More recently, these methods have been extended to assess whether multiple individuals within the same cohort exhibit extrema in the same spatial location (e.g., voxel or region of interest). However, the statistical validity of this approach has not been rigorously established. The current study evaluated the potential for a spatial bias in the distribution of SSA using several common z-transformation algorithms (leave-one-out [LOO]; independent sample [IDS]; Enhanced Z-Score Microstructural Assessment of Pathology [EZ-MAP]; distribution-corrected z-scores [DisCo-Z]) using both simulated data and DTI data from 50 healthy controls. Results indicated that methods which z-transformed data based on statistical moments from a reference group (LOO, DisCo-Z) led to bias in the spatial location of extrema for the comparison group. In contrast, methods that z-transformed data using an independent third group (EZ-MAP, IDS) resulted in no spatial bias. Importantly, none of the methods exhibited bias when results were summed across all individual elements. The spatial bias is primarily driven by sampling error, in which differences in the mean and standard deviation of the untransformed data have a higher probability of producing extrema in the same spatial location for the comparison but not reference group. In conclusion, evaluating SSA overlap within cohorts should be either be avoided in deference to established group-wise comparisons or performed only when data is available from an independent third group.