Analytic Bounds on GAMLSS Model Variability of Normative White Matter Brain Charts

Brain charts, or normative models of quantitative neuroimaging measures, can identify trajectories of brain development and abnormalities in groups and individuals by leveraging large populations. Recent work has extended these brain charts to model microstructural and macrostructural features of white matter. Assessments of variance for these brain charts are necessary to determine whether the models being used for these data are stable. We implement an analytic approach to characterize variability of the parameters in previously released brain charts created using the generalized additive models for location, scale, and shape (GAMLSS) framework. Additionally, we empirically validate the accuracy of each analytic model through a comparison to a bootstrapping approach from 0.2 to 90 years of age. We find that across all models, the analytic coefficient of variation (COV) remains below 5% for ages greater than 0.25 years, with the maximum empirical observed COV reaching 7% at 0.2 years of age. Further, the empirical assessment shows high agreement with the analytic assessment, with COV estimates averaged across the lifespan for all models having a Pearson correlation coefficient of 0.776 and a mean difference of 4 x 10^-4. Both methods exhibit volume and surface area as the features with the largest average COV for the majority of tracts. However, the analytic assessment yields axial diffusivity as the feature most frequently having the smallest COV, whereas the corresponding feature for the empirical assessment is average length. These results suggest that the analytic approach overestimates model stability for WM brain charts when the COV is low and that the validation method is suitable for assessing whether GAMLSS models are unstable.