Charting confidence in white matter brain charts: enabling study planning through stability validation

Normative modeling of quantitative brain measurements is being widely adopted as a promising method for charting population-level developmental trajectories and identifying abnormalities in groups and individuals. Generalized additive models for location, scale, and shape (GAMLSS) are a statistical framework that has been identified by the World Health Organization as a robust method for large-scale population modeling. Validating the stability of normative models is essential for appropriate benchmarking and detecting anomalies, especially for patients with neurodegenerative or developmental disorders. As these models continue to expand in the number of features and amount of data, it becomes increasingly important to assess the stability of the models and their predictions.

An analytic approach is extended from previous work to assess variability of the GAMLSS framework for normative modeling of white matter measurements across the lifespan. The analytic variance and bias are compared with empirical bootstrapping estimates and those of an analogous model that is a nonparametric, data-driven analog.

Across all models, the analytic approach showed low model variability ( $<0.5\%$ Coefficient of Variation) for lifespan trajectories that increased with age. Empirical variability of trajectories was slightly elevated by comparison, especially at the beginning of the lifespan. The trajectory variability for the data-driven analog was even larger, showing a ten-fold increase from the empirical GAMLSS variability. For individual centile prediction, the majority of data points for the analytic assessment had a mean absolute difference (MAD) in centile score prediction as $z$ -scores that was less than 0.003 with the standard deviation of these errors below 0.06. The empirical assessment showed an elevated standard deviation (0.15) and MAD of $z$ -score centile predictions (0.06) for the majority of datapoints. By contrast, when compared with the empirical assessment, the nonparametric, data-driven analog showed over a two-fold increase in the MAD of centile $z$ -score predictions (0.14) and a three-fold increase in standard deviation (0.45) for the majority of data points. The divergences in variability across assessments suggest that individual centile predictions are more sensitive to random fluctuations in the data, which the nonparametric data-driven approach exacerbates.

Results suggest that the GAMLSS brain charts are a stable method of defining and charting normative white matter development as well as planning future clinical or research studies. Overall, this study provides an assessment of GAMLSS-derived brain chart variance in a large-scale population.