Normative Modeling of Brain Morphometry Across the Lifespan Using CentileBrain: Algorithm Benchmarking and Model Optimization

Abstract

We present an empirically benchmarked framework for sex-specific normative modeling of brain morphometry that can inform about the biological and behavioral significance of deviations from typical age-related neuroanatomical changes and support future study designs. This framework was developed using regional morphometric data from 37,407 healthy individuals (53% female; aged 3-90 years) following a comparative evaluation of eight algorithms and multiple covariate combinations pertaining to image acquisition and quality, parcellation software versions, global neuroimaging measures, and longitudinal stability. The Multivariate Factorial Polynomial Regression (MFPR) emerged as the preferred algorithm optimized using nonlinear polynomials for age and linear effects of global measures as covariates. The MFPR models showed excellent accuracy across the lifespan and within distinct age-bins, and longitudinal stability over a 2-year period. The performance of all MFPR models plateaued at sample sizes exceeding 3,000 study participants. The model and scripts described here are freely available through CentileBrain (https://centilebrain.org/).

Figure 1.. Flowchart of normative model optimization

(1) The study sample was stratified by sex and then split into training (80%) and testing (20%) datasets, followed by outlier removal, and mean-centering; (2) Normative models were generated using eight different algorithms and compared in terms of accuracy and computational efficiency; (3) Explanatory variables were added to identify the appropriate combination for optimal model performance. ICV=intracranial volume; IQR=interquartile range

Figure 2.. Illustrative examples of comparative algorithm performance

Algorithm performance for each regional morphometric measure was assessed separately in males and females using the mean absolute error (MAE), the root mean square error (RMSE), explained variance (EV), and the central processing unit (CPU) time. The MAE, RMSE, EV, and CPU times of the models for left thalamic volume (left panel), the left medial orbitofrontal cortical thickness (middle panel) and surface area (right panel) as exemplars here for females and in appendix 1, p 4, figure S3 for males. The pattern identified was the same across all region-specific models and in both sexes (appendix 1, pp 5–6, figures S4-S5). HBR=Hierarchical Bayesian Regression; OLSR=Ordinary Least Squares Regression; BLR=Bayesian Linear Regression; GAMLSS=Generalized Additive Models for Location, Scale and Shape; LMS=Lambda (λ), Mu (μ), Sigma (σ) Quantile Regression; GPR=Gaussian Process Regression; WBLR=Warped Bayesian Linear Regression; MFPR=Multivariate Fractional Polynomial Regression.

Figure 3.. Illustrative examples of the performance of MFPR-derived models as a function of explanatory variables

For each regional morphometric measure, sex-specific models derived from all algorithms were trained and tested using nine different covariate combinations that included effects of age, FreeSurfer version (FS), Euler Number, scanner vendor, intracranial volume (ICV) and global estimates of mean cortical thickness or area. The mean absolute error (MAE) and root mean square error (RMSE) of models for left thalamic volume (left panel), the left medial orbitofrontal cortical thickness (middle panel), and surface area (right panel) derived from Multivariate Fractional Polynomial Regression (MFPR) for females are presented as exemplars; the optimal variable combination is marked with a dashed frame. The corresponding data for males are presented in appendix 1 (p 7, figure S6). The data for other algorithms are shown in appendix 1 (pp 8–12, figures S7-S11 and S2). In both sexes, the pattern identified was identical for all region-specific models.

Figure 4.. Illustrative examples of the comparative performance of OLSR, BLR, HBR, GPR, GAMLSS, WBLR, and MFPR-derived optimised models

Region-specific models with the optimised covariate combination were estimated in males and females separately using Ordinary Least Squares Regression (OLSR), Bayesian Linear Regression (BLR), Hierarchical Bayesian Regression (HBR), Gaussian Process Regression (GPR), Generalized Additive Models for Location, Scale, and Shape (GAMLSS), Warped Bayesian Linear Regression (WBLR), and Multivariable Fractional Polynomial Regression (MFPR). Model performance was assessed in terms of mean absolute error (MAE), root mean square error (RMSE), and central processing unit (CPU). The MAE, RSME, and CPU time of the models for left thalamic volume (left panel), the left medial orbitofrontal cortical thickness (middle panel), and surface area (right panel) in females are presented as exemplars and in appendix 1 (p 10, figure S9) for males.

Figure 5.. Performance of region-specific MFPR-derived models as a function of sample size

Models for each regional morphometric measure were estimated in random sex-specific subsets of 200 to 15,000 participants, in increments of 200, generated from the study sample. Each line represents the values of the mean absolute error (MAE), or root mean square error (RMSE) derived from the optimized Multivariate Fractional Polynomial Regression (MFPR) models of all regional morphometric measure as a function of sample size; shadowed area represents the standard deviation. The pattern identified was identical in both sexes. The data for females are shown here and for males in appendix 1 (p 13, figure S12).

Figure 6.. Performance of region-specific models in distinct age bins

Sex- and region-specific models of all morphometric measures for different age bins were estimated by partitioning the sex-specific training and testing subsets of the study sample into nine age bins (i.e., age≤10 years; 10

Figure 7.. Stability of the normative deviation scores (Z-scores) in longitudinal neuroimaging data

We illustrate the stability of the optimized MFPR-derived models over an average interval of two years in data from the SLIM and QTAB samples using the left thalamic volume (left panel), the left medial orbitofrontal cortical thickness (middle panel), and surface area (right panel) as exemplars. Within each panel, the left-hand figure shows the Z-scores of each participant at baseline and follow-up and the right-hand figure shows the distribution of the mean absolute error (MAE) and root mean squared error (RMSE) at baseline and follow-up. SLIM=Southwest Longitudinal Imaging Multimodal Study; QTAB= Queensland Twin Adolescent Brain Study.

Figure 8.. Accuracy of diagnostic classification and accuracy of psychotic symptom prediction using brain regional normative deviation scores or observed neuromorphometric data

Left panel: Diagnostic classification accuracy in the Human Connectome Project -Early Psychosis (HCP-EP) sample. Receiver Operating Characteristic (ROC) curves of the models distinguishing patients from controls using the observed regional neuromorphometric measures (blue curve) or the deviation Z-scores from the normative model (orange curve); Middle panel: the area under the curve (AUC) difference between a support vector machine classifier using the observed regional neuromorphometric measures and another using regional normative deviation scores (Z-scores) derived from the optimised multivariate fractional polynomial regression (MFPR) model was examined through 1000 permutations. The AUC difference is marked by a vertical dotted line. Right panel: Predictive Accuracy of Psychotic Symptoms in the HCP-EP sample. The mean absolute error (MAE) difference between a ridge regression using the observed regional neuromorphometric measures and another using Z-scores derived from the optimised MFPR model was examined through 1000 permutations. The MAE difference is marked by a vertical dotted line. Information on other models in appendix 1, p 22, figure S19