Insight into Morphometricity Through BLUP Accuracy on Voxel/Vertex-wise data
Poster No:
1148
Submission Type:
Abstract Submission
Authors:
Baptiste Couvy-Duchesne1, Elise Delzant2, Nicholas Salvy3, Thomas Nichols4
Institutions:
1The University of Queensland, Brisbane, Queensland, 2Sorbonne University, Paris Brain Institute - ICM, CNRS, Inria, Inserm, AP-HP, Hopital de la Pitie Sa, Paris, France, 3Universite Paris-Saclay, Inria, CEA, Palaiseau, 91120, France, Paris, France, 4University of Oxford, Oxford, Oxfordshire
First Author:
Co-Author(s):
Elise Delzant
Sorbonne University, Paris Brain Institute - ICM, CNRS, Inria, Inserm, AP-HP, Hopital de la Pitie Sa
Paris, France
Sorbonne University, Paris Brain Institute - ICM, CNRS, Inria, Inserm, AP-HP, Hopital de la Pitie Sa
Paris, France
Introduction:
Morphometricity measures the variance explained in a phenotype (e.g. IQ) by a high-dimensional imaging measure (e.g. cortical thickness) (Couvy-Duchesne et al. 2020). It is analogous to heritability, with brain similarity replacing genetic similarity and it uses the connection between a linear mixed effects (LME) model and an analogous variance component model for efficient estimation. A LME can be used to compute a Best Linear Unbiased Predictor (BLUP), and morphometricity BLUPs were found to equal or surpass the prediction accuracy of the LASSO (Couvy-Duchesne et al. 2020) without requiring any tuning parameters or cross-validation. Here we present a connection between BLUP accuracy and morphometricity (adapted from (Dudbridge 2013)), connecting variance explained to training sample size and imaging feature dimension, allowing estimation of the number of effective independent vertices/voxels across the brain.
Methods:
We applied our method to the UK Biobank, training BLUP predictors for a range of traits (e.g., alcohol use, diabetes, education level, chronic pain, blood pressure, maternal smoking around birth, and depression score), which have varying morphometricity and sample size (Ns ranging between 6,117 and 23,183). Participants' age was 63.1 on average (SD=7.5), and 52% were women. We evaluated the prediction accuracy of BLUP scores in an independent UK Biobank sample of 16,538 individuals aged 62.2 on average (SD=7.7), with 54% women. We performed the analyses using several vertex/voxel-wise representations of grey-matter structure (from CAT12, FSL, FreeSurfer 6.0 [thickness and surface area]) to empirically test our results across a wide range of use cases.
Results:
We have derived the prediction R2 of a morphometricity BLUP to predict phenotype Y in an independent sample as:
R2Y=m2 N/M / (1 + m2 N/M ) x m2/Var(Y)
Where m2 is the morphometricity of the trait (estimated in the training sample), N is the training sample size, and M is the effective number of brain features. Figure 1 illustrates the theoretical relationship between prediction accuracy and morphometricity for several values of the N/M ratio (Figure 1). We further converted the R2 into AUC (assuming equal-size groups) (Ruscio 2008) to visualise the relationship in the context of classification tasks (Figure 1, right panel). Using results from the UK Biobank, we showed that the empirical prediction accuracies aligned with the theory across different vertex/voxel-wise representations and training samples (Figure 2). With a collection of different phenotypes, all predicted with the same imaging measures, we estimated M (shown as dashed lines in Figure 2) to be 7,541 for the ENIGMA-CAT12 volume-based processing, 19,001 for FSLVBM processing, and 24,422 for FreeSurfer.
Our results indicate that a training sample of 20,000 images is not sufficient to train BLUP predictors that capture the full morphometricity, although the theory suggests it should be achievable with a sample 3-5 times larger (Figure 2). Lastly, we explored the limitations of our framework, which relate to the mixed model assumption of widespread small associations across the brain.
R2Y=m2 N/M / (1 + m2 N/M ) x m2/Var(Y)
Where m2 is the morphometricity of the trait (estimated in the training sample), N is the training sample size, and M is the effective number of brain features. Figure 1 illustrates the theoretical relationship between prediction accuracy and morphometricity for several values of the N/M ratio (Figure 1). We further converted the R2 into AUC (assuming equal-size groups) (Ruscio 2008) to visualise the relationship in the context of classification tasks (Figure 1, right panel). Using results from the UK Biobank, we showed that the empirical prediction accuracies aligned with the theory across different vertex/voxel-wise representations and training samples (Figure 2). With a collection of different phenotypes, all predicted with the same imaging measures, we estimated M (shown as dashed lines in Figure 2) to be 7,541 for the ENIGMA-CAT12 volume-based processing, 19,001 for FSLVBM processing, and 24,422 for FreeSurfer.
Our results indicate that a training sample of 20,000 images is not sufficient to train BLUP predictors that capture the full morphometricity, although the theory suggests it should be achievable with a sample 3-5 times larger (Figure 2). Lastly, we explored the limitations of our framework, which relate to the mixed model assumption of widespread small associations across the brain.
Conclusions:
Our framework emphasizes that beyond training sample size, morphometricity and the complexity of the data (measured by M ) contribute to the performance of linear predictors. Although our framework relates to BLUP, it is also relevant for other predictors that exhibit similar performance (e.g., other linear models such as LASSO, or Convolutional Neural Networks in some cases). Overall, our results can assist the design of machine or deep learning studies of the brain, as the expected prediction accuracy can yield accurate estimates of statistical power.
Modeling and Analysis Methods:
Classification and Predictive Modeling 1
Methods Development
Neuroanatomy, Physiology, Metabolism and Neurotransmission:
Cortical Anatomy and Brain Mapping 2
Keywords:
Computational Neuroscience
Data analysis
Machine Learning
STRUCTURAL MRI
1|2Indicates the priority used for review
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Provide references using APA citation style.
Dudbridge, F. (2013). Power and Predictive Accuracy of Polygenic Risk Scores. PLOS Genetics, 9(3):1–17
Ruscio, J. (2008). A probability-based measure of effect size: robustness to base rates and other factors. Psychological Methods, 13(1):19–30.