Correlation Constraints for Regression Models: Controlling Bias in Brain Age Prediction

Abstract

In neuroimaging, the difference between chronological age and predicted brain age, also known as brain age delta, has been proposed as a pathology marker linked to a range of phenotypes. Brain age delta is estimated using regression, which involves a frequently observed bias due to a negative correlation between chronological age and brain age delta. In brain age prediction models, this correlation can manifest as an overprediction of the age of young brains and an underprediction for elderly ones. We show that this bias can be controlled for by adding correlation constraints to the model training procedure. We develop an analytical solution to this constrained optimization problem for Linear, Ridge, and Kernel Ridge regression. The solution is optimal in the least-squares sense i.e., there is no other model that satisfies the correlation constraints and has a better fit. Analyses on the PAC2019 competition data demonstrate that this approach produces optimal unbiased predictive models with a number of advantages over existing approaches. Finally, we introduce regression toolboxes for Python and MATLAB that implement our algorithm.

Multimodal biological brain age prediction using magnetic resonance imaging and angiography with the identification of predictive regions

“…This observation is further supported by the plots directly comparing the predicted and true chronological age, which are presented in Figure S2. All models show small mean differences between the chronological and predicted age, with the highest difference found for the CNN T1 model (À0.39) indicating no systematic biases although the three models seem to slightly overpredict the age of young adults and underpredict the age of elderly, which has also been previously observed (de Lange & Cole, 2020; Le et al, 2018;Liang, Zhang, & Niu, 2019;Treder et al, 2021). in Figure 4 where the importance in these regions decreases with aging.…”

Machine learning for brain age prediction: Introduction to methods and clinical applications

“…Chronological age is increasingly recognised as an important source of systematic bias [ 11 , 36 , [51] , [52] , [53] , [54] , [55] ]. Brain age models tend to be affected by regression to the mean, so the age of younger subjects is overestimated and the age of older subjects is underestimated.…”

“…Brain age models tend to be affected by regression to the mean, so the age of younger subjects is overestimated and the age of older subjects is underestimated. Various statistical approaches have been proposed to correct for this age bias [ 10 , 11 , 36 , [51] , [52] , [53] , [54] , [55] ]. Whether a study took age bias into account therefore is an important factor for their interpretation.…”

Brain-age prediction: a systematic comparison of machine learning workflows

“…We included eight ML algorithms covering diverse inductive biases: ridge regression (RR), least absolute shrinkage and selection operator (LASSO) regression (LR), elastic net regression (ENR), kernel ridge regression (KRR), GPR, RFR, RVR with the linear kernel (RVRlin), and polynomial kernel of degree 1 (RVRpoly). These algorithms have been widely used in the prediction of age and other behavior variables from neuroimaging data (Franke et al ., 2010; Gaser et al ., 2013; Su et al ., 2013; Cole et al ., 2015, 2018; Varikuti et al ., 2018; Jonsson et al ., 2019; Liang et al ., 2019; Zhao et al ., 2019; Cole, 2020; He et al ., 2020, Baecker et al ., 2021 b ; Boyle et al ., 2021; Lee et al ., 2021; Peng et al ., 2021; Treder et al ., 2021; Vidal-Pineiro et al ., 2021; Beheshti et al ., 2022) (Table S1). Details of these algorithms are provided in the Supplementary Methods.…”