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

Area of Science:

• Neuroimaging
• Biomedical data analysis
• Machine learning in medicine

Background:

• Brain age delta, the difference between chronological and predicted brain age, is a potential pathology marker.
• Current regression methods for brain age estimation exhibit bias due to the negative correlation between chronological age and brain age delta.
• This bias leads to inaccurate age predictions, particularly for younger and older individuals.

Purpose of the Study:

• To address the bias in brain age delta estimation.
• To develop an optimal and unbiased method for predicting brain age.
• To introduce practical tools for implementing the improved prediction algorithm.

Main Methods:

• Incorporating correlation constraints into the regression model training procedure.
• Developing an analytical solution for constrained optimization in Linear, Ridge, and Kernel Ridge regression.
• Validating the approach using data from the PAC2019 competition.

Main Results:

• The proposed method effectively controls for the bias in brain age delta estimation.
• The analytical solution provides an optimal fit in the least-squares sense while satisfying correlation constraints.
• The approach yields unbiased predictive models with superior performance compared to existing methods.

Conclusions:

• Constrained optimization offers an effective solution for unbiased brain age prediction.
• The developed algorithm and accompanying software tools (Python, MATLAB) facilitate the application of this improved method.
• This work advances the utility of brain age delta as a reliable pathology marker in neuroimaging.