Image Response Regression via Deep Neural Networks
This work addresses the challenge of delineating associations between images and covariates in medical imaging studies, offering a method that accounts for spatial smoothness and subject heterogeneity, though it appears incremental as it builds on existing spatially varying coefficient models with deep learning enhancements.
The authors tackled the problem of image response regression in medical imaging by proposing a novel nonparametric approach using deep neural networks within spatially varying coefficient models, which demonstrated high flexibility and accuracy in capturing complex associations, as validated through simulations and analyses of two fMRI datasets.
Delineating the associations between images and a vector of covariates is of central interest in medical imaging studies. To tackle this problem of image response regression, we propose a novel nonparametric approach in the framework of spatially varying coefficient models, where the spatially varying functions are estimated through deep neural networks. Compared to existing solutions, the proposed method explicitly accounts for spatial smoothness and subject heterogeneity, has straightforward interpretations, and is highly flexible and accurate in capturing complex association patterns. A key idea in our approach is to treat the image voxels as the effective samples, which not only alleviates the limited sample size issue that haunts the majority of medical imaging studies, but also leads to more robust and reproducible results. Focusing on a broad family of piecewise smooth functions, we establish the estimation and selection consistency, and derive the asymptotic error bounds. We demonstrate the efficacy of the method through intensive simulations, and further illustrate its advantages with analyses of two functional magnetic resonance imaging datasets.