Adaptive Shrinkage Estimation For Personalized Deep Kernel Regression In Modeling Brain Trajectories

TL;DR

The paper tackles predicting longitudinal brain biomarker trajectories under heterogeneity and sparse sampling by introducing a two-component deep kernel regression framework. It combines a population DKGP (p-DKGP) that learns from a large cohort with a subject-specific DKGP (ss-DKGP) that refines predictions using individual follow-ups, and fuses them with an Adaptive Shrinkage Estimation to yield pers-DKGP predictions: $y_c=\alpha y_p+(1-\alpha)y_s$ with $\alpha$ learned adaptively. Key contributions include (i) a scalable DKGP architecture for high-dimensional neuroimaging data, (ii) a principled, interpretable mechanism to balance population and subject-specific information, (iii) demonstrations on ROI volumes and SPARE biomarkers with improved predictive accuracy and uncertainty quantification, and (iv) robust generalization to external datasets (OASIS, AIBL, PreventAD) confirming real-world applicability. The work also provides ablation and explainability analyses, showing that $T_{obs}$ strongly drives the adaptive shrinkage and that the approach maintains plausible, monotonic progression while leveraging new data. Overall, the method offers a practical, interpretable tool for personalized brain trajectory forecasting with potential impact on clinical trial design and disease monitoring.

Abstract

Longitudinal biomedical studies monitor individuals over time to capture dynamics in brain development, disease progression, and treatment effects. However, estimating trajectories of brain biomarkers is challenging due to biological variability, inconsistencies in measurement protocols (e.g., differences in MRI scanners), scarcity, and irregularity in longitudinal measurements. Herein, we introduce a novel personalized deep kernel regression framework for forecasting brain biomarkers, with application to regional volumetric measurements. Our approach integrates two key components: a population model that captures brain trajectories from a large and diverse cohort, and a subject-specific model that captures individual trajectories. To optimally combine these, we propose Adaptive Shrinkage Estimation, which effectively balances population and subject-specific models. We assess our model's performance through predictive accuracy metrics, uncertainty quantification, and validation against external clinical studies. Benchmarking against state-of-the-art statistical and machine learning models -- including linear mixed effects models, generalized additive models, and deep learning methods -- demonstrates the superior predictive performance of our approach. Additionally, we apply our method to predict trajectories of composite neuroimaging biomarkers, which highlights the versatility of our approach in modeling the progression of longitudinal neuroimaging biomarkers. Furthermore, validation on three external neuroimaging studies confirms the robustness of our method across different clinical contexts. We make the code available at https://github.com/vatass/AdaptiveShrinkageDKGP.

Figures (14)

• Figure 1: Overview of the proposed framework. In Figure 1a, we illustrate the training process of the two models, p-DKGP. The population dataset $D_p$ contains multiple longitudinal acquisitions of subjects, where $N$ is the total number of samples across all subjects, and $L$ is the latent dimension obtained from transformation $\Phi$. Different shades of green in the population dataset indicate different subjects in $D_p$. In Figure 1b, we illustrate the training process of the ss-DKGP. We denote the observed trajectory of subject $j$ with $h$ samples as $D_{s_{j}|h}$. These samples are utilized to train the ss-DKGP. During the training of the ss-DKGP, the transformation $\Phi$ is fixed, and only the subject-specific Gaussian process is optimized. In Figure 1C, we visualize the personalization process through the adaptive shrinkage parameter $\alpha$. For subject $j$, we extrapolate biomarker values over time using both the p-DKGP and ss-DKGP models. These extrapolated values are then used to infer the adaptive shrinkage $\alpha$ for posterior correction, yielding the personalized posterior predictive mean $Y_c$ variance $V_c$ of the subject's trajectory.
• Figure 2: We compare the mean MAE per subject stratified by the progression status (top) and the AE with time from the last observation (bottom) of our method with the baselines for (a) the 7 ROI Volume biomarkers, (b) SPARE-AD score and (c) SPARE-BA. Error bars, in the top row, denote the 95th percentile of the MAE across all subjects. Our method is denoted as pers-DKGP.
• Figure 3: We present personalized ROI volume trajectories for three test subjects as observations increase from 4 to 7 acquisitions. The dashed lines represent the prediction using LMM. The first two panels visualize the Hippocampus R and Thalamus Proper R Volume trajectories of Healthy Control subject. Last panel shows the Lateral Ventricle R Volume for an AD Progressor. The shaded bands represent the predictive uncertainty over time.
• Figure 4: We evaluate the mean absolute error for the seven ROI Volume biomarkers across three external neuroimaging studies. Error bars denote the 95th percentile of the absolute error. Notice that the pers-DKGP achieves the lowest error across all external studies, in comparison with the competing baselines.
• Figure 5: We present MAE and $R^2$ from 5-fold cross-validation using the 200 held-out subjects from ADNI and BLSA subjects for the Adaprive Shrinkage estimator using XGBoost, GBM, RF and DNN as non-linear functions