<![CDATA[Alzheimer’s disease is one of the most prevalent neurodegenerative disorders, and modeling its longitudinal progression is essential for improving early intervention and clinical decision-making. While spline-based approaches have been widely used to capture nonlinear patterns, their application to longitudinal Alzheimer’s progression remains limited, particularly with respect to adaptive knot selection and clinical interpretability. This study addresses this gap by applying adaptive spline regression with automatic knot selection via Generalized Cross Validation (GCV) to longitudinal Alzheimer’s disease modeling. Using a simulated longitudinal dataset of 200 patients explicitly designed to reflect realistic clinical characteristics such as cognitive decline (MMSE), hippocampal volume change, and APOE ε4 genetic status we systematically evaluate the proposed method under controlled conditions. The adaptive spline model is compared against linear regression and static (fixed-knot) spline regression using 5-fold cross-validation. The results show that adaptive spline regression achieves lower RMSE (0.191) and MAE (0.152), and a higher R² (0.130) than the baseline models. Although the explained variance remains modest, the adaptive spline more effectively captures nonlinear progression patterns and yields smoother, clinically interpretable trajectories. These findings demonstrate that adaptive knot selection enhances both flexibility and interpretability in longitudinal disease modeling. From a practical perspective, the resulting progression curves have potential value for exploratory clinical analysis and hypothesis generation. Future work will focus on validating the framework using real-world datasets such as OASIS and ADNI, and extending the model to incorporate multimodal biomarkers for improved clinical relevance.]]>
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