Longitudinal Alzheimer’s Disease Progression Modelling Using Adaptive Spline Regression
##plugins.themes.bootstrap3.article.main##
Abstract
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.
##plugins.themes.bootstrap3.article.details##
[2] A. P. Porsteinsson, R. S. Isaacson, S. Knox, M. N. Sabbagh, and I. Rubino, “Diagnosis of Early Alzheimer’s Disease: Clinical Practice in 2021,” J. Prev. Alzheimer’s Dis., vol. 8, no. 3, pp. 371–386, 2021, doi: 10.14283/jpad.2021.23.
[3] I. Nagarajan and G. G. Lakshmi Priya, “A comprehensive review on early detection of Alzheimer’s disease using various deep learning techniques,” Front. Comput. Sci., vol. 6, 2024, doi: 10.3389/fcomp.2024.1404494.
[4] S. Golriz Khatami, C. Robinson, C. Birkenbihl, D. Domingo-Fernández, C. T. Hoyt, and M. Hofmann-Apitius, “Challenges of Integrative Disease Modeling in Alzheimer’s Disease,” Front. Mol. Biosci., vol. 6, no. January, pp. 1–13, 2020, doi: 10.3389/fmolb.2019.00158.
[5] D. Chen, M. Zhang, H. Han, Y. Wen, and H. Yu, “Reflections on dynamic prediction of Alzheimer’s disease: advancements in modeling longitudinal outcomes and time-to-event data,” BMC Med. Res. Methodol., vol. 25, no. 1, 2025, doi: 10.1186/s12874-025-02618-x.
[6] A. Perperoglou, W. Sauerbrei, M. Abrahamowicz, and M. Schmid, “A review of spline function procedures in R,” BMC Med. Res. Methodol., vol. 19, no. 1, pp. 1–16, 2019, doi: 10.1186/s12874-019-0666-3.
[7] A. Araveeporn, “The Estimating Parameter and Number of Knots for Nonparametric Regression Methods in Modelling Time Series Data,” Modelling, vol. 5, no. 4, pp. 1413–1434, 2024, doi: 10.3390/modelling5040073.
[8] V. Goepp, O. Bouaziz, and G. Nuel, “Spline regression with automatic knot selection,” Comput. Stat. Data Anal., vol. 202, no. August 2024, p. 108043, 2025, doi: 10.1016/j.csda.2024.108043.
[9] A. Fajry, A. Barra, D. Retno, and S. Saputro, “Knot Optimization For Bi-Response Spline Nonparametric Regression With Generalized Cross-Validation ( GCV ),” BAREKENG J. Math. Its Appl., vol. 19, no. 1, pp. 271–280, 2025.
[10] T. Handayani, S. Sifriyani, and A. T. R. Dani, “Nonparametric Spline Truncated Regression with Knot Point Selection Method Generalized Cross Validation and Unbiased Risk,” JTAM (Jurnal Teor. dan Apl. Mat., vol. 7, no. 3, p. 848, 2023, doi: 10.31764/jtam.v7i3.14034.
[11] S. Yu, G. Wang, L. Wang, and L. Yang, “Multivariate spline estimation and inference for image-on-scalar regression,” Stat. Sin., vol. 31, no. 3, pp. 1463–1487, 2021, doi: 10.5705/ss.202019.0188.
[12] H. Zhao, Y. Zhang, X. Zhao, and Z. Yu, “A nonparametric regression model for panel count data analysis,” Stat. Sin., vol. 29, no. 2, pp. 809–826, 2019, doi: 10.5705/ss.202016.0534.
[13] M. C. Donohue et al., “Natural cubic splines for the analysis of Alzheimer’s clinical trials,” Pharm. Stat., vol. 22, no. 3, pp. 508–519, 2023, doi: 10.1002/pst.2285.
[14] D. A. Jenkins, M. Sperrin, G. P. Martin, and N. Peek, “Dynamic models to predict health outcomes: current status and methodological challenges,” Diagnostic Progn. Res., vol. 2, no. 1, p. 23, 2018, doi: https://doi.org/10.1186/s41512-018-0045-2.
[15] A. Cascarano et al., “Machine and deep learning for longitudinal biomedical data: a review of methods and applications,” Artif. Intell. Rev., vol. 56, no. Suppl 2, pp. 1711–1771, 2023, doi: https://doi.org/10.1007/s10462-023-10561-w.
[16] J. G. Ibrahim and G. Molenberghs, “Missing data methods in longitudinal studies: a review,” Test, vol. 18, no. 1, pp. 1–43, 2009, doi: https://doi.org/10.1007/s11749-009-0138-x.
[17] M. E. Griswold et al., “Reflection on modern methods: shared-parameter models for longitudinal studies with missing data,” Int. J. Epidemiol., vol. 50, no. 4, pp. 1384–1393, 2021, doi: https://doi.org/10.1093/ije/dyab086.
[18] G. Chen et al., “Beyond linearity in neuroimaging: Capturing nonlinear relationships with application to longitudinal studies,” Neuroimage, vol. 176, no. 3, pp. 139–148, 2019, doi: 10.1016/j.neuroimage.2021.117891.Beyond.
[19] G. Chen et al., “Beyond linearity in neuroimaging: Capturing nonlinear relationships with application to longitudinal studies,” Neuroimage, vol. 233, no. 2, p. 117891, 2021, doi: https://doi.org/10.1016/j.neuroimage.2021.117891.
[20] S. C. Villeneuve et al., “Latent class analysis identifies functional decline with Amsterdam IADL in preclinical Alzheimer’s disease,” Alzheimer’s Dement. Transl. Res. Clin. Interv., vol. 5, pp. 553–562, 2019, doi: 10.1016/j.trci.2019.08.009.
[21] S.-C. Villeneuve et al., “Latent class analysis identifies functional decline with Amsterdam IADL in preclinical Alzheimer’s disease,” Alzheimer’s Dement. Transl. Res. Clin. Interv., vol. 5, pp. 553–562, 2019, doi: https://doi.org/10.1016/j.trci.2019.08.009.
[22] A. Wearn, L. L. Raket, D. L. Collins, and R. N. Spreng, “Longitudinal changes in hippocampal texture from healthy aging to Alzheimer’s disease,” Brain Commun., vol. 5, no. 4, pp. 1055–1064, 2023, doi: 10.1093/braincomms/fcad195.
[23] D. S. Marcus et al., “Open Access Series of Imaging Studies ( OASIS ): Cross-sectional MRI Data in Young , Middle Aged , Nondemented , and Demented Older Adults Citation Nondemented , and Demented Older Adults,” Digit. Access to Scholarsh. Harvard, 2007, doi: 10.1162/jocn.2007.19.9.1498.Published.
[24] D. S. Marcus, A. F. Fotenos, J. G. Csernansky, J. C. Morris, and R. L. Buckner, “Open Access Series of Imaging Studies (OASIS): Longitudinal MRI Data in Nondemented and Demented Older Adults,” J. Cogn. Neuoscience, vol. 22, no. 12, 2010, doi: 10.1162/jocn.2009.21407.
[25] C. R. J. Jr et al., “NIA‐AA Research Framework Toward a biological definition of Alzheimer s disease.pdf,” 2018.
[26] F. Pedregosa, R. Weiss, and M. Brucher, “Scikit-learn : Machine Learning in Python,” J. ofMachine Learn. Res., vol. 12, pp. 2825–2830, 2011.
[27] M. J. Azur, E. A. Stuart, C. Frangakis, P. J. Leaf, and D. C. Washington, “Multiple imputation by chained equations : what is it and how does it work ?,” Int. J. Methods Psychiatr. Res., vol. 20, no. 1, pp. 40–49, 2011, doi: 10.1002/mpr.
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.