Longitudinal Bayesian Learning of Continuous Disease Position across the Alzheimer's Disease Continuum
Authors: Yingying Zhang, Kun Zhao, Guodong Liu, Qi Huang, Pengfei Gu, Dongchul Kim, Erik Enriquez, Alex D. Leow, Paul M. Thompson, Heng Huang, Hongchang Gao, Liang Zhan, Haoteng Tang
Alzheimer's disease (AD) progresses as a continuous biological process, whereas most existing neuroimaging-based artificial intelligence methods remain limited to discrete diagnosis or clinical score prediction from cross-sectional imaging. In this work, we propose Disease Continuum Positioning (DCP), a longitudinal Bayesian Learning framework that continuously estimates disease severity from longitudinal diffusion tensor imaging (DTI). Specifically, DCP models disease severity as a low-dimensional probabilistic latent variable by jointly integrating longitudinal observations with weak clinical supervision, from which the proposed Disease Continuum Score (DCS) is derived to quantify an individual's position along the Alzheimer's disease continuum together with its associated uncertainty. Extensive experiments on the Alzheimer's Disease Neuroimaging Initiative (ADNI) cohort demonstrate that DCP consistently outperforms representative disease progression methods. More importantly, comprehensive validation analyses show that DCS accurately characterizes disease severity, exhibits strong clinical relevance, preserves longitudinal disease evolution, and predicts future disease conversion. These results suggest that DCS provides a quantitative imaging-derived representation for continuous assessment of Alzheimer's disease progression beyond conventional diagnostic labels and clinical scores.
Figures & tables
Figure 1: Overview of the proposed DCP framework. A 3D encoder factors each longitudinal DTI scan into a one-dimensional disease-order-aware latent s~ and a residual zr , from which a decoder reconstructs the input; a diagnosis-anchored prior, an ordinal ranking loss Lrank , and a soft monotonicity loss Lmono jointly position s~ on a continuous, diagnosis-ordered severity axis. The reported DCS, s=Softplus(s~) , is uncertainty-aware, with higher values indicating more advanced disease.
Methods
Spearman ρ (vs. MMSE)
ANOVA F↑
Stage C ↑
Long. C ↑
Avg. C ↑
SuStaIn ( Young et al., 2018 )
-0.4138 ± 0.0729
35.97 ± 11.56
0.7194 ± 0.0417
0.7879 ± 0.0116
0.7536 ± 0.0200
DLMRI ( Feng et al., 2022 )
-0.1994 ± 0.0890
22.47 ± 13.89
0.6590 ± 0.0354
0.3840 ± 0.0554
0.5215 ± 0.0360
LSSL ( Ouyang et al., 2022 )
-0.2266 ± 0.0756
7.7884 ± 4.3366
0.6092 ± 0.0489
0.7612 ± 0.0141
0.6855 ± 0.0190
MedicalNet ( Ma et al., 2026 )
-0.3396 ± 0.1068
14.7468 ± 8.0318
0.7003 ± 0.0581
–
–
DCP (Ours)
-0.5481 ± 0.0748
40.76 ± 8.68
0.7794 ± 0.0063
0.8367 ± 0.0187
0.8076 ± 0.0135
Table 1: Quantitative comparison of DCP with baseline methods. Spearman’s ρ measures the association between the derived DCS and MMSE, ANOVA F evaluates population-level variation across CN, MCI, and AD, and Stage C and Long. C quantify concordance with diagnostic-stage ordering and within-subject longitudinal ordering, respectively. Avg. C denotes the average of Stage C and Long. C. Best and second best performance are highlighted in red and blue .
Setting
Spearman ρ (vs. MMSE)
ANOVA F↑
Stage C ↑
Long. C ↑
Avg. C ↑
DCP (Full)
-0.5481 ± 0.0748
40.76 ± 8.68
0.7794 ± 0.0063
0.8367 ± 0.0187
0.8076 ± 0.0135
Objective Component Ablation
w/o Lrank
-0.4235 ± 0.0823
28.33 ± 9.04
0.7330 ± 0.0267
0.8686 ± 0.0112
0.7990 ± 0.0131
w/o Lmono
-0.5084 ± 0.0307
41.42 ± 2.70
0.8071 ± 0.0058
0.6713 ± 0.0109
0.7377 ± 0.0096
w/o LKL
-0.4239 ± 0.0612
30.15 ± 7.42
0.7673 ± 0.0240
0.7605 ± 0.0451
0.7612 ± 0.0292
DTI Measure Ablation
Table 2: Ablation study of DCP with respect to objective components and DTI input measures. The objective component ablation evaluates the contributions of the ordinal ranking loss Lrank , longitudinal monotonicity loss Lmono , and probabilistic latent regularization LKL . The DTI modality ablation evaluates DCP using each DTI-derived measure individually (FA, MD, AD, or RD), compared with the full model using all four measures.
Figure 2: Distributional characterization of the Disease Continuum Score (DCS) across the clinically defined AD continuum. (a) DCS distributions for CN, MCI, and AD. Group differences were assessed using the Kruskal–Wallis test followed by FDR-corrected pairwise Mann–Whitney U tests; rrb denotes the rank-biserial effect size. (b) Raincloud plots showing individual DCS values and their distributions within each diagnostic group, illustrating both within-stage variability and overlap between adjacent diagnostic stages.
Figure 3: Clinical validation of the Disease Continuum Score (DCS) through its associations with established clinical assessments. Scatter plots show the relationships between DCS and MMSE, CDR-SB, ADAS-Cog-13, FAQ, GDS, and NPI, with subjects colored according to diagnostic group (CN, MCI, and AD). Pearson’s correlation coefficient ( r ) and Spearman’s rank correlation coefficient ( ρ ), together with their corresponding p -values, are reported for each assessment.
Figure 4: Prospective analysis of future clinical conversion using the Disease Continuum Score (DCS) derived from baseline scans. (a) Baseline DCS distributions between stable and progressive subjects for CN → MCI and MCI → AD conversion. Group differences were assessed using the Mann–Whitney U test, with rrb denoting the rank-biserial effect size. (b) Observed conversion rates after stratifying subjects into quartiles according to baseline DCS, from Q1 (lowest) to Q4 (highest), separately within the CN and MCI cohorts. (c) Receiver operating characteristic (ROC) curves for CN → MCI and MCI → AD conversion. For each method, the disease score derived from the baseline scan was used as the sole predictor in logistic regression, with AUC reported as mean ± standard deviation across cross-validation folds. Solid lines represent the mean ROC curves, shaded regions indicate variability across folds, and the diagonal dashed line represents chance-level discrimination.
Method
AUC (CN → MCI) ↑
AUC (MCI → AD) ↑
SuStaIn ( Young et al., 2018 )
0.6266 ± 0.0551
0.7345 ± 0.0674
DLMRI ( Feng et al., 2022 )
0.5695 ± 0.0736
0.6531 ± 0.0576
LSSL ( Ouyang et al., 2022 )
0.5900 ± 0.0535
0.6615 ± 0.0745
MedicalNet ( Ma et al., 2026 )
0.7027 ± 0.0531
0.6564 ± 0.1000
DCP (Ours)
0.7246 ± 0.0851
0.7957 ± 0.0355
Table 3: Comparison of future clinical conversion prediction using disease scores derived from the baseline scan. For each method, the derived continuous score was used as the sole predictor in a logistic regression model to distinguish stable from progressive subjects. Performance was evaluated for CN → MCI and MCI → AD conversion using the area under the receiver operating characteristic curve (AUC), reported as mean ± standard deviation across cross-validation folds. The best performance is highlighted in bold.
Figure 5: Analysis of posterior uncertainty associated with the Disease Continuum Score (DCS). (a) Distributions of posterior uncertainty σ derived from baseline scans for stable and progressive subjects in the CN and MCI cohorts. Group differences were assessed using the Mann–Whitney U test, with rrb denoting the rank-biserial effect size. (b) Observed conversion rates after stratifying subjects into quartiles according to baseline posterior uncertainty, from Q1 (lowest uncertainty) to Q4 (highest uncertainty), separately within the CN and MCI cohorts. Unlike DCS, baseline posterior uncertainty shows neither a significant difference between stable and progressive subjects nor an ordered relationship with subsequent clinical conversion.