Longitudinal Boundary Sharpness Coefficient Slopes Predict Time to Alzheimer's Disease Conversion in Mild Cognitive Impairment: A Survival Analysis Using the ADNI Cohort

Background. Predicting conversion from mild cognitive impairment (MCI) to Alzheimer's disease (AD) is central to trial enrichment and care planning, yet existing models provide no individual-level uncertainty estimates and rarely include transparent leakage audits. We introduce the first application of persistent homology to longitudinal clinical trajectory point clouds for this task, and the first split-conformal individual risk guarantee for any AD-conversion model. Methods. We analysed 741 MCI subjects (240 converters, 32.4%) from ADNI with a uniform 4-year follow-up cap. Five leakage sources were corrected; without them a naive pipeline achieved AUC=0.934, inflated by +0.075. Vietoris-Rips persistent homology and sublevel-set proxies were combined with trajectory slopes and engineered features (76 total) in a stacking ensemble evaluated by 5-fold cross-validation. Results. Cox and Random Survival Forest models with TDA features achieved concordance C=0.799 and C=0.826 versus C=0.753 and C=0.812 without (+0.045 and +0.014). The primary nested AUC is 0.840 (same-fold bound 0.866); external AUC was 0.879 on a zero-overlap ADNI-2/GO/3 cohort. H0 persistence entropy was the top SHAP feature and significantly associated with APOE4 dosage (Spearman r=-0.191, p<0.0001, Bonferroni-corrected). Cross-conformal coverage was 90.4%+-2.2% (target 90%); empirical external coverage 96.9%. Maximum fairness gap in false-negative rate across seven subgroups was 0.092. Conclusions. We propose H0 persistence entropy as a topological biomarker of cognitive decline and demonstrate that a leakage-audited, conformally calibrated pipeline reaches competitive accuracy with individual-level uncertainty quantification not previously available for this task.

Individualized Alzheimer's disease (AD) progression prediction requires models that use irregular visits, account for censoring, avoid diagnostic leakage, and provide calibrated horizon risks. We propose PROgression-aware MultI-horizon Survival Estimation for Alzheimer's Disease (PROMISE-AD), a leakage-safe survival framework for predicting conversion from cognitively normal (CN) to mild cognitive impairment (MCI) and from MCI to AD dementia using ADNI/TADPOLE tabular histories. PROMISE-AD converts pre-index visits into tokens with standardized measurements, missingness masks, longitudinal changes, time-normalized slopes, visit timing, and non-diagnostic categorical attributes. A temporal Transformer fuses global, attention-pooled, and latest-visit representations to estimate a progression score and latent discrete-time mixture hazards. Training combines survival likelihood, horizon-specific focal risk loss, progression ranking, hazard smoothness, and mixture-balance regularization, followed by validation-set isotonic calibration for 1-, 2-, 3-, and 5-year risks. In held-out testing across three seeds, PROMISE-AD achieved an integrated Brier score (IBS) of 0.085 $\pm$ 0.012, C-index of 0.808 $\pm$ 0.015, and mean time-dependent AUC of 0.840 $\pm$ 0.081 for CN-to-MCI conversion, yielding the lowest IBS among compared methods. For MCI-to-AD conversion, PROMISE-AD achieved the highest C-index (0.894 $\pm$ 0.018) and near-ceiling 5-year discrimination (AUROC 0.997 $\pm$ 0.003; AUPRC 0.999 $\pm$ 0.001), although some baselines had lower IBS. Ablations and interpretability supported longitudinal change features, fused temporal representations, mixture hazards, cognitive and functional measures, APOE4 status, and recent conversion-proximal visits. These findings suggest that progression-aware survival modeling can provide interpretable multi-horizon AD conversion risk estimates.

Predicting which people with mild cognitive impairment (MCI) will develop dementia matters for starting treatment early, yet computational work on structural brain imaging has relied almost entirely on a single scan. We propose TAFNet, a temporal attention fusion network that combines a baseline and a follow-up T1-weighted scan. A pretrained Siamese encoder represents each scan, and a fusion module combines the two through anatomical difference, cross-temporal attention and joint context, mixed by a learned per-patient gate. We evaluate it on paired scans from participants with MCI in the Alzheimer's Disease Neuroimaging Initiative, taken up to two years apart, with a dementia diagnosis within three years of the first scan as the outcome. The evaluation is designed to hold up under scrutiny: conversion is defined from recorded diagnoses, the pretraining pool shares no participants with the evaluation cohort, a held-out test partition is kept apart from model development, and uncertainty is estimated by resampling participants. TAFNet discriminates converters from non-converters well on the held-out partition. It outperforms conventional single-scan networks and a model that subtracts the two scans; both differences are significant in cross-validation and have the same direction on the smaller held-out partition. With everything else held fixed, adding the follow-up scan gives a significant gain in cross-validation. Against a recurrent CNN-LSTM baseline built on the same encoder, TAFNet performs comparably, with neither model consistently ahead. Operating points chosen on validation data, in place of the default threshold, give high sensitivity at a clinically reasonable specificity.