# Calibrated Alzheimer's Conversion Risk in Mild Cognitive Impairment: Persistent Homology of Clinical Trajectories with Conformal Guarantees

arXiv: https://arxiv.org/abs/2607.17442 · HTML: https://mlsanity.com/paper/2607.17442/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 22 references that are in the map.
- First posted on arXiv 20 Jul 2026.

## Builds on (most cited first, 6 of 6)

- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [An introduction to Topological Data Analysis: fundamental and practical aspects for data scientists](https://mlsanity.com/paper/1710.04019/) (2017)
- [Ripser: efficient computation of Vietoris-Rips persistence barcodes](https://mlsanity.com/paper/1908.02518/) (2019)
- [An Empirical Characterization of Fair Machine Learning For Clinical Risk Prediction](https://mlsanity.com/paper/2007.10306/) (2020)
- [PROMISE-AD: Progression-aware Multi-horizon Survival Estimation for Alzheimer's Disease Progression and Dynamic Tracking](https://mlsanity.com/paper/2604.28055/) (2026)

## Abstract (arXiv)

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.