用拓扑方法分析认知轨迹，首次实现阿尔茨海默病转化风险的个体化置信保障。
Calibrated Alzheimer's Conversion Risk in Mild Cognitive Impairment: Persistent Homology of Clinical Trajectories with Conformal Guarantees
- 基于临床轨迹点云的持久同调分析，提取拓扑特征提升预测能力。
- 模型在内部与外部数据上分别达到0.840和0.879的AUC，误差控制在90.4%±2.2%。
- 首次提供个体风险置信区间，适合临床决策与试验人群筛选场景。
预测轻度认知障碍（MCI）向阿尔茨海默病（AD）转化是临床试验筛选与照护规划的核心问题。现有模型缺乏个体不确定性估计，且罕见透明的数据泄漏审计。本文首次将持久同调应用于纵向临床轨迹点云，构建首个基于分层共形保证的个体风险预测框架。基于ADNI中741名MCI受试者（240人转化，占比32.4%）的4年随访数据，修正5类泄漏源后，朴素流程的AUC由0.934降至0.859（下降0.075）。结合维托里斯-里普斯持久同调与子水平集代理，融合轨迹斜率及工程特征（共76维），采用堆叠集成模型并进行5折交叉验证。结果表明，加入拓扑特征后，Cox与随机生存森林模型的协方差一致性分别达0.799和0.826，优于无拓扑特征的0.753和0.812（提升0.045与0.014）。主嵌套AUC为0.840（同折边界0.866），外部验证集（零重叠的ADNI-2/GO/3）AUC达0.879。H0持久熵为SHAP重要特征，与APOE4基因剂量显著相关（Spearman r=-0.191, p<0.0001，Bonferroni校正）。交叉共形覆盖率90.4%±2.2%（目标90%），外部实证覆盖率达96.9%。七个亚组间假阴性率的最大公平差距为0.092。结论：提出H0持久熵作为认知衰退的拓扑生物标志物，并验证了经泄漏审计、共形校准的流程可在保持竞争力的同时提供此前未有的个体风险置信度。
原文摘要 · Abstract (English)
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.
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