Event-based models (EBMs) infer disease progression from cross-sectional data, and standard EBMs assume a single underlying disease per individual. In contrast, mixed pathologies are common in neurodegeneration. We introduce the Joint Progression Model (JPM), a probabilistic framework that treats single-disease trajectories as partial rankings and builds a prior over joint progressions. We study several JPM variants (Pairwise, Bradley-Terry, Plackett-Luce, and Mallows) and analyze three properties: (i) calibration -- whether lower model energy predicts smaller distance to the ground truth ordering; (ii) separation -- the degree to which sampled rankings are distinguishable from random permutations; and (iii) sharpness -- the stability of sampled aggregate rankings. All variants are calibrated, and all achieve near-perfect separation; sharpness varies by variant and is well-predicted by simple features of the input partial rankings (number and length of rankings, conflict, and overlap). In synthetic experiments, JPM improves ordering accuracy by roughly 21 percent over a strong EBM baseline (SA-EBM) that treats the joint disease as a single condition. Finally, using NACC, we find that the Mallows variant of JPM and the baseline model (SA-EBM) have results that are more consistent with prior literature on the possible disease progression of the mixed pathology of AD and VaD.

翻译：基于事件的模型（EBMs）从横断面数据推断疾病进展，标准EBMs假设每个个体仅存在单一潜在疾病。然而，在神经退行性疾病中，混合病理现象普遍存在。本文提出联合进展模型（JPM），这是一个概率框架，将单疾病轨迹视为部分排序，并构建联合进展的先验分布。我们研究了JPM的多种变体（成对比较型、布拉德利-特里型、普拉克特-卢斯型及马洛斯型），并分析了三个特性：（i）校准性——模型能量较低时是否更接近真实排序；（ii）分离性——采样排序与随机排列的可区分程度；（iii）锐度——采样聚合排序的稳定性。所有变体均具备校准性，且均实现近乎完美的分离性；锐度因变体而异，可通过输入部分排序的简单特征（排序数量与长度、冲突性及重叠度）准确预测。在合成实验中，JPM相较于将联合疾病视为单一条件的强基准模型（SA-EBM），排序准确率提升约21%。最后，通过应用NACC数据，我们发现JPM的马洛斯变体与基准模型（SA-EBM）的结果，更符合先前关于阿尔茨海默病与血管性痴呆混合病理潜在进展路径的文献研究。