AI 中文总结
本文针对多变量纵向分类数据的分析挑战，提出CLOUD框架，结合IRT测量组件与时变OU过程，经模拟和ALS数据验证，可灵活刻画受试者特异性疾病演化。
AI 中文摘要
纵向生物医学研究越来越多地收集不规则采样的多变量分类数据，这些数据无法完美反映疾病进展，带来三大关键分析挑战：受试者间疾病进展高度异质；存在驱动多项测量的未观测协同演化潜变量；患者内部及患者间采样间隔高度不规则。为应对这些挑战，本文提出连续潜变量奥恩斯坦-乌伦贝克动力学（CLOUD）框架，用于从多变量纵向分类数据中建模复杂疾病轨迹。CLOUD将多变量分类观测与潜在功能域关联，通过结合经项目反应理论（IRT）调整的测量组件与基于多变量奥恩斯坦-乌伦贝克（OU）过程的动态组件，刻画它们的耦合时间演化。方法上，本文引入时变OU过程，在潜动力学的平移均值函数中加入协变量依赖组件，使基线生物标志物可调节个体水平疾病轨迹；还提出OU漂移矩阵的可扩展参数化方式，无需限制潜在功能域数量即可实现有效交互建模。本文确立了所提框架的理论性质，包括模型的解析可处理性、漂移矩阵重参数化的通用性以及整个模型的可识别性。通过模拟研究和肌萎缩侧索硬化（ALS）纵向临床数据应用，本文证明CLOUD是刻画多交互功能域中受试者特异性疾病演化的原则性且灵活的工具。
英文摘要
Longitudinal biomedical studies increasingly collect irregularly sampled, multivariate categorical data that imperfectly reflect disease progression. This presents three key analytical challenges: highly heterogeneous disease progression across subjects; the presence of unobserved, co-evolving latent variables driving multiple measurements; and highly irregular sampling intervals both within and across patients. To address those challenges, we present the Continuous Latent Ornstein-Uhlenbeck Dynamics (CLOUD) framework for modeling complex disease trajectories from multivariate longitudinal categorical data. CLOUD links multivariate categorical observations to underlying latent functional domains and characterizes their coupled temporal evolution via the integration of a measurement component adjusted from item response theory (IRT) with a dynamic component based on multivariate Ornstein-Uhlenbeck (OU) processes. Methodologically, we introduce a time-inhomogeneous OU process that incorporated covariate-dependent components into the shifting mean function of the latent dynamics, allowing baseline biomarkers to modulate individual-level disease trajectories. We further propose a scalable parameterization of the OU drift matrix that enabled valid interaction modeling without restricting the number of latent functional domains. We establish theoretical properties of the proposed framework, including the analytical tractability of the model, the generality of the drift matrix reparameterization, and the identifiability of the entire model. Through simulation studies and an application to longitudinal amyotrophic lateral sclerosis (ALS) clinical data, we demonstrate that CLOUD provided a principled and flexible tool for characterizing subject-specific disease evolution across multiple interacting functional domains.
