Recurrent binary outcomes within individuals, such as hospital readmissions, often reflect latent risk processes that evolve over time. Conventional methods like generalized linear mixed models and generalized estimating equations estimate average risk but fail to capture temporal changes in variability, asymmetry, and tail behavior. We introduce two statistical frameworks that model each binary event as the outcome of a thresholded value drawn from a time-varying latent distribution defined by its location, scale, skewness, and kurtosis. Rather than treating these four quantities as nonparametric moment estimators, we model them as interpretable latent moments within a flexible latent distributional family. The first, BLaS-Recurrent, is a Bayesian model using the sinh-arcsinh distribution (a parametric family that provides explicit control over asymmetry and tail weight) to estimate latent moment trajectories; the second, QuaD-Recurrent, is a quasi-distributional approach that maps simulated moment vectors to event probabilities using a flexible nonparametric surface. Both models support time-dependent covariates, serial correlation, and multiple membership structures. Simulation studies show improved calibration, interpretability, and robustness over standard models. Applied to ICU readmission data from the MIMIC-IV database, both approaches uncover clinically meaningful patterns in latent risk, such as right-skewed escalation and widening dispersion, that are missed by traditional methods. These models provide interpretable, distribution-sensitive tools for longitudinal binary outcomes in healthcare while explicitly acknowledging that latent "moments" summarize but do not uniquely determine the underlying distribution.

翻译：个体内部的复发性二元结局（如医院再入院）通常反映随时间演化的潜隐风险过程。传统方法如广义线性混合模型和广义估计方程能够估计平均风险，但无法捕捉变异性、非对称性和尾部行为的时间变化。本文提出两种统计框架，将每个二元事件建模为从时变潜隐分布中抽取的阈值化结果，该分布由其位置、尺度、偏度和峰度定义。我们并非将这四个量视为非参数矩估计量，而是将其建模为灵活潜隐分布族内的可解释潜隐矩。第一种模型BLaS-Recurrent采用双曲正弦-反正弦双曲分布（一种能显式控制非对称性和尾部权重的参数族）估计潜隐矩轨迹的贝叶斯模型；第二种模型QuaD-Recurrent是通过灵活非参数曲面将模拟矩向量映射到事件概率的准分布化方法。两种模型均支持时变协变量、序列相关性和多重隶属结构。仿真研究表明，相较于标准模型，新模型在校准性、可解释性和鲁棒性方面均有提升。应用于MIMIC-IV数据库的ICU再入院数据时，两种方法均揭示了传统方法遗漏的潜隐风险中具有临床意义的模式，如右偏态风险升级和扩散化离散。这些模型为医疗领域的纵向二元结局提供了可解释且对分布敏感的建模工具，同时明确承认潜隐“矩”能够概括但非唯一确定底层分布。