[Paper Review] Latent Moment Models for Recurrent Binary Outcomes: A Bayesian and Quasi-Distributional Approach

Niloofar Ramezani, Lori P. Selby+2 more|arXiv (Cornell University)|Feb 22, 2026

Sepsis Diagnosis and Treatment0 citations

TL;DR

The paper introduces two frameworks (Bayesian BLaS-Recurrent and quasi-distributional QuaD-Recurrent) to model recurrent binary outcomes via time-varying latent moments, improving calibration and interpretability over standard methods.

ABSTRACT

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.

Motivation & Objective

• Motivate the need to model temporal changes in variability, asymmetry, and tail behavior in recurrent binary outcomes.
• Propose latent moment frameworks where location, scale, skewness, and kurtosis evolve over time.
• Develop two approaches: a Bayesian model using the sinh-arcsinh latent distribution and a quasi-distributional mapping of moments to probabilities.
• Allow time-dependent covariates, serial correlation, and multi-membership structures to capture latent risk trajectories.

Proposed method

• Model each binary event as a thresholded draw from a time-varying latent distribution with latent moments (location, scale, skewness, kurtosis).
• Use BLaS-Recurrent, a Bayesian approach with the sinh-arcsinh distribution to estimate latent moment trajectories.
• Introduce QuaD-Recurrent, a quasi-distributional method that maps simulated moment vectors to event probabilities via a flexible nonparametric surface.
• Accommodate time-dependent covariates, serial correlation, and multiple membership structures within both frameworks.
• Demonstrate improved calibration, interpretability, and robustness relative to standard models through simulations.

Experimental results

Research questions

• RQ1 Can latent moments (location, scale, skewness, kurtosis) capture temporal changes in variability and tail behavior of recurrent binary outcomes?
• RQ2 Do Bayesian (BLaS-Recurrent) and quasi-distributional (QuaD-Recurrent) approaches provide better calibration and interpretability than traditional GLMMs or GEE for longitudinal binary data?
• RQ3 How do these models handle time-dependent covariates, serial correlation, and multi-membership structures in practice?
• RQ4 What latent-risk patterns (e.g., right-skewed escalation, widening dispersion) emerge in real healthcare data when using these models?

Key findings

• 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.
• Both models reveal right-skewed escalation and widening dispersion in latent risk that traditional methods miss.
• The frameworks provide interpretable, distribution-sensitive tools for longitudinal binary outcomes in healthcare.
• They acknowledge that latent moments summarize but do not uniquely determine the underlying distribution.