🤖 AI Summary
Traditional approaches struggle to capture the temporal evolution of variability, skewness, and tail behavior in the underlying risk distribution of recurrent binary events such as hospital readmissions. This work proposes two novel frameworks: BLaS-Recurrent, a Bayesian model based on the sinh-arcsinh distribution, and QuaD-Recurrent, a quasi-distributional model leveraging nonparametric surface mapping. Both frameworks uniquely embed time-varying location, scale, skewness, and kurtosis into a flexible distributional family, jointly modeling dynamic shifts in both risk level and distributional shape. Moving beyond the limitation of estimating only mean risk, the proposed methods demonstrate superior calibration, robustness, and clinical interpretability in both simulations and real-world MIMIC-IV readmission data, uncovering previously overlooked patterns such as increasing right-skewness and expanding dispersion over time.
📝 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.