Unobserved Heterogeneity in Threshold Regression Based on the Hitting Times of a Reflected Brownian Motion for Recurrent Hypoglycemia

2026-05-25

AI Summary

This study addresses a critical limitation in existing recurrent hypoglycemia models, which rely on first-passage times of reflected Brownian motion but ignore unobserved heterogeneity across patient subpopulations. To overcome this, the authors propose a novel finite mixture model wherein each component features distinct regression coefficients and frailty parameters. Bayesian inference with Markov chain Monte Carlo (MCMC) methods is employed for estimation, and model selection is guided by the Deviance Information Criterion (DIC) and Log-Pseudo Marginal Likelihood (LPML). Application to real-world data reveals two clinically distinct subgroups: a low-volatility subgroup exhibiting greater heterogeneity, for which component-specific volatility regression models significantly outperform homogeneous alternatives. This approach enables a refined characterization of risk factor effects within each latent subpopulation.

Abstract

Analyses of recurrent hypoglycemia are critical for effective treatment management in diabetic patients. Typically, within-subject dependency in such analyses is captured through subject-level frailty. Recent research has modeled recurrent hypoglycemia using the first hitting times of a reflected Brownian motion. A close examination of this approach reveals that it does not adequately account for varying frailties among individuals, which indicate notable heterogeneity. To address this gap, we propose a finite mixture model of the first hitting time distribution of the reflected Brownian motion. This model allows for component-specific regression coefficients and frailty parameters, providing nuanced insights into how risk factors differently affect patient subgroups. We employ a Bayesian framework for inference, utilizing Markov chain Monte Carlo for estimation. Model selection is conducted using the Deviance Information Criterion and the Logarithm of the Pseudo-Marginal Likelihood. The effectiveness of these criteria is assessed through simulation studies. Application to recurrent hypoglycemia modeling revealed two subgroups with different risk profiles, as reflected in their volatilities. Bayesian model comparison criteria favor the model with component specific regression coefficients for volatilities. The subgroup with lower volatility exhibits a larger variance and, hence, a greater level of heterogeneity.

Problem

• unobserved heterogeneity
• threshold regression
• reflected Brownian motion
• recurrent hypoglycemia
• frailty

Innovation

• finite mixture model
• reflected Brownian motion
• unobserved heterogeneity
• Bayesian inference
• first hitting time