Recurrent Events Modeling Based on a Reflected Brownian Motion with Application to Hypoglycemia

Yingfa Xie; Haoda Fu; Yuan Huang; Vladimir Pozdnyakov; Jun Yan

doi:10.48550/arxiv.2403.09042

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Recurrent Events Modeling Based on a Reflected Brownian Motion with Application to Hypoglycemia

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Recurrent Events Modeling Based on a Reflected Brownian Motion with Application to Hypoglycemia

Yingfa Xie, Haoda Fu, Yuan Huang, Vladimir Pozdnyakov and Jun Yan

ArXiv.org

Cornell University

03/13/2024

DOI: 10.48550/arxiv.2403.09042

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https://doi.org/10.48550/arxiv.2403.09042View

Preprint (Author's original)This preprint has not been evaluated by subject experts through peer review. Preprints may undergo extensive changes and/or become peer-reviewed journal articles. Open Access

Abstract

Patients with type 2 diabetes need to closely monitor blood sugar levels as their routine diabetes self-management. Although many treatment agents aim to tightly control blood sugar, hypoglycemia often stands as an adverse event. In practice, patients can observe hypoglycemic events more easily than hyperglycemic events due to the perception of neurogenic symptoms. We propose to model each patient's observed hypoglycemic event as a lower-boundary crossing event for a reflected Brownian motion with an upper reflection barrier. The lower-boundary is set by clinical standards. To capture patient heterogeneity and within-patient dependence, covariates and a patient level frailty are incorporated into the volatility and the upper reflection barrier. This framework provides quantification for the underlying glucose level variability, patients heterogeneity, and risk factors' impact on glucose. We make inferences based on a Bayesian framework using Markov chain Monte Carlo. Two model comparison criteria, the Deviance Information Criterion and the Logarithm of the Pseudo-Marginal Likelihood, are used for model selection. The methodology is validated in simulation studies. In analyzing a dataset from the diabetic patients in the DURABLE trial, our model provides adequate fit, generates data similar to the observed data, and offers insights that could be missed by other models.

Statistics - Methodology

Details

Title: Subtitle: Recurrent Events Modeling Based on a Reflected Brownian Motion with Application to Hypoglycemia
Creators: Yingfa Xie
Haoda Fu
Yuan Huang
Vladimir Pozdnyakov
Jun Yan
Resource Type: Preprint
Publication Details: ArXiv.org
DOI: 10.48550/arxiv.2403.09042
ISSN: 2331-8422
Publisher: Cornell University; Ithaca, New York
Language: English
Date posted: 03/13/2024
Academic Unit: Biostatistics
Record Identifier: 9984572459902771

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