  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.
