Threshold Selection for the Bayesian Logistic Latent Variable Model of Hypoglycemia Symptom Reporting Consistency

Abstract

Individual symptom patterns are unique, and consistent reporting of hypoglycemia symptoms is crucial for early detection and swift action. Symptoms occur when an individual's propensity combined with episode intensity exceeds a patient-specific threshold. Selecting an appropriate threshold form for consistency modeling is vital, as different forms can affect reporting patterns significantly. This study explores variations in symptom reporting consistency and precision using various threshold types and distributions within a logistic-type latent variable Bayesian model. The optimal threshold form is determined through analysis of real and simulated data, providing posterior estimates of consistency and precision values, along with Bayesian intervals and MCMC errors. This study examines five threshold forms: product, summation, interaction, sum of squared and square of product, along with two threshold distributions: Log-normal and Weibull. The square product threshold with a Log-normal threshold distribution proved most effective for modeling hypoglycemia symptom reporting consistency, achieving high specificity (83.76%) and strong negative predictive value (94.03%), but with moderate sensitivity (56.25%).