Incorporating Physiology to Improve Estimates of Postprandial Insulin Secretion Rates with Quantified Uncertainty

Abstract.

A Bayesian perspective in the data-driven modeling of complex processes offers the flexibility to construct hybrid models that consider both domain knowledge and statistical assumptions. With this approach, physical or physiological constraints can be naturally enforced across estimated values and uncertainty. In this study, we develop a Bayesian hierarchical model (BHM) that models insulin secretion rate (ISR) as a mixed-effects, log-Gaussian process, ensuring positive estimates across the inferred posterior distribution. Our approach improves upon a previously developed BHM that allowed for nonphysiological negative ISR estimates. By applying a logarithmic transformation, we integrate positivity directly into the model and leverage a quadratic mean trend to capture ISR’s natural rise and fall. We implement an inversion method based on Newton–Raphson, allowing for computationally efficient inference and uncertainty quantification. Applying our model to oral glucose tolerance test (OGTT) data from youth with and without cystic fibrosis (CF), we find that ISR estimates obtained using the log-Gaussian approach are generally consistent with estimates using the Gaussian approach. However, the log-Gaussian approach eliminates negative predictions for both the ISR and its credible envelopes and generally reduces uncertainty in ISR estimates. By incorporating physiological constraints directly into the model structure, this novel framework enhances ISR inference for metabolic research and offers a robust tool for assessing beta-cell function in health and disease.