Using WinBUGS to Fit Nonlinear Mixed Models with an Application to Pharmacokinetic Modelling of Insulin Response to Glucose Challenge in Sheep Exposed Antenatally to Glucocorticoids

Many chronic diseases of adulthood, such as hypertension and diabetes, are now believed to have at least some of their origins before birth. Extensive studies in animal models have identified antenatal exposure to excess glucocorticoids as a leading candidate for the physiological cause of fetal compromise. The resulting adverse intra-uterine environment appears to "program" the individual for higher risk of subsequent disease. We present an analysis of blood glucose and insulin concentrations collected during glucose tolerance tests at 6 and 12 months postnatal age in a cohort of sheep that were treated antenatally with injections of betamethasone (a synthetic glucocorticoid) which, when injected into the mother, cross the placenta to the fetus. A simple pharmacokinetic model, essentially a modification of the single compartment model with first-order absorption and elimination, is developed to describe the time course of glucose concentration and the associated insulin response. The resulting nonlinear mixed model is implemented in a Bayesian framework using the Markov chain Monte Carlo technique Gibbs Sampling via the software package BUGS. This sampling process allows inferences to be made directly about derived quantities with an immediate physical interpretation, such as the maximum insulin concentration in response to glucose challenge. At 6 months postnatal age, sheep treated with antenatal injections of synthetic glucocorticoids had raised insulin concentration in comparison to controls after bolus administration of glucose. This effect persisted to 12 months postnatal age only in the sheep that received multiple doses of glucocorticoids. Moreover, the raised insulin concentration in sheep that received direct injections of synthetic glucocorticoid as fetuses is accompanied by better glucose clearance than in those sheep that received only saline injections, a phenomenon that is not observed in the animals that received maternal injections. It is argued that the fitting of an appropriate statistical model to complex physiological data does not necessarily proclude a result that has a clear interpretation for clinical scientists.