Pharmacokinetic-pharmacodynamic models are useful tools for predicting the dynamic distribution of a substance throughout the human body. However, care is required, as uncertainty in the values of the model's parameters can affect the nature of the model prediction. Parameter uncertainty can originate with a number sources, including imprecision in the collection of patient data or from any physical variability within the patients themselves. Furthermore, correlation among the model parameters can indicate that degree of allowable uncertainty for each model parameter. We use published clinical data from frequently sampled intravenous glucose tolerance tests (FSIGTT) and the Oral Glucose Tolerance Test (OGTT) to identify correlation structures among the parameters of gluco-regulatory models. The correlation were identified by performing Monte Carlo simulation on the regression of the parameters. We show that the correlation structure of the parameters plays a major role on the stability and robustness of the models studied, which means in order to perform uncertainty analysis on the parameters of these models, one must take into the correlation structures.