A mechanistic model of the steady-state relationship between HbA1c and average glucose levels in a mixed population of healthy volunteers and diabetic subjects
Rocío Lledó-García, PhD1, Norman A. Mazer, MD, PhD2 and Mats O. Karlsson, PhD1
(1) Pharmacometrics research group. Department of Pharmaceutical Biosciences, Uppsala University, Uppsala, Sweden. (2) F. Hoffmann-La Roche Ltd., Pharma Research and Early Development (pRED), Translational Research Sciences (TRS), 4070 Basel, Switzerland
Background: A mechanism-based model exists that describes the fasting plasma glucose (FPG) and HbA1c relationship[1]. However, a mechanistic description of the underlying relationship between average glucose concentration (Cg,avg) - a better descriptor of chronic glycemia- and HbA1c is lacking.
Objective: To build a dynamic, mechanism-based, model for the Cg,avg - HbA1c relationship using information from the literature.
Methods: Different sources were combined to build a mechanism-based model. Pairs of Cg,avg-HbA1c digitized measurements from Nathan et al. publication[2] (N=507 diabetic patients and healthy volunteers) were re-analysed in a formal population analysis with NONMEM VI using the prior functionality[3] to incorporate literature prior information in RBC life-span and life-span distribution (LS)[4], erythroid cell life-span (LSP)[5], glycosylation rates (KG)[6-9] and Cg,avg and HbA1c measurement errors[2]. Finally, literature data was used as external validation for the mechanisms incorporated in the relationship[1, 10].
Results: The integration of the information made it clear that a mechanistic component beyond those previously described quantitatively for the glucose - HbA1c relationships was required. A model incorporating a decrease in RBC LS with increasing glucose concentrations was in good agreement with all literature sources and the formal integration allowed estimation of the strength of this relationship. The estimated strength was in good agreement with additional literature sources[1, 10-12].
The RBC model consisted of 12 transit compartments -previously shown to describe well the LS[4]- with a LS estimate of 91.7 days and IIV of 8.22 %. RBC LS covaries with Cg,avg, so that LS is shorter at higher Cg,avg.
At any given age stage, Hb can become glycosilated to HbA1c. KG (8.37x10-6 dL/mg/day) was in agreement with literature values[6-9]. HbA1c erythroid cells contribution depends on Cg,avg and LSP. A LSP (8.2 days) close to that published[5] and the same KG as for RBCs was in agreement with the data.
Conclusions: To our knowledge this is the first quantitative description of the Cg,avg-HbA1c relationship on mechanistic basis. This was possible by combining different literature data sources: i) digitized literature data as main source of information; ii) mechanistic reinforcement by literature priors in the structural and variability parameters; iii) digitized data and clinical data to support the mechanisms with highest impact on driving the relationship.
Our mechanism-based model describes well the relationship observed in HV and diabetic patients. The model can predict the impact of changes in Cg,avg (due to diet changes/therapeutic interventions) on HbA1c levels. It can predict the time-course of HbA1c in response to changes in Cg,avg, or conversely. If any of the processes involved changes in an individual patient (e.g. LS decreased in uremic patients[10]), the expected temporal and steady state change of HbA1c can also be predicted.
This shows how literature data can be used not only to support parameter estimates, but combined from different sources to test hypotheses and build structurally novel models.
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