2010 - Berlin - Germany

PAGE 2010: Integration of literature data
Rocio Lledo

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.

[1].  Hamren B, Bjork E, Sunzel M and Karlsson M. Models for plasma glucose, HbA1c, and hemoglobin interrelationships in patients with type 2 diabetes following tesaglitazar treatment. Clin Pharmacol Ther. 2008; 84(2): 228-235.
[2]. Nathan DM, Kuenen J, Borg R, Zheng H, Schoenfeld D and Heine RJ. Translating the A1C assay into estimated average glucose values. Diabetes Care. 2008; 31(8): 1473-1478.
[3]. Gisleskog PO, Karlsson MO and Beal SL. Use of prior information to stabilize a population data analysis. J Pharmacokinet Pharmacodyn. 2002; 29(5-6): 473-505.
[4]. Kalicki R, Lledó-García R and karlsson M, Modeling of Red Blood Cell (RBC) Lifespan (LS) in a Hematologically Normal Population, in PAGE meeting. 2009: St. Petersburg.
[5]. Woo S, Krzyzanski W, Duliege AM, Stead RB and Jusko WJ. Population pharmacokinetics and pharmacodynamics of peptidic erythropoiesis receptor agonist (ERA) in healthy volunteers. J Clin Pharmacol. 2008; 48(1): 43-52.
[6]. Beach KW. A theoretical model to predict the behavior of glycosylated hemoglobin levels. J Theor Biol. 1979; 81(3): 547-561.
[7]. Higgins P and Bunn F. Kinetic Analysis of the Nonenzymatic Glycosylation of Hemoglobin. J Biol Chem. 1981; 256(10): 5204-5208.
[8]. Mortensen HB, Volund A and Christophersen C. Glucosylation of human haemoglobin A. Dynamic variation in HbA1c described by a biokinetic model. Clin Chim Acta. 1984; 136(1): 75-81.
[9]. Ladyzynski P, Wojcicki JM, Bak M et al. Validation of hemoglobin glycation models using glycemia monitoring in vivo and culturing of erythrocytes in vitro. Ann Biomed Eng. 2008; 36(7): 1188-1202.
[10]. Nuttall FQ, Gannon MC, Swaim WR and Adams MJ. Stability over time of glycohemoglobin, glucose, and red blood cell survival in hematologically stable people without diabetes. Metabolism. 2004; 53(11): 1399-1404.
[11]. Virtue MA, Furne JK, Nuttall FQ and Levitt MD. Relationship between GHb concentration and erythrocyte survival determined from breath carbon monoxide concentration. Diabetes Care. 2004; 27(4): 931-935.
[12]. Peterson CM, Jones RL, Koenig RJ, Melvin ET and Lehrman ML. Reversible hematologic sequelae of diabetes mellitus. Ann Intern Med. 1977; 86(4): 425-429.

Reference: PAGE 19 (2010) Abstr 1783 [www.page-meeting.org/?abstract=1783]
Oral presentation: Integration of literature data
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