A NonLinear Mixed-Effects Approach to the Estimation of the Glucose Disposition Index
Paolo Denti (1), David Salinger (2,3), Paolo Vicini (2,4), Gianna Maria Toffolo (1), Claudio Cobelli (1)
(1)Department of Information Engineering, University of Padua, Italy; (2)Department of Bioengineering, University of Washington, Seattle, WA, USA; (3)Current address: Amgen Inc. Research and Development, Seattle, WA 98119, USA; (4)Current address: Pfizer Global Research and Development, San Diego, CA 92121, USA.
Objectives: The glucose Disposition Index (DI) was first introduced Bergman et al. [1] with the purpose of assessing the efficiency of glucose-insulin metabolism by calculating the product of insulin sensitivity and secretion indices. This paradigm is called Hyperbolic Law. A more complex model, proposed by Kahn et al. [2], suggests the use of an additional exponent α. This work proposes a NLMEM to analyse the DI in a population and assess the statistical significance of the parameter α.
Methods: As explained in Cobelli et al. [3], the classic method to apply and investigate the validity of the DI laws consists in studying a population of subjects with similar glucose disposal efficiency and supposedly sharing the same DI level. For each individual, insulin sensitivity and secretion indices are estimated (e.g. with an IVGTT) together with their precision, then a geometrical fit is used to find the best curve. Since many simplifications have been proposed to deal with the difficulties of a 2-variable fit [4, 5], we first suggest an exact Total Least Square (TLS) fit approach. However, all geometrical fits account only for the variability caused by the estimation uncertainty of insulin sensitivity and secretion, but the statistical analysis of a real dataset [6] and common sense suggest that, even in a relatively homogenous population, a certain degree of biological variability is inevitably present in the DI values. Therefore, a NLME approach is proposed, which estimates the DI information from population features such as the typical values and covariance matrix. Simulated data, with and without variability in the DI, were used to compare the methodologies. Matlab [7], NONMEM [8] and SPK [9] were used for the fits.
Results: On our simulated data, TLS proves superior to the approximated approaches, but, as all geometric fits, it fails when in presence of population variability. In this context, the NLMEM is much more reliable and works well also with no or small population variability in the DI. Current work on real IVGTT data suggests a value of α significantly smaller than 1, supporting Kahn's model.
Conclusions: When analysing the DI in a population, it is important to account for both estimation uncertainty and population variability. These results also suggest that, if a population model were used to jointly assess both insulin sensitivity and secretion, the population features could be used directly to provide prior information on the DI.
References:
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[7] The MathWorks. Matlab 2007b. Available from: http://www.mathworks.com/.
[8] Beal, S.L., Sheiner, L.B., and Boeckmann, A.J., NONMEM Users Guides. 1989-2006, Icon Development Solutions, Ellicott City, Maryland, USA.
[9] The RFPK team - University of Washington. System for Population Kinetics (SPK). Available from: http://spk.rfpk.washington.edu/.
