Assessment of the oral glucose minimal model by nonlinear mixed-effects approaches
A. Lagajolli (1), A. Bertoldo (1), P. Denti (2), C. Cobelli (1)
(1) Department of Information Engineering, University of Padova, Italy (2) Division of Clinical Pharmacology, University of Cape Town, South Africa
Objectives: The oral minimal model (OMM) coupled with a parametric model of Ra, the piecewise linear model (PLM) (1), has been proposed and validated to estimate, at individual level, the rate of appearance of glucose (Ra) and the insulin sensitivity (SI) from plasma glucose and insulin concentrations measured after an oral glucose perturbation. The current study aims at investigating the performance of the nonlinear mixed-effects modeling to the OMM.
Methods: Population modeling was performed using a dataset comprising 50 normal subject (20 males and 30 females, age 47.42±24.7, body weight 69.72±10.6 Kg) who received a triple tracer mixed meal (10 kcal/kg, 45% carbohydrate, 15% protein, and 40% fat) containing 1 ± 0.02 g/kg glucose. The plasma samples were collected at -120, -30, -20, -10, 0, 5, 10, 15, 20, 30, 40, 50, 60, 75, 90, 120, 150, 180, 210, 240, 260, 280, 300, 360, 420 minutes. The OMM coupled with the Ra PLM was used for identification of [SI, p2, α1, α2, α3, α4, α5, α6, α7] where α1,...,α7 are the PLM parameters, and p2 is the insulin action. First, individual parameters were estimated using SAAM II (2) and, from these values, population parameters were obtained with the Standard Two-Stage method (STS). This approach provided the individual results considered as reference (REF) for further comparisons. After, the model was implemented and identified in NONMEM by using the FO Conditional Estimation (FOCE) INTERACTION since it has been proved suitable for a similar model (3). The population parameter distribution was assumed lognormal, BSV was modeled with a diagonal covariance matrix, proportional error structure was assumed and the scale parameter for the residual unknown variability (RUV) was optimized along with the other fixed effects. was assumed to be normally distributed with mean 0.11 and variance 0.011. Parameter uncertainty was assessed with a non parametric bootstrap (200 repetitions).
Results: Population estimates of SI were very similar for FOCE and REF (8.45 10-4 vs 8.52 10-4 min-1 per μU/ml respectively), whereas the FOCE estimate of SI variability was smaller than REF (2.22 10-7 vs 2.35 10-7). However, overestimation of BSV has been previously reported for STS (4). At individual level, the FOCE individual estimates of SI are also well correlated with the REF values (r2=0.99). We also detected high correlations among the REF and FOCE individual estimates of the parameters of PLM (average r2 = 0.92). Similar agreement we also found with both population and individual estimates of p2. In addition, to investigate the discrepancy in the goodness of fit provided by the reference model and that obtained with population modeling, we compared the residual sum of squares of each subject via linear regression. The high correlation that we obtained (r2=0.93) indicates that the two approaches provide comparable goodness of fit at individual level. .
Conclusions: These results show that the population approach to the OMM parameter estimation is consistent with the already validated individual approach. This paves the way for further exploration of the application of population analysis methods in the context of an information-rich protocol like the meal glucose tolerance test.
References:
[1] The oral glucose minimal model: estimation of insulin sensitivity from a meal test. Dalla Man C, Caumo A, Cobelli C. 2002, IEEE Trans Biomed Eng , Vol. 49, pp. 419-429.
[2] SAAM II: Simulation, Analysis, and Modeling Software for tracer and pharmacokinetic studies. al, Barret PH et. 1998, Metabolism, Vol. 47, pp. 484-92.
[3]Nonlinear mixed effects to improve glucose minimal model parameter estimation: a simulation study in intensive and sparse sampling. Denti P, Bertoldo A, Vicini P, Cobelli C. 2009, IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, Vol. 56.
[4]Nonlinear models for repeated measurements data. . M. Davidian, D.M. Giltinian. s.l. : Chapman & Hall/CRC, 1998.
