Comparison of Different Population Analysis Approaches to the IVGTT Glucose Minimal Model
Paolo Denti (1), Alessandra Bertoldo (1), Paolo Vicini (2) and Claudio Cobelli (1)
(1) Department of Information Engineering, University of Padova, Italy; (2) Resource Facility for Population Kinetics, Department of Bioengineering, University of Washington, Seattle, WA, USA
Objectives: Assessment of the performance of several different population approaches to the estimation of population parameters of the intravenous glucose tolerance test (IVGTT) glucose minimal model.
Methods: The population analysis was performed using SPK [1] on a dataset of 204 healthy subjects (mean age 56 yrs, range 18-87; mean BMI 27 kg/m2, range 20-35) who underwent a full sampling schedule insulin-modified IVGTT (240 min, 21 samples). The IVGTT glucose minimal model [2] was used for identification as follows. First the individual parameters were identified with the individual modeling program SAAM II [3] by using weighted least squares (WLS), or when necessary, maximum a posteriori (MAP) estimation. Secondly, a statistical analysis of the results provided population information. This "supervised Standard Two-Stage" approach, provided the results considered as reference (REF) for further comparisons. We still expect this method to yield overestimates of between-subject variation (BSV) [4]. Subsequently, estimates of fixed and random effects were obtained with the following population methods: Iterative Two-Stage (ITS), Global Two-Stage (GTS) [5], First-Order (FO), FO Conditional Estimation (FOCE) and Laplacian (LAP) [6, 7]. The population parameter distribution was assumed lognormal, BSV was modeled with a full covariance matrix, proportional error structure was assumed and the scale parameter for the residual unknown variability (RUV) was optimized by all algorithms along with the other fixed effects.
Results: Interestingly, FO fails to obtain reasonable estimates: it provides very low values for the mean of SI and very large estimates for the variability of SI and P2. The results yielded by all the other methods, in particular for population means, are very consistent, even if some discrepancies are detected with respect to REF. All approaches detect smaller population variability than REF. The most affected parameters are SG (~18% vs. 28%) and P2 (~50% vs. 67%). This phenomenon is more evident with LAP (11% vs. 28% for SG, 46% vs. 67% for P2) and affects much less SI and VOL (the apparent glucose volume of distribution). Only the SI variability provided by ITS and GTS is slightly smaller than REF (~64% vs. 70%). The off-diagonal terms of the population covariance matrix are estimated with low precision, as indicated by large confidence intervals. The largest correlations, however, detected between SI-P2 and SG-VOL, are well estimated by all methods. The values for the other elements of the matrix are in general very unreliable. Estimated RUV is for all methods bigger (~4%) than the CV normally assumed for glucose concentration, ~2%. As a general trend the two-stage methods tend to yield a slightly smaller value (~3.7%) as opposed to NLMEMs (~4.3%).
Conclusion: These results will form the starting point for a comprehensive evaluation of population analysis methods in the context of an information-rich protocol like the IVGTT.
This includes testing various block structures for the population covariance matrix, and investigating the effect of starting values on the performance of NLMEMs, in particular shrinkage of individual random effects towards the mean. In addition, in order to further inspect the quality of the results provided by the different approaches, we plan to run true likelihood profiling calculations via Monte Carlo integration [8]. Moreover, further study is required to understand the reasons underlying the failure of FO. In doing this, an approach with the use of simulated datasets will be undertaken and different settings for RUV structure probed.
References:
[1] System for Population Kinetics, University of Washington, Seattle, WA, http://spk.rfpk.washington.edu/
[2] Bergman, R. N., Ider, Y. Z., Bowden, C. R. & Cobelli, C. (1979). Quantitative estimation of insulin sensitivity. Am J Physiol, 236, E667-77.
[3] Barrett PH, Bell BM, Cobelli C, Golde H, Schumitzky A, Vicini P, Foster DM. (1998) SAAM II: Simulation, Analysis, and Modeling Software for tracer and pharmacokinetic studies. Metabolism 47: 484-92. University of Washington, Seattle, WA, http://depts.washington.edu/saam2
[4] Davidian, M. and Giltinan, D.M. (1995). Nonlinear Models for Repeated Measurement Data. Chapman and Hall.
[5] Steimer, J. L., Mallet, A., Golmard, J. L. & Boisvieux, J.F. (1984). Alternative approaches to estimation of population pharmacokinetic parameters: comparison with the nonlinear mixed-effect model.. Drug Metab Rev, 15, 265-92.
[6] Beal, S. L. & Sheiner, L.B. (1982). Estimating population kinetics. Crit Rev Biomed Eng, 8, 195-222.
[7] Bell B.M. (2001). Approximating the marginal likelihood estimate for models with random parameters. Appl. Mathem. Comput., 119: 57-75.
[8] Vicini P, Bell BM, Burke JV, Salinger DH and the RFPK (2008). Assessing Nonlinear Mixed Effects Model Parameter Estimates via Profiling of the True Likelihood. Abstracts of the ACOP Meeting, http://www.mosaicnj.com/acop/pdfs/Abstract_Vicini.pdf
