A. Largajolli (1), A. Bertoldo (1), C. Cobelli (1)
(1) Department of Information Engineering, University of Padova, Italy
Objectives: VPC [1] is commonly used to evaluate the performance of PK and PKPD models. However this diagnostic tool presents some pitfalls in the simulation step when models with forcing functions (FF) are evaluated. In fact in this case there is a mismatch between each set of simulated parameters and the associated individual FF which can cause an incorrect profile simulation. This study aims to overcome this VPC limitation by taking into account in the simulation step a correlation term that bounds the set of simulated parameters with the most appropriate FF. This is a non-trivial aspect since FF exhibit a large inter-individual variability. We assessed the technique on four nonlinear models that present one or two FFs: the IVGTT and the ORAL glucose and C-peptide minimal models (MM) [2-3-4-5].
Methods:To introduce the correlation term in the simulation step of the VPC we calculated for each set of simulated parameters (SIM) the Mahalanobis distance (MD) between the SIM and the previously estimated parameters (EST). This helped us to find the vector of EST parameters that was closer to SIM and consequently to match the EST corresponding FF to the SIM parameters in the simulation step.
Results: When VPC was used in its original formulation, we found implausible simulated curves especially with the oral glucose MM. This is essentially due to the fact that the large variability between the FFs makes the match between the simulated parameters and the associated FF critical. With the newly proposed approach to VPC the oral glucose MM results show plausible simulated curves and consequently a better agreement with the real data. Also results on the other three models with FFs [2-3-4] show an improved pattern of simulated curves but its impact was less evident with respect to the oral glucose MM where there are two independent FFs.
Conclusions: This work proposes a refinement of the simulated based diagnostic VPC which is relevant for a particular subset of models. Despite the simplicity of the method, the results show an evident improvement of VPC. Another approach has also been developed in case of a low FF variability that is a common situation in PK/PD experiments. This method adds an elaboration step before applying the MD. A clustering analysis detects the most important FF kinetics that are used to simulate a new dataset whose parameters are estimated, then the MD is applied. The VPC performance further improves since there is no error in the association of FF with the set of SIM.
References:
[1] Holford N, VPC: the visual predictive check superiority to standard diagnostic (Rorschach) plots, [Abstr 738], PAGE 14 (2005), [www.page-meeting.org/?abstract=738].
[2] Bergman RN, Ider YZ, Bowden CR, Cobelli C, Quantitative estimation of insulin sensitivity,1979, Am J Physiol, Vol 236, pp E667-E677.
[3] Toffolo G, De Grandi F, Cobelli C, Estimation of β-cell sensitivity from IVGTT C-peptide data. Knowledge of the kinetics avoids errors in modeling secretion, 1995, Diabetes, Vol 44, pp 845-854.
[4] Breda E, Cavaghan M K, Toffolo G, Polonsky K S, Cobelli C, Oral glucose tolerance test minimal model indexes of β-cell function and insulin sensitivity, 2001, Diabetes, Vol 50, pp 150-158.
[5] Dalla Man C, Caumo A, Cobelli C, The oral glucose minimal model: estimation of insulin sensitivity from a meal test, 2002, IEEE Trans Biomed Eng , Vol 49,no 5, pp 419-429.
Reference: PAGE 21 (2012) Abstr 2556 [www.page-meeting.org/?abstract=2556]
Poster: Model evaluation