ODE solvers and stiffness issues for complex population PK models
Ribba B., Tod M., Girard P., You B., Mercier C., Vassal G., Freyer G., Tranchand B.
Therapeutic Targeting in Oncology (EA3738), Faculty of Medicine Lyon-Sud, University of Lyon
Objectives: With the aim to study PK/PD with a system biology approach, we wish to address the question of parameter estimation for complex (physiologically-based) PK/PD population models. The specific objective of this work is to evaluate the performance of FO (First Order) and FOCE (First Order Conditional Estimation) versus SAEM (Stochastic Approximation of Expectation Maximisation) methods in estimating the parameters of Irinotecan PK model including four metabolites: 7-ethyl-10-Hydroxycamptothecin (SN38), 7-ethyl-10-Hydroxycamptothecin glucuronide (SN38G), 7-ethyl-10-[4-N-(acid5-aminopentanoïque)-1-piperidino]-carbonyloxycamptothécine (APC) and 7-ethyl-10-(4-amino-1-piperidino)-carbonyloxycamptothécine (NPC).
Methods: Irinotecan and its metabolites concentration data were collected from 177 patients included in a phase I and a phase II clinical trial. Nonmem VI was used for parameters estimation with FO and FOCE while Monolix [1,2] was used for parameter estimation through SAEM method.
The methodology consists of building the full model step by step [3], starting from Irinotecan concentration data only (step 1) and plugging successively SN38 (step 2), SN38G (step 3), APC (step 4) and finally NPC (step 5).
For all steps, we intend to run both sequential and simultaneous analysis described in [4,5]. Comparison criteria will be goodness of fit plot, parameter precision, and computational time.
Results: By now, step 1 has been completed with Nonmem (FO method) and Monolix. Step 2 has been performed sequentially with Nonmem (FO method) only.
For Irinotecan concentration data only, Monolix gave better parameter estimations than Nonmem VI while computational time was significantly higher (see Table below). Nevertheless Monolix CPU time is expected to be comparable to Nonmem FOCE.
|
| Nonmem VI (FO) | Monolix (SAEM) |
| Parameters estimation (CV in % of IIV*) | ||
| Clearance (L/h) | 14.3 (61%) | 11.8 (52%) |
| Central volume (L) | 41.8 (61%) | 42.8 (65%) |
|
| SE** (parameter) (SE(IIV)) | |
| Clearance | 1.1 (0.44) | 0.7 (0.22) |
| Central volume | 4.02 (0.36) | 3.4 (0.28 |
|
| Computational time (seconds) | |
|
| 5 | 54 |
*IIV: Inter-Individual Variability
**SE: Standard Error
Conclusions: On a methodological point of view, this study may highlight the potential of existing and innovative parameter estimation algorithms for highly complex (physiological) models integrating both anti-cancer drug metabolisms and cancer biological processes. Hopefully, the full PK model of Irinotecan will provide a rational identification of covariates and will be informative on the role of its metabolites. Forthcoming results will be compared to a study of Irinotecan PK by Xie et al. [3].
References:
[1] Kuhn E, Lavielle M. Maximum likelihood estimation in nonlinear mixed effects models. Comp Stat Data Anal. 2005. 49(4):1020-38.
[2] Donnet S, Samson A. Estimation of parameters in incomplete data models defined by dynamical systems. J Stat Plan Inf. 2007. To appear.
[3] Xie R, Mathijssen RH, Sparreboom A,Verweij J, Karlsson MO. Clinical pharmacokinetics of irinotecan and its metabolites: a population analysis. J Clin Oncol. 2002. 20(15):3293-301.
[4] Zhang L, Beal S, Sheiner L. Simultaneous vs. Sequential Analysis for Population PK/PD Data I: Best-case Performance. J Pharmacokinet Pharmacodyn. 2003. 30(6): 387-404.
[5] Zhang L, Beal S, Sheiner L. Simultaneous vs. Sequential Analysis for Population PK/PD Data II: Robustness of Methods. J Pharmacokinet Pharmacodyn. 2003. 30(6): 387-404.
