Performing Monte Carlo Simulation Based on Nonparametric Pharmacokinetic Parameter Distributions: Evaluation of Various Methods Applied to a Paediatric Population Study on Busulfan
S. Goutelle (1,2), L. Bourguignon (1,2), N. Bleyzac (1,3), P. Maire (1,2), R.W. Jelliffe (4)
(1) UMR CNRS 5558, University of Lyon 1, Lyon, France; (2) Department of Pharmacy and ADCAPT, Antoine Charial Hospital, University Hospitals of Lyon, Francheville, France; (3) Institute of Paediatric Haematology and Oncology, University Hospitals of Lyon, Lyon, France; (4) Laboratory of Applied Pharmacokinetics, USC Keck School of Medicine, Los Angeles CA, USA
Objectives: Monte Carlo (MC) simulation techniques are increasingly used in population pharmacokinetic (PK) studies. Nonparametric (NP) population methods often result in singular distribution shapes. Little information exists about the way to perform MC simulation compatible with such results. The main objective of this study was to evaluate the ability of various MC simulation methods to reproduce the characteristics of a NP parameter distribution observed in real patients.
Methods: A population PK study was performed using the NPAG algorithm in 42 children who received busulfan (Bu) intravenously before bone marrow transplantation. Bu concentrations (N=166) were determined by a validated HPLC-UV method [1]. Various compartmental models were fitted to concentration data. Goodness of fit was assessed using standard criteria.
Then, seven methods were evaluated in a 1,000 subject MC simulation using Matlab software. Various options regarding parameter distributions, covariance, and other settings were tested. Methods 1 to 4 were fully parametric (FP) methods. Methods 5 to 7 were iterative, semi-parametric, two-step (TS) methods: first, one point is selected in the NPAG grid according to its probability, and then, it is used as a mean vector of an assumed multivariate distribution. Simulated distributions were compared with the actual NPAG parameter distributions using basic statistics and graphical analysis.
Results: A linear two-compartment model fitted the data very well. NPAG provided a 27 point grid as population parameter distribution of the four parameters. For Bu volume of distribution (VD), the probability distribution was typically multimodal. Mean, 25, 50, and 75 percentile values (all in liters) were 5.66, 0.649, 1.52, and 2.53, respectively. Overall, FP methods failed to reproduce all characteristics of the original NP distribution. Best results were observed with TS methods using a reduced covariance matrix derived from the NPAG one. For example, 25, 50 and 75 percentile values for the VD distribution were 3.39, 6.83, 11.2 with method 4, and 0.927, 1.84, and 3.29 with method 7, respectively. On scatter plots, parameter values provided by TS methods with a reduced covariance matrix were much more clustered around NPAG support points than those from FP methods.
Conclusions: Performing MC simulation based on NP parameter distribution requires specific methods. A new approach of MC simulation designed for such application has been presented.
References:
[1] Bleyzac N, Barou P, Aulagner G. Rapid and sensitive high-performance liquid chromatographic method for busulfan assay in plasma. J Chromatogr B Biomed Sci Appl 2000;742:427-32.
