Evaluation of an optimal design for examining melphalan pharmacokinetics in patients with multiple myeloma

Background: The optimal design of population pharmacokinetics allows parameter estimation with minimum variance and reduced cost by identifying (1) the minimum number of blood samples required from each subject, (2) the optimal blood sampling times and (3) the minimum number of subjects required. Aim: To evaluate the results of an optimal design experiment that was used in a study on the population pharmacokinetics of high dose melphalan in patients with multiple myeloma.

Methods: A prior pharmacokinetic model was developed from extraction and re-analysis of literature reports for the purpose of the optimal design using data from the literature and the WinPOPT software. WinPOPT was used to optimise a design that was robust to the prior estimates of the parameters using HClnD [1]. The structure of the model and the values of the pharmacokinetic parameters, including between-subject variability were then compared with those obtained from the posterior model, which was developed using the NONMEM VI software. The executed design was compared with the nominal design computed using WinPOPT by calculating the proportion of blood samples that were taken from within the optimal design windows.

Results: The posterior and prior models both had 2 compartment structures in which the pharmacokinetic parameters of clearance (CL), apparent volume of the first compartment (V1), distributional clearance (Q) and apparent volume of the second compartment (V2) had log-normal distributions and in which residual error had both additive and proportional components. The population mean estimates of CL, V1, Q and V2 from the posterior model (27.8 L/h, 13.1 L, 31.3 L/h and 15.1 L, respectively) were very similar (or within the range) to those of the prior model (29-41 L/h, 10-16 L, 35.5 L/h and 14.9 L, respectively), as were the relative standard errors (all <10%). Relative standard errors predicted by the prior model for between-subject variability were generally similar to those from the posterior model for all parameters except V1. A 5 sample optimal design was generated using the prior model. In those patients in whom the optimal design was executed 94 % of samples were collected at times within the optimal sampling windows.

Conclusions: The prior model utilized for the optimal design experiment conducted for examining melphalan population pharmacokinetics in patients with multiple myeloma provided the basis of a design that predicted the population estimates of the pharmacokinetic parameters very well.


  1. L-K Foo, J McGree, J Eccleston, S Duffull. Comparison of robust criteria for D-optimal design. J Biopharm Stat [in press].