Design optimisation in nonlinear mixed effects models using cost functions: application to a joint model of infliximab and methotrexate pharmacokinetics
S. Retout (1, 2), E. Comets (1), F. Mentré (1, 2)
(1) INSERM, U738, Paris, France; Université Paris 7, Paris, France; (2) AP-HP, Hôpital Bichat, Paris, France;
Objectives: We recently extended the R function PFIM  for population design evaluation and optimisation to deal with multiple response models and we proposed the Fedorov-Wynn algorithm to optimise both the group structure (number of groups, proportions of subjects and number of samples per group) and the sampling times . However, optimisation is done for a fixed total number of samples without any consideration on the relative feasibility of the optimised sampling times or the group structure. Our objectives are to extend PFIM with cost functions to take into account those feasibilities and to illustrate this extension on design optimisation of a joint population model of infliximab and methotrexate pharmacokinetics administered in rheumatoid arthritis.
Methods: We introduce cost functions as described in Mentré et al.  in the Fedorov-Wynn algorithm allowing thus optimisation for a fixed total cost. Regarding the application, infliximab is administered every 8 weeks by infusion and is described by a one compartment model with first order elimination whereas methotrexate is orally administered every week and is described by a two compartment with first order absorption and elimination. We first evaluate a design at steady state (called empirical design) composed of 50 subjects with 12 sampling times per subject common to both drugs. We then optimise four designs, each one with a different cost function but for a same total cost. The four different cost functions investigated are the following: the first one is the classical one, i.e. the cost of an individual design is proportional to the number of samples; the second one penalizes samples late during the dose interval; the third one involves a cost for each new subject in the study; the fourth one combines the second and the third one.
Results: The optimised designs provide reasonable parameter estimate precisions. They are different according to the choice of the cost function, in term of sampling times but also group structure with, for instance, a higher number of samples per subject and thus a smaller number of subjects when penalising in the cost function the addition of new subjects.
Conclusions: Cost functions have been successfully introduced in PFIM. This work illustrates the usefulness of PFIM for design optimisation especially when substantial constraints on the design are imposed.
 Retout S, Comets E, Samson A and Mentré F. Design in nonlinear mixed effects models: Optimization using the Fedorov-Wynn algorithm and power of the Wald test for binary covariates. Statistics in Medicine, 2007. 26: 5162-5179.
 Mentré F, Mallet A, and Baccar D. Optimal design in random-effects regression models. Biometrika, 1997. 84: 429-442.