**Limited sampling strategy for a population pharmacokinetic modelling of cocktail of phenotyping drugs**

Thu Thuy Nguyen (1,2), Henri Bénech (3), Marcel Delaforge (3), France Mentré (1), Natacha Lenuzza (2)

(1) IAME-UMR 1137, INSERM and University Paris Diderot, Paris, France; (2) CEA, LIST, LADIS, Gif-sur-Yvette, France; (3) CEA, DSV, iBiTecS, Gif-sur-Yvette, France

**Objectives:** Cocktail approach using a combination of probes to phenotype several cytochromes P450 and transporters, is of high interest in anticipating drug-drug interactions and personalized medicine [1]. Phenotyping indexes (PI) which are obtained from the area under the concentration-time curves, can be derived from a few samples using nonlinear mixed effect models (NLMEM) and maximum a posteriori estimation. We aimed to 1) propose a limited sampling strategy, allowing correct estimation of PI for several probes while providing as much flexibility as possible in sampling timing; 2) illustrate this strategy for two drugs often used in phenotyping tests: midazolam (probe for CYP3A) and digoxin (P-glycoprotein).

**Methods: **Data of a previous study with ten healthy volunteers [1] were analyzed to develop population parent/metabolite models for several drugs. In order to optimize joint design for a cocktail, we proposed to use the compound D-optimality [2] by maximizing a weighted sum of log determinants of the expected population Fisher information matrix (FIM) [3] for these models. Sampling windows were computed around the optimal fixed times, based on recursive random sampling and Monte-Carlo simulation [4,5], satisfying an expected joint loss of efficiency below 10% for each molecule. We illustrated this strategy to find a sparse and flexible design common to three compounds: midazolam, its metabolite 1-OH-midazolam and digoxin. The obtained design was evaluated by clinical trial simulations for estimation of population and individual PI.

**Results: **A two-compartment model (first order absorption, linear elimination) adequately fitted the concentrations of digoxin while a joint two-compartment-parent/one-compartment-metabolite model was found for midazolam and 1-OH-midazolam. The common design ξ was composed of six samples (0.25, 1, 2.5, 5, 12, 48h post-administration) instead of nine samples if optimizing separately design for each drug, giving predicted relative standard errors below 20% for both PI. The window design achieved an efficiency above 90% relative to ξ for population analysis of each drug and showed good performance for estimation of individual PI.

**Conclusions:** By combining NLMEM, compound design and sampling windows based on FIM, we were able to determine sparse and flexible samples allowing correct estimation of PI for three compounds [6]. This approach can be used to efficiently design studies with cocktails including more drugs.

**References:**

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[5] Ogungbenro K, Aarons L. An effective approach for obtaining optimal sampling windows for population pharmacokinetic experiments. J Biopharm Stat 2009; 19(1): 174–189.

[6] Nguyen TT, Bénech H, Delaforge M, Lenuzza N. Design optimisation for pharmacokinetic modeling of a cocktail of phenotyping drugs. Pharm Stat 2015 [Epub ahead of print].