2003
Verona, Italy
Design and power PK/PD experiments using very sparse data
Gianluca Nucci and Roberto Gomeni
Clinical Pharmacokinetics/Modelling and Simulation, GlaxoSmithKline, Verona, Italy
Objectives: The design of PK/PD experiments is a critical issue for improving the efficiency of pharmacology trials. An optimal design should account for the number and timing of samples, inter-individual variability, prior information on mechanistic model structure and parameter values, and, finally on the practical constraints linked to the feasibility of the experiment. In drug development the number of PK/PD samples that can be obtained may be limited to only one PK and PD measurement for practical (destructive sampling) or ethical reasons (exposure to radiation in imaging experiments). In this work we propose a novel method to design and power very sparse PK/PD experiments (one PK/PD sample per subject) accounting for inter-/intra-individual variability on PK and PD measurements and uncertainty on structural model parameters Methods: Initially, the proposed approach optimized the Fisher population information matrix (1) using a grid search algorithm, for the selection of optimal sparse sampling times (one sample/subject). The PD fixed and random effect model parameters were assumed precisely known from previous experiments and the PD was assumed driven by error free PK. Then, we relaxed these hypotheses assuming uncertainty on PD prior parameter estimates and inter-/intra-subject variability on PK measurements. Finally, the power of the optimally designed experiment was estimated by adjusting the sample size based on the expected parameter precision while the validation of the optimal design was assessed by evaluating bias on simulated experiment outcomes. Optimal design and Simulation Results: A one-compartment model characterized the simulated PK profile with a PK/PD link described by an Emax model with uncertainty on EC50 expected in the 8-16 ng/ml range and on Emax expected to lie between 80 and 100 %. Inter-individual variability for each model parameter was assumed log normal with a CV of 10% and measurement error assumed to be additive (variance=25). The optimal design was based on one sample/subject and four PD measurements that were: 2 hours post dose (PK Tmax) and 15, 18 (times related to the range of EC50 values explored) and 24 hours post dose (the latter being the time point corresponding to PK Cmin). The simulation study indicated that this design provided unbiased estimates for any parameter randomly selected within the uncertainty domain. The precision of parameter estimates was heavily linked to the number of subjects tested and to a lesser extent to the PK variability levels. Changing the expected PD variability had a noticeable impact on both bias and precision of estimates. Conclusion: The methodology developed addresses for the first time the impact of uncertainty in the parameters driving the design optimization for very sparse PK/PD experiments. The proposed approach showed that one measurement per subject and four subjects were sufficient to obtain unbiased PK/PD parameter estimates while an acceptable precision on the model parameters (<20%) required at least 16 subjects using a sparse sampling design. Reference Retout S, Duffull S, Mentre F. Comput Methods Programs Biomed 65, 141-51, 2001