Optimal design for a study of butadiene toxicokinetics in humans

The derivation of the optimal design for an upcoming toxicokinetic study of butadiene in humans is presented. The specific goal of the planned study is to obtain a precise estimate of butadiene metabolic clearance for each study subject, together with a good characterization of its population variance. We used a two-compartment toxicokinetic model, imbedded in a hierarchical population model of variability, in conjunction with a preliminary set of butadiene kinetic data in humans, as a basis for design optimization. Optimization was performed using Monte Carlo simulations. Candidate designs differed in the number and timing of exhaled air samples to be collected. Simulations indicated that only 10 air samples should be necessary to obtain a coefficient of variation of 15% for the estimated clearance rate, if the timing of those samples is properly chosen. Optimal sampling times were found to closely bracket the end of exposure. This efficient design will allow the recruitment of more subjects in the study, in particular to match prescribed levels of accuracy in the estimate of the population variance of the butadiene metabolic rate constant. The techniques presented here have general applicability to the design of human and animal toxicology studies.