Averaging pharmacokinetic parameter estimates from experimental studies: Statistical theory and application

In most experimental pharmacokinetic studies, parameter estimates are computed separately for each subject, then averaged across subjects. Average estimators for ratios and functions of parameters are often of interest; examples include half-life and clearance. For these parameters, recommendations regarding averaging using the arithmetic versus the harmonic mean have been based on computer simulations. The goal in this paper was to demonstrate that these empirically generated results can be derived using approximations for the expected values of reciprocals and ratios. We first consider estimating the reciprocal of a parameter, and predict the earlier simulation results for half-life. We additionally predict results for clearance when computed as dose divided by area under the curve. Next we consider estimating the ratio of two parameters, and predict the earlier simulation results for clearance in a first-order exponential model. As a further example, we predict results for the mean residence time in noncompartmental analysis. These approximations provide a unifying approach that can be used to determine optimal summary estimators, without the need for extensive computer simulations.