Numerical estimation of the noncompartmental pharmacokinetic parameters variance and coefficient of variation of residence times.

Noncompartmental investigation of the distribution of residence times from concentration-time data requires estimation of the second noncentral moment (AUM2C) as well as the area under the curve (AUC) and the area under the moment curve (AUMC). The accuracy and precision of 12 numerical integration methods for AUM2C were tested on simulated noisy data sets representing bolus, oral, and infusion concentration-time profiles. The root-mean-squared errors given by the best methods were only slightly larger than the corresponding errors in the estimation of AUC and AUMC. AUM2C extrapolated "tail" areas as estimated from a log-linear fit are biased, but the bias is minimized by application of a simple correction factor. The precision of estimates of variance of residence times (VRT) can be severely impaired by the variance of the extrapolated tails. VRT is therefore not a useful parameter unless the tail areas are small or can be shown to be estimated with little error. Estimates of the coefficient of variation of residence times (CVRT) and its square (CV2) are robust in the sense of being little affected by errors in the concentration values. The accuracy of estimates of CVRT obtained by optimum numerical methods is equal to or better than that of AUC and mean residence time estimates, even in data sets with large tail areas.