Why are pharmacokinetic data summarized by arithmetic means?

Abstract

The main aim of many studies in clinical pharmacology is to describe the pharmacokinetic activity of a given compound. This pharmacokinetic activity for an individual is then evaluated through a series of summary parameters, such as area under the concentration-time curve (AUC), maximum concentration (Cmax) and the rate constant lambda, and it is evaluated across individuals by descriptive statistics of these parameters, such as the mean and range and a measure of spread such as the standard deviation. How the pharmacokinetic parameters are derived is described here. It is demonstrated that the assumption of an exponential half-life is often fundamental to the derivation of pharmacokinetic parameters. Given this fact, one would think it logical that data are analyzed with the appropriate statistics on the log-scale and not by summary statistics, such as arithmetic means, on the original scale. Why arithmetic means are used to describe the data is explored and the special nature of the log-transformation highlighted.