the ‘Area Under the Curve’ or AUC. The AUC is taken as a measure of exposure of the drug to the subject. The peak or maximum concen-tration is referred to as Cmax and is an important safety measure. For regulatory approval of bioequivalence it is necessary to show from the trial results that the mean values of AUC and Cmax for T and R are not significantly different. The AUC is calculated by adding up the ar-eas of the regions identified by the vertical lines under the plot in Figure 7.1 using an arithmetic technique such as the trapezoidal rule (see, for example, Welling, 1986, 145–149, Rowland and Tozer, 1995, 469–471). Experience (e.g., FDA Guidance, 1992, 1997, 1999b, 2001) has dictated that AUC and Cmax need to be transformed to the natural logarithmic scale prior to analysis if the usual assumptions of normally distributed errors are to be made. Each of AUC and Cmax is analyzed separately and there is no adjustment to significance levels to allow for multiple testing (Hauck et al., 1995). We will refer to the derived variates as log(AUC) and log(Cmax), respectively. In bioequivalence trials there should be a wash-out period of at least five half-lives of the drugs between the active treatment periods. If this is the case, and there are no detectable pre-dose drug concentrations, there is no need to assume that carry-over effects are present and so it is not necessary to test for a differential carry-over effect (FDA Guidance, 2001). The model that is fitted to the data will be the one used in Section 5.3 of Chapter 5, which contains terms for subjects, periods and treatments. Following common practice we will also fit a sequence or group effect and consider subjects as a random effect nested within sequence. An example of fitting this model will be given in the next section. In the following sections we will consider three forms of bioequivalence: average (ABE), population (PBE) and individual (IBE). To simplify the following discussion we will refer only to log(AUC); the discussion for log(Cmax) is identical. To show that T and R are average bioequivalent it is only necessary to show that the mean log(AUC) for T is not significantly different from the mean log(AUC) for R. In other words we need to show that, ‘on average’, in the population of intended patients, the two drugs are bioequivalent. This measure does not take into account the variability of T and R. It is possible for one drug to be much more variable than the other, yet be similar in terms of mean log(AUC). It was for this reason that PBE was introduced. As we will see in Section 7.5, the measure of PBE that has been recommended by the regulators is a mixture of the mean and variance of the log(AUC) values (FDA Guidance, 1997, 1999a,b, 2000, 2001). Of course, two drugs could be similar in mean and variance over the