Statistical analysis of pharmacokinetic data with special applications to bioequivalence studies

The objectives of this investigation are: 1) to describe techniques for determining the validity of the assumptions; 2) to suggest data transformations which may validate the use of parametric procedures; and 3) to describe a non-parametric alternative to the analysis of variance for crossover designs. Two assumptions common to all parametric procedures include the underlying normal distribution of the observations and equality of variances across treatment groups. Normal probability plots and/or stem and leaf plots are good diagnostic techniques to address the assumption of normality, while Bartlett's test is the most common method of determining equality of variances. To evaluate bioequivalence data, the Food and Drug Administration suggests the use of analysis of variance for crossover designs. If the underlying assumptions are valid, the appropriate statistical models are well known. On the other hand, if the assumptions are not valid, the investigator has one of two choices: 1) transform the data in such a way as to satisfy the assumptions, or 2) use a non-parametric procedure. Square root or logarithmic transformations are commonly used in this situation. However, if a suitable transformation cannot be found, then a non-parametric procedure should be used. Koch (Biometrics (1972) 28, 577-584) developed a non-parametric crossover test, which is relatively easy to apply, but the corresponding power calculations required by the FDA are less obvious.