ABSTRACT
In Chapter 4, based on the 20 rule, we introduced several statistical methods for assessment of average bioequivalence. Most of these methods were derived under a raw data model [i.e., model 4.1.1 or 4.1.2] for the standard 2 2 crossover design, with normality assumptions on the between-subject and within-subject random variables. The intra-subject variability is assumed to be the same from subject to subject and from formulation to formulation. As a result, the responses (e.g., AUC or Cmax) are assumed to be normally distributed. One of the difficulties commonly encountered in bioavailability studies, however, is whether the assumption of normality is valid. Often, distributions of the responses are positively skewed and exhibit a lack of homogeneity of variances (e.g., variance being dependent on the mean). In this situation, a log-transformation on the responses is often considered to reduce the skewness and to achieve an additive model with relatively homogeneous variances. In addition, the FDA guidances on Statistical Approaches to Establishing Bioequivalence, issued in 2001, and Bioavailability and Bioequivalence Studies for Orally Administrated Drug Products-General Considerations, issued in 2003, suggest the routine use of logarithmic transformation for AUC01 and Cmax for assessment of average bioequivalence. A justification of multiplicative (or a logtransformed) model is provided by the guidance. From the transformed data, the methods introduced in Chapter 4 can then be applied directly and followed by an antilog-transformation to assess average bioequivalence. Under a multiplicative model, the ratio of means, which is usually considered
as a measure of average bioequivalence, may be confounded with the period effect or intra-subject variabilities. Therefore, in this chapter, we consider several estimators for the ratio of average bioavailabilities that reflect the effect caused by only differences in the formulations. These estimators include the maximum likelihood estimator and the minimum variance unbiased estimator (Liu and Weng, 1992). These estimators are derived under the multiplicative model with normality assumptions on the transformed data. Based on these estimators, a (1 2a) 100%
to bioequivalence. If the normality assumptions are seriously violated and there is no period effect,
Peace (1986) suggested studying individual subject ratios to remove the heterogeneity of intra-subject variability from the comparison between formulations. Under his model, however, distribution of the ratios is unknown; therefore, the statistical procedures are not exact. Under the assumption of no period effects, Tse (1990) examined several approaches, which are derived assuming that the ratios follow a lognormal distribution, for constructing the confidence interval for mean and median of individual subject ratios. Anderson and Hauck (1990) also examined individual bioequivalence using individual subject ratios. Peace (1990) recommended the use of individual subject ratios as a preliminary test for assessment of bioequivalence. In this chapter, the ratio of least squares means (RM) and the least squares mean of individual subject ratios (MIR), which are often considered as alternative estimators for the average bioavailabilities ratio, are examined. This chapter is organized as follows: In Section 6.2, a brief description of a
multiplicative model for the standard 2 2 crossover design is given. Various bioequivalence measures are discussed in Section 6.3. The maximum likelihood estimator, the minimum variance unbiased estimator, the mean of individual subject ratios, and the ratio of least square (LS) means for estimation of the ratio of average bioavailabilities are described from Sections 6.4 through 6.7. Section 6.8 provides statistical evaluation for the performances of these methods using a simulation study. An example concerning the comparison of two erythromycin formulations is presented in Section 6.9. Finally, a brief discussion is given in Section 6.10.
