ABSTRACT
In Chapter 9, we introduced statistical methods for the assessment of average bioequivalence under a higher-order crossover design for comparing two formulations of a drug product. The statistical methods depend on the estimation of the direct formulation effect and its variance. The analysis of a higher-order crossover design for comparing two formulations is quite straightforward because there are only two formulations to be compared regardless of how many sequences or periods in the design. In practice, however, it is often of interest to compare more than two (e.g., three or four) formulations of the same drug in a bioavailability=bioequivalence study. In this case, a standard highway (or higher-order) crossover design is usually considered. For example, for comparing three formulations, we may consider a standard three-sequence, three-period crossover design. The analysis for assessing average bioequivalence, however, is much more complicated because there are three pairs of formulation effects to be compared and the variance of these pairs of formulation effects may differ from one another. Moreover, a standard crossover design may not be useful when the carryover effect is present. To overcome the disadvantages that a standard crossover design may have, as
indicated in Chapter 2, variance-balanced designs are usually recommended because (1) it possesses the property of equal variances for each pairwise average differences among formulations; (2) it provides an estimate for each pairwise average difference in the presence of the carryover effect. A variance-balanced design allows us to estimate each pairwise average difference with the same degree of precision and provides analyses for assessing average bioequivalence in the presence of carryover effects. The most common variance-balanced design used for comparing three or four formulations in bioavailability=bioequivalence studies is the so-called Williams design. The Williams designs for comparing three or four formulations were briefly described earlier in Chapter 2. In this chapter, statistical methods for assessment of average bioequivalence under a Williams design are discussed. Frequently, pharmaceutical companies may be interested in comparing a large
number of formulations in a bioavailability study. For this, a complete standard
be (1) it is too time consuming to complete the study; (2) it is not desirable to draw many blood samples from each subject; (3) a subject is more likely to drop out when he or she is required to return frequently for evaluations. In addition, a complete higher-order crossover design may increase the chance of making errors in the randomization schedules, which has an influence on valid statistical inference. To accommodate these concerns, Westlake (1973, 1974) suggested that a balanced incomplete block design be used when comparing a large number of formulations. Several methods for constructing a balanced incomplete block design have been introduced earlier in Chapter 2. In the absence of carryover effects, a balanced incomplete block design is also a variance-balanced design. In this chapter, statistical methods for assessment of average bioequivalence under a balanced incomplete block design is also discussed. Section 10.2 describes a statistical model and methods like the confidence interval
and the two one-sided tests procedure for a general K J crossover design are derived. The application of these methods to the two Williams designs and an incomplete balanced block design is given in Sections 10.3 and 10.4, respectively. A brief discussion is presented in the Section 10.5.
