Bayesian Analysis of an Optimal Five Period Cross-over Design

Abstract

A crossover design is a repeated measurements design such that each experimental unit receives different treatments during the different time periods. In a majority of bioequivalence studies, design and analysis of cross-over using classical methods such as analysis of variance (ANOVA) and test are normally associated with erroneous results. The Bayesian method is desirable in the analysis of crossover designs to eliminate errors associated with carryover effects. The objective of this study was to compare the Bayesian and the - test analysis methods on treatments and carryover effects for an optimal two treatments, five periods and four sequence C (2, 5, 4) design. The treatments and residual estimates were obtained using Best Linear Unbiased Estimation (BLUE) method. In the Bayesian method of analysis, the posterior quantities were obtained for the mean intervals of treatments and carry-over effects and the highest posterior density (HPD) graphs were plotted and interpreted using conditional probability statements. For validation purposes, the Bayesian method results were compared with the existing -tests results. From the Bayesian analysis, the probability of significant treatment difference in the presence of carryover effects was 1, while from the -test, the calculated value of 11.73 was greater than the two sided tabulated value at 95  level of significance. The two analysis methods implied significant differences in the treatment effects. In conclusion, it was established that Bayesian method of analysis can be used for bioequivalence analysis even when the carry-over effects are present and hence it is highly recommended for bioequivalence studies.