A Bayesian approach for assessment of therapeutic equivalence of three proportions

Nonrejection of the null hypothesis when comparing two response rates in a clinical trial does not necessarily imply that the two treatments are equivalent with respect to their therapeutic effectiveness. Recently, researchers have invested much time and effort in describing situations in which therapeutic equivalence (TE) may be achieved. These have involved direct hypothesis-testing procedures and confidence interval techniques. The latter involves determining whether such an interval lies within predefined equivalent regions. The committee chairs (Al Bartolucci and Karan Singh) have published previously on this subject when the parameters of interest were from growth curve or survival distributions. In this research endeavor, the focus is to determine whether three treatments are equivalent with respect to their therapeutic effectiveness. The prior information involves the natural conjugate beta family of distributions. The primary parameter of interest is the ratio of the two binomial parameters. Limiting values of the hyperparameters of the conjugate family are used to demonstrate the robustness of the outcomes. Several equivalence regions are used to test whether equivalence has been achieved and under what conditions the attainment of equivalence may not be established. The procedure has wide applications as well in the quality control setting.