Design and analysis of three treatment equivalence trials

We consider design and analysis of clinical trials aimed at demonstrating equivalence of three treatments. We discuss analysis methods that require demonstrating that each pair of treatments has an unimportant difference. The critical values that we provide are smaller than the standard normal critical values, pointing out that the adjustment is counter to the usual multiplicity adjustments. Special issues in demonstrating equivalence of three rather than two treatments are discussed. We propose some conservative criteria for estimating sample size. Procedures for choosing pairs of treatments that are equivalent to each other, even when all three treatments are not shown equivalent, are also discussed along with implications for control of type I errors. We also demonstrate the methods with data from the literature.