Establishing equivalence by showing that a specified percentage of the effect of the active control over placebo is maintained.

We propose a procedure for establishing equivalence that determines whether a specified percentage of the treatment effect of a known active agent over placebo is maintained. This procedure accounts for the error in the estimates from the historical studies of the known active agent and placebo as well as the error in the estimates from the equivalence study of the new test treatment versus the active control. After the procedure is presented, it is compared analytically to a procedure in which the equivalence boundary is estimated from historical data and then used with a one-sided test. We address sample size requirements for the proposed equivalence procedure. We also illustrate the use of the proposed procedure with an example from the clinical area of thrombolytic therapy in acute myocardial infarction.