Choice of Delta in Equivalence Testing

Abstract

A valid interpretation of an active control equivalence study without a concurrent placebo control depends on the assumptions that 1. The active control is effective in the current trial (ie, assay sensitivity), and 2. The effect size is the same across the studies (ie, constancy assumption). The equivalence margin 8 should be a small fraction (eg, 0.2) of the therapeutic effect of the active control as compared to placebo. However, a larger 8 can be justified if the objective is to establish the efficacy of the experimental treatment as compared to placebo through its comparison to the standard therapy without claiming equivalence.

The proposed 8 may be interpreted as preserving a percentage of the active control effect as compared to placebo. The assumption that the active control effect is constant across studies may be discounted by using a smaller 8. Preservation and discounting are two distinct concepts, although they are indistinguishable mathematically.

Placebo controls are not necessarily unethical when known effective therapy exists for a condition. When a placebo control is ethical, it is a clear choice if the study objective is to establish the efficacy of the test treatment. A three-arm trial (test treatment, active control, and placebo) would be an ideal design if the study objective is to establish the efficacy of the test treatment relative to an active control.

When a placebo control is unethical and there can be no concurrent placebo, an evaluation of the efficacy of the test treatment depends on the discount factor to be used. The discount factor is often difficult to justify. In such a situation, an evaluation of the efficacy of the test treatment may be supplemented by other designs such as an “add on” design or an early escape design. In fact, a hybrid of the active control design with the “add on” design (test treatment, active control, and combination) is an ideal design when the test treatment and the active control possess different pharmacologic mechanisms. On the other hand, the discounting factor plays a less important role in an evaluation of the relative efficacy of the test treatment.