Sample size calculations for risk equivalence testing in pharmacoepidemiology

Equivalence testing has been widely discussed and is commonly used in pharmacokinetics (bioequivalence) and clinical trials (therapeutic equivalence). It can also be applied to pharmacoepidemiology, where the aim may be to test with a known risk (one-group design) or with another drug (two-group design). Whether the approach is two-sided or one-sided, predefined equivalence limits are required. The definition of the equivalence region can be based on either risk difference or risk ratio. Risk equivalence testing is complicated by the binary nature of the outcome, its low frequency, and by the absence of commonly defined equivalence limits for differences or ratios. In this context, we consider usable formulae for sample sizes. In most cases, at least when the risk studied is large enough (above 1/1,000), it appears that these formulae result in sample sizes that may be acceptable for practical purposes. For example, demonstrating equivalence with a known risk of 0.01, a 20% maximal risk difference, and a one-sided test (alpha = 0.05 and beta = 0.2) requires: under the one-group design (known risk), 15,309 patients; and under the two-group design, 30,617 patients per group. This approach is the appropriate way to conclude equivalence, rather than the commonly used approach of difference testing and concluding equivalence when the null hypothesis of equality is not rejected.