Equivalence Testing

Frequently, the objective of an investigation is not to determine if a drug or treatment is superior to another but just equivalent. For instance, it is often of interest to investigate if a new drug, with say fewer side effects or lower price, is as efficacious as the one currently used. This situation occurs when new or generic drugs are evaluated for approval by the Food and Drug Administration (FDA).

In standard hypotheses testing, equivalence (i.e., equality) is the null hypothesis, and the alternative is the nonequivalence hypothesis. One problem with using this procedure, and determining equivalence when the null is not rejected, is that the test is designed to reject the null hypothesis only if the evidence against it is strong (e.g., p < .05). In other words, the burden of proof is in nonequivalence. The correct procedure to establish equivalence reverses the roles of null and alternative hypotheses so that the burden of proof lies in the hypothesis of equivalence. Consequently, the Type I error is tantamount to favoring equivalency when the drugs are not equivalent. This is the error that the FDA wants to minimize, and its probability is controlled at a low level (e.g., .05 or lower).

Some issues arise when testing for equivalence. A critical one is that perfect equivalence is impossible to establish. This problem is solved by introducing limits of equivalence that establish a range within which equivalence is accepted. Frequently, these limits are symmetric around a reference value. An example should help clarify the situation.

Suppose that a new drug for eliminating (or reducing to a prespecified level) a toxin in the blood is being evaluated. It has fewer side effects and the manufacturer is interested in proving that [Page 443]it is as efficacious as the currently used drug. Let pC and pN be the true (population) proportion of patients who respond to the current and the new drug, respectively. The problem consists of testing

A more informative way to write the alternative is H1: pC – δ < pN < pC + δ, which states that the efficacy of the new drug is within δ units from that of the current drug. The role of δ is crucial, and its value should be chosen with great care. Clearly, the probability of favoring equivalency increases as δ increases, so its value should be based on acceptable levels of deviation from perfect equivalence. The value of δ should be determined based on sound medical and biological considerations, independently of statistical issues. For example, if the potential benefits (fewer side effects) of the new drug are high, a larger value of δ could be justified. When the effect of the current drug is well established, the value of pC is fixed and the test becomes a one-sample equivalence test.

Using data from the National Immunization Survey (NIS), in 2002, Lawrence Barker and colleagues investigated whether vaccination coverage was equivalent between children of three minority groups and white children. Since the NIS data for 2000 were supposed to detect coverages at the 5 percentage point level, δ was chosen to be 5. Thus, the alternative hypothesis was H1: −5 < pM – pW < 5, where pW and pM are the coverage for white and minority children, respectively. The equivalence of the coverage was to be established if the data provided enough evidence to support H1.

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