# Equivalence Trial

## "Equally as good" treatment effects are established in equivalence trials

If a research question is focused on testing if a treatment is equal in its ability to cause an outcome , then an equivalence trial is the correct choice. Within applied statistics and data analysis, there are no existing statistical tests that can prove evidence of equivalence, just evidence of two treatments being statistically different or statistically NOT different. Equivalence trials allow for researchers to make the types of hypotheses where two treatments can be tested to see if they are statistically similar, instead of statistical different. To establish equivalence of a treatment, it must be compared to the current "gold standard" treatment or method of diagnosis.

In inferential statistics and hypothesis testing, researchers are always trying to reject the null hypothesis to test for significant differences. With equivalence trials, the main goal is to NOT REJECT the null hypothesis, meaning the two treatments ARE EQUALLY GOOD* at what they are supposed to do.

The most important part of conducting equivalence trials is to specify the margin of equivalence

In inferential statistics and hypothesis testing, researchers are always trying to reject the null hypothesis to test for significant differences. With equivalence trials, the main goal is to NOT REJECT the null hypothesis, meaning the two treatments ARE EQUALLY GOOD* at what they are supposed to do.

The most important part of conducting equivalence trials is to specify the margin of equivalence

*a priori*. The margin of equivalence is the area above and below the point on a continuum associated with the "gold standard" treatment that is clinically defined as being EQUALLY GOOD. Think of the margin of equivalence as the confidence interval wrapped around the cut-point on deciding if a treatment is beneficial.Another interesting wrinkle of the margin of equivalence is that instead of the traditional 95% confidence interval used in the majority of statistical inferences, equivalence trials use a more constricted 90% confidence interval. One would think that this drop in confidence would mean something detrimental to the internal validity of your study, however, in this ONE instance, researchers are actually increasing the chance of detecting equivalence because a constricted confidence interval is

If the new treatment being assessed in an equivalence trial and its respective 90% confidence interval falls WHOLLY within the margin of equivalence both above and below the cut-point for the "gold standard" treatment, then you can assume that the two treatments are EQUALLY GOOD or equivalent.

*narrower*than a 95% confidence interval. Thus, it has a better chance of falling within the margin of equivalence wrapped around the cut-point.If the new treatment being assessed in an equivalence trial and its respective 90% confidence interval falls WHOLLY within the margin of equivalence both above and below the cut-point for the "gold standard" treatment, then you can assume that the two treatments are EQUALLY GOOD or equivalent.

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*Lesaffre, E. Superiority, equivalence, and non-inferiority trials. Bull NYU Hosp Jt Dis. 2008;66(2): 150-154.