### Superiority, Equivalence and Noninferiority Trials

The RCT is generally accepted as the best method of comparing effects of therapies. In this scenario, three types of trials exist: superiority, equivalence and noninferiority trials.^{[3,7–9]}

When the aim of the study is to demonstrate that an experimental treatment is superior to a control treatment, the RCT is called a superiority trial, and the underlying statistical test is a superiority test.^{[8]} When a statistically significant result is observed, it can be concluded that the effects of the experimental treatment differ from those of the control.^{[8]}

When the aim of the RCT is simply to show that a new therapy is not superior but equivalent or not inferior to an established therapy, equivalence trials or noninferiority trials are planned, respectively (Figure 1).

Figure 1.

Differences between equivalence and noninferiority trials. Equivalence trials aim to show that the effects between the active control and the test drug differ by no more than a specific amount of tolerance (− Δ to Δ, equivalence margins). Conversely, a noninferiority trial is designed as a one-sided trial aiming to demonstrate that the difference in effect is no less than − Δ (noninferiority margin)

The term "noninferiority" is relatively new and is often referred to as "equivalence". Nonetheless, noninferiority and equivalence trials differ in several aspects.^{[3]}

Although it is not statistically possible to prove that two treatments are identical (i.e., it is fundamentally impossible to prove that two treatments have exactly equivalent effects), equivalence trials aim to show that the effects differ by no more than a specific amount of tolerance (equivalence margin; generally denoted by the symbol Δ). In other words, an equivalence trial tries to conclude that the effects of the two treatments differ by no more than the equivalence margin *in either direction* (Figure 1, left panel).

On the other hand, it is possible to determine that a new treatment (experimental treatment, T) is not worse than an active control (C) by an acceptably small amount, with a given degree of confidence.^{[6]} The premise of a randomized noninferiority trial is to demonstrate that the difference in effect (*T* − *C*) is no less than − Δ (noninferiority margin). Noninferiority of the new therapy is demonstrated if the lower confidence limit for the difference in effect between the therapies turns out to lie above − Δ (Figure 1, right panel).^{[10,11]} Of note, the position of the upper confidence limit is not of primary interest and, thus, the noninferiority trial is designed as a one-sided trial (Figure 1).

More specifically, a noninferiority experiment tries to show that the new intervention is not "inferior" to the previous one, or—more precisely—that the new intervention is "not unacceptably worse" than the intervention used as the control. Thus, the null hypothesis seems backwards, in a sense, as this hypothesis is not "null" at all. Instead, it states that the new treatment is worse than the old by more than − Δ. The alternative hypothesis states that the difference in the effect between the new and old interventions is less than − Δ.

In the inverted world of noninferiority, the alternative hypothesis seems "null", whereas the null hypothesis includes a specified treatment difference of − Δ.^{[10–12]}

As depicted in Figure 2, a noninferiority trial can have six possible types of outcomes:^{[12,13]}

Figure 2.

Possible outcomes of a noninferiority trial.^{13,24} Vertical lines indicate zero (the same effect between test drug and control) and − Δ (noninferiority margin). For each outcome, the estimated treatment effect is denoted by the dot, with horizontal lines representing 95% confidence intervals. See text for details

point estimate of

*T*−*C*is 0 (equal effect of*C*and*T*) and lower bound of the 95% confidence interval (CI) for*T*−*C*> − Δ: noninferiority is demonstrated,point estimate of

*T*−*C*favors*C*; the lower bound of the 95% CI for*C*−*T*is < − Δ: noninferiority is not demonstrated,point estimate of

*T*−*C*is zero, which suggests an equal effect, but the lower bound of the 95% CI for*T*−*C*is < − Δ: noninferiority is not demonstrated,point estimate favors

*T*, and the lower bound of the 95% CI for*T*−*C*is > − Δ: noninferiority is demonstrated,point estimate favors

*T*, and the CI sits wholly above zero: noninferiority is concluded and superiority can be also demonstrated (if prespecified in the protocol),point estimate of

*T*−*C*favors the control, the lower bound of the 95% CI for*T*−*C*is > − Δ and at the same time the upper bound of the 95% CI for*T*−*C*is below zero:*T*is inferior to*C*, even while meeting the noninferiority standard.

Am J Cardiovasc Drugs. 2020;20(3):229-238. © 2020 Adis Springer International Publishing AG

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