6b.3 - Equivalence Trials

For an equivalence trial, it is necessary to determine a “zone of clinical equivalence” prior to the trial onset.

For example, consider standard (active control) and experimental antihypertensive drugs (a drug that controls blood pressure). Suppose that the standard drug yields a mean reduction of 5 mm Hg in diastolic blood pressure for a certain patient population. The investigator may decide that the experimental drug is clinically equivalent to the standard drug if its mean reduction in diastolic blood pressure is 3-7 mm Hg. This is based on clinical judgment and there may be differences of opinion on this 'arbitrary' level of equivalence.

Thus, the difference in means between the two therapies does not exceed 2 mm Hg. Let's suppose that we are willing to accept this level.

In general, the zone of equivalence is defined by \(±\Psi\). The difference in population means between the experimental therapy and the active control, \(\mu_E - \mu_A\), should lie within \((-\Psi, +\Psi)\). Differences in response less than \(\Psi\) are considered 'equally effective' or 'noninferior'.

In nearly every equivalence trial, the selection of \(\Psi\) is arbitrary and can be controversial. Some researchers recommend that Ψ be selected as less than one-half of the magnitude of the effect observed from the superiority trials comparing the active control to placebo.

Given what we know in the the antihypertensive example above, \(\Psi = 2\) satisfies this requirement \((\dfrac{2}{5} = 0.4 < 0.5)\), but why not select \(\Psi = 1\)?

Here is a second issue to consider...

Unlike a placebo-controlled trial, an equivalence trial does not provide a natural check for internal validity because equivalence of the experimental and active control therapies does not necessarily imply that either of them is effective. In other words, if a third treatment arm of placebo had been included in the trial, it is possible that neither the experimental therapy nor the active control therapy would demonstrate superiority over placebo. There is no direct establishment of superiority inherent in the way the trial is set up.

The investigator needs to select an active control therapy for the equivalence trial that has been proven to be superior to the placebo. An important assumption is that the active control would be superior to placebo (had placebo been a treatment arm in the current trial).

In the past, a few equivalence trials incorporated appropriate active controls, but at doses less than recommended (rendering them ineffective). It is important to select the proper control and use it at an appropriate dose level.

One way to ascertain internal validity is through an external validity check, e.g., compare the experimental and active control therapies of the current study to published reports for comparative trials that involve the active control therapy versus a placebo control. Are similar results observed for the active therapy in the equivalence trial as in the published study against a placebo?

External comparisons should examine response levels, patient compliance, withdrawal rates, use of rescue medications, etc. An external validity check is only possible if the chosen active control therapy for the equivalence trial was determined effective in a superiority trial. An under-dosed or over-dosed regimen for the active control therapy in an equivalence trial can bias the results and interpretations. In addition, the design for the equivalence trial should mimic (within reason) the design for the superiority trial. Some of this advice is difficult to follow and may be impossible to implement.

(Another aspect of internal validity, of course, is the quality of the trial, in terms of inclusion/exclusion criteria, dosing regimens, quality control, etc. Do not run a sloppy study!)

The U.S. Food and Drug Administration (FDA) and the National Institutes of Health (NIH) typically require intent-to-treat (ITT) analyses in placebo-controlled trials. In an ITT analysis, data on all randomized patients are included in the analysis, regardless of protocol violations, lack of adherence, withdrawal, incorrectly taking the other treatment, etc. The ITT analysis reflects what will happen in the real world, outside the realm of a controlled clinical trial.

Is this appropriate? In a superiority trial, the ITT analysis usually is conservative because it tends to diffuse the difference between the treatment arms. There is more 'noise' in an ITT study. This is due to the increased variability from protocol violations, lack of adherence, withdrawal, etc. You can overcome this noise by increasing the sample size.

In an equivalence trial, the ITT analysis still is appropriate. There is a misconception that the ITT analysis will have the opposite effect in an equivalence trial, i.e., it will be easier to demonstrate equivalence. This is not so. Even with an ITT analysis in an equivalence trial, it still is important to conduct a well-designed study with a sufficient sample size and good quality control.

An alternative to an intent-to-treat analysis is a protocol analysis, whereby subjects are analyzed according to the treatment received. A protocol analysis excludes subjects who did not satisfy the inclusion criteria, did not comply with taking study medications, violated the protocol, etc. You are excluding data from the patients that do not follow the protocol when it comes to the analysis. A protocol analysis is expected to enhance differences between treatments, so it usually will be conservative for an equivalence trial. Obviously, a protocol analysis is susceptible to many biases and must be performed very carefully. You may think that you are removing all of the biases, when in fact you may not be. A protocol analysis could be considered as supplemental to the ITT analysis. The U.S. FDA moved to ITT studies years ago to avoid biases introduced when researchers selectively excluded patients from analysis because of various protocol deviations. Many of the major medical journals also will only accept ITT studies for these reasons as well.