Comparisons of Superiority, Non-superiority, Non-inferiority, and Equivalence Trials

The purpose of a randomized clinical trial (RCT) is to identify a treatment that is superior to standard therapy or placebo. It means an RCT can be planned and performed as a superiority trial.

However, sometimes the aim of an RCT is just to show that a new drug is equivalent to or not inferior to a standard drug. For example, if a new treatment enjoys lower cost and lesser side effects, then a standard drug should be replaced if the new drug is equivalent to or not inferior to a standard drug.

Consequently, we will discuss four types of trials, including superiority, non-superiority, non-inferiority, and equivalence trials. Before that, we introduce some notation.

• p_T: the level of effectiveness with treatment group
• p_C: the level of effectiveness with the control/placebo group
• M: a positive constant

Superiority Trials

In statistics, the hypothesis can be constructed as followed.

Futility Designs (Non-superiority Trials)

The purpose of the design is to screen out an unpromising treatment with fewer patients and a much shorter study time period. The designs can be used in a single-arm study with the threshold.

Statistically speaking, the hypothesis test can be established as

where M is the margin that should be prespecified in the protocol. Note that the choice of margin is very important; margins have clinical meaning and the choice should be supported by the rationale

In this design,

• Type I error should be defined as the chance of seeing an effective treatment as ineffective.
• Type II error refers to the chance of failing to identify an ineffective treatment.

Futility trials can be more efficient and cost-effective than superiority trials. Since they do not require the new treatment to be better than the standard treatment, they can be conducted with smaller sample sizes and shorter follow-up periods. This can reduce the costs and resources needed to conduct the trial, and can make it more feasible to evaluate the new treatment in a wide range of clinical settings.

Non-inferiority trials

A common misunderstanding is that the trials are caused by safety and efficacy regulations, which would suggest that a new therapy first needs to show non-inferiority before it can be tested in a superiority trial. However, non-inferiority trials were originally designed for studies in which it is unethical to include a placebo arm. In a non-inferiority trial, the goal is to indicate that a new treatment is not much worse than the standard treatment.

The hypothesis testing can be generated as followed.

Non-inferiority trials are usually conducted to show that a particular intervention may be acceptably worse than the current standard of care treatment (control) but has ancillary benefits over the control such as lower costs, lesser side effects, easier administration, etc.

Finally, a non-inferiority trial design usually requires a smaller sample size as compared to a superiority trial and hence fewer resources. This plays a huge role in lowering the cost of a trial. Lower cost and sample size also make it a more convenient endeavor!

The choice of the margin of non-inferiority is an important consideration in the design of a non-inferiority trial.

• Pre-specified in the protocol
• Represents the maximum difference in treatment effect that the experimental treatment can have relative to the control treatment and still be considered non-inferior.
• Based on the minimum clinically important difference (MCID) in the treatment effect, which is the smallest difference in the outcome measure that is considered to be meaningful to patients.

Why is it reasonable to plan for testing non-inferiority and then superiority?

It is reasonable to plan for testing non-inferiority and then superiority, but not the other way around because non-inferiority is a weaker hypothesis than superiority. Hence, the anon-inferiority trial can be seen as a gatekeeper to show that the new treatment is not worse than a threshold with a smaller sample size and lesser time duration. If the new drug is non-inferiority to the placebo, a superiority trial can be conducted to further determine whether we should implement the new intervention.

Equivalence Trials

The hypothesis is shown as followed.

Equivalence trials have several advantages over superiority and non-inferiority trials.

• They can provide more precise and relevant information about the relative effectiveness of the new treatment compared to the standard treatment. By demonstrating that the difference in treatment effect is within a pre-specified margin of equivalence, equivalence trials can provide evidence that the new treatment is not clinically different from the standard treatment in terms of the outcome measure. This can inform clinical decision-making and help guide the use of the new treatment in clinical practice.
• Equivalence trials can also be more efficient and cost-effective than superiority and non-inferiority trials. Since they do not require the new treatment to be better or worse than the standard treatment, they can be conducted with smaller sample sizes and shorter follow-up periods. This can reduce the costs and resources needed to conduct the trial, and can make it more feasible to evaluate the new treatment in a wide range of clinical settings.
• The trials can be more ethical than superiority and non-inferiority trials. Since they do not require the new treatment to be better or worse than the standard treatment, they do not involve withholding the standard treatment from some participants in order to evaluate the new treatment. This can reduce the risk of harm to participants, and can help ensure that all participants receive the best available treatment.

Reference:

1. Non-inferiority study design: lessons to be learned from cardiovascular trials.
2. Understanding the vortex of non-inferiority trials.