The primary purpose of a clinical trial is to address a scientific hypothesis. To address a hypothesis, different statistical methods are used depending on the type of question to be answered. Most often the hypothesis is related to the effect of one treatment as compared to another. For example, one trial could compare the effectiveness of a new antibiotic to that of an older antibiotic. Yet the specific comparison to be used will depend on the hypothesis to be addressed. Let’s use this two antibiotic example for this discussion.

We can construct 3 possible hypothesis to be addressed when comparing these two antibiotics. The three hypothesis are:

- The New Antibiotic is
**at least as good as**the Old Antibiotic. - The New Antibiotic is
**better than**the Old Antibiotic. - The New Antibioitic is
**equivalent to**the Old Antibiotic.

While each of these hypothesis may seem similar, they are slightly different scientific questions, thus each requires a slightly different statistical test. For the first hypothesis (“at least as good as”), the New Antibiotic must be as good as the Old Antibiotic, but it can also be better than the Old Antibioitic. In mathematical terms:

1.

For the second hypothesis (“better than”), the New Antibiotic can no longer be equivalent to the Old Antibiotic. In mathematical terms:

2.

The last hypothesis (“equivalent to”) indicates that the New Antibiotic cannot be worse than or better than the Old Antibiotic. In mathematical terms:

3.

As you can see, each hypothesis contains a slightly different mathematical arrangement. These mathematical expressions have been given “lay names” by satisticians in an effort to describe the math to non-statisticians; these names are:

- Non-inferiority
- Superiority
- Bioequivalence

Of these three comparisons, the non-inferiority has the largest range of successful trial outcomes (equivalence or superiority). Thus a calculated sample size for a non-inferiority trial is usually the smallest of the three hypothesis. The superiority comparison is a subset of the non-inferiority and will have a sample size that is similar to the non-inferiority or a sample size that is much larger. As the expected difference between the two treatments decreases, the sample size will increase, often dramatically. Finally, the bioequivalence comparison is the most restrictive because it requires that the two treatments be identical within some acceptable range defined by α (normally ±20%). In general a bioequivalence trial will have a sample size that is larger than a non-inferiority trial.

So which is best to use? It all depends on which scientific question you are trying to answer. All three study types are useful in the development of drugs. Non-inferiority studies are used to show that a minimum level of efficacy has been achieved. In comparison studies with a current therapy, non-inferiority is used to demonstrate that the new therapy provides at least the same benefit to the patient. Superiority trials are always used when comparisons are made to placebo or vehicle treatments. In these studies, it is critical that the effect in the treatment group be clearly superior to any effects in the placebo groups. Failure to demonstrate superiority over vehicle suggests that the drug is not effective. Superiority trials are also used for marketing purposes (“our drug is better than your drug” studies). Bioequivalence trials are used to show that a new treatment is identical (within an acceptable range) to a current treatment. This is used in the registration and approval of generic drugs that are shown to be bioequivalent to their branded reference drugs.

In the end, ask yourself which hypothesis am I trying to address, then use the appropriate study design. Best of luck!

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I would like to have more clarity on your comment, ” As the expected difference between the two treatments decreases, the sample size will increase, often dramatically.” here i understand that you are referring to the confidence interval limits. If we expect a difference of 20 %, the confidence intervals will have limits of 80-125. If we expect a difference of 10 %, the confidence intervals will have limits of 90-111. The sample size in the second case would be very high. I agree with you if this is the case.

However, when we assume that the two treatments are identical (no difference or T/R= 1) the sample size is low but when we assume the difference is more (T/R= 0.95 to 1.05 or .0.90 to 1.10), the sample size is more. Thus, here with more difference, the sample size is more and this appears contradictory to your statement.

Requesting you to clarify my doubt.

Thank you for the question. You make a very good point, if you are just looking at two identical treatments, the sample size can be small.. I should clarify that the sample size increases as the difference between treatments decreases *** if you want to characterize the size of that difference ***.

Is it possible to have a primary endpoint that will assess non-inferiority but prespecify a superiority sub analysis without changing the sample size? My gut says no.

Great question Ken. Generally sample sizes are for a single endpoint. In your example, the trial would be sized based on the primary endpoint (non-inferiority). And since non-inferiority studies require smaller sample sizes than superiority endpoint, it is unlikely that the superiority sub analysis would have adequate power, unless the effect was sufficiently large. In the end, I’m going with your gut feelings.

What design is appropriate when assessing generic drugs? And why? Thank you very much 🙂

Generic drugs normally use an equivalence design based on regulations.