A Binary Outcome Non-Inferiority Trial is a clinical trial method that aims to prove that a new treatment is not inferior to an established treatment with regard to a binary outcome. Such outcomes can be, for example, “success” vs. “failure” or “survival” vs. “death”.
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Goal and concept
The aim of a non-inferiority trial is to show that the new treatment has no clinically relevant disadvantage compared to the existing treatment. In contrast to superiority trials, which aim to achieve a better result, or equivalence trials, which are intended to prove equivalence, an acceptable level of inferiority is defined here, the so-called non-inferiority threshold.
Free online calculator to calculate the sample size
Use our online calculator to calculate the required sample size for your non-inferiority study quickly and easily.
Calculation of the sample size
Sample size calculation is essential to ensure that the study has sufficient statistical power to demonstrate non-inferiority. A pre-specified difference (the non-inferiority cut-off) is used to define the clinically acceptable difference between the groups. Our special calculator supports you in determining the optimal sample size based on these parameters.
Application and requirements
An example of a binary outcome non-inferiority trial would be the comparison of a new generic drug with a branded drug for the treatment of a disease where the primary outcome is “success” vs. “failure”. Setting the non-inferiority threshold at 10% means that the cure rate of the new drug must not be more than 10% worse than that of the branded drug to be considered non-inferior.
Conducting such a trial requires a clear definition of the non-inferiority threshold as well as careful planning and analysis to avoid bias and ensure valid results.
Notes on sample size calculation for non-inferiority studies with binary outcomes
The calculation of the sample size is based on the expected success rate in both groups, the defined non-inferiority threshold and the statistical parameters significance level and power.
Significance level (alpha)
The significance level, also known as alpha (α) , describes the risk of falsely detecting a difference between the groups when none exists. An alpha of 0.05 is usually used.
Power (1-Beta)
The power of a study (1-β) shows how likely it is to detect a real difference when it actually exists. In non-inferiority trials, a power of 80% to 90% is often aimed for to ensure reliable results.
Percentage success rate in both groups
The success rate (π\pi) is the proportion of patients who achieve the desired result in both groups. In non-inferiority trials, it is assumed that the success rates of both groups are similar but not identical.
Non-inferiority limit (d)
The non-inferiority threshold (dd) defines the maximum acceptable difference between the success rates of the two groups at which the new treatment is still considered non-inferior. For example, a value of 10% (d = 10) could mean that a difference of up to 10% is considered acceptable.
Formula for calculation
The sample size is calculated using the following formula:
n=f(α,β)⋅[π1(100-π1)+π2(100-π2)]d2n = \frac{f(\alpha, \beta) \cdot \left[ \pi_1 (100 – \pi_1) + \pi_2 (100 – \pi_2) \right]}{d^2}
Where π1\pi_1 represents the success rate in the experimental group, π2\pi_2 represents the success rate in the control group, and f(α,β)f(\alpha, \beta) represents the Z-values determined by the significance level and power. This formula ensures that the sample size calculation is precise and provides meaningful results in your non-inferiority study.