A Binary Outcome Equivalence Trial is a clinical trial method that aims to prove that two treatment methods are equivalent in terms of a binary outcome. A binary outcome can be, for example, “success” vs. “failure” or “survival” vs. “death”.
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Goal and concept
The aim of such a study is to show that the difference in outcome between two groups is not clinically significant. In contrast to superiority studies, in which one treatment is to be shown to be better than the other, the focus here is on demonstrating equivalence. This means that the new treatment has no significant advantage or disadvantage compared to the existing treatment.
The calculation of the sample size for a binary outcome equivalence trial is crucial. It ensures that the study offers a high level of statistical certainty. This involves defining an acceptable difference between the two groups within which the results are considered equivalent. Our calculator for such studies helps to calculate this difference and the corresponding sample size.
Free online calculator to calculate the sample size
Use our online calculator to quickly and easily determine the required sample size for your equivalence study.
Application and requirements
A typical example of a binary outcome equivalence trial would be the comparison of two medications for the treatment of a disease where the primary outcome is the cure rate, e.g. “cured” vs. “not cured”). If a difference of 5% is considered clinically irrelevant, the trial would show that the two drugs are equivalent in this respect if the cure rates in both groups are within this 5% range.
Overall, conducting a binary outcome equivalence trial requires careful planning and precise definition of equivalence boundaries as well as sound statistical analysis to ensure that the results are valid and clinically relevant.
Notes on calculating the sample size for equivalence studies with binary results
In order to make a binary outcome equivalence trial statistically valid, the sample size must be calculated in such a way that the desired significance level and statistical power are achieved. The calculation is based on a defined significance level and a desired power. In addition, a defined equivalence limit is used, which indicates the acceptable difference between the two treatment groups.
Significance level (alpha)
The significance level, usually referred to as alpha (α) , indicates the probability that a result is falsely considered significant. In equivalence research, an alpha of 0.05 is often specified, which corresponds to a 5% probability of a first type error.
Power (1-Beta)
The power of a study, represented as 1-β, indicates how likely it is that the study will detect a true equivalence if it actually exists. A power of 95% means that the probability of correctly detecting an equivalence is 95%. The remaining beta (β) of 5% represents the probability of a second type of error.
Percentage success rate in both groups
The success rate, shown here with the symbol π, indicates the percentage that achieves the desired treatment success in both groups. In many studies, an assumed success rate of 10% is used for both groups.
Equivalence limit (d)
The equivalence threshold defines the maximum acceptable difference between the success rates of the two groups within which the treatments are considered equivalent. A value of 5% (d = 5) means that a difference of up to 5% is considered clinically irrelevant.
Formula for calculation
The calculation of the sample size is based on the following formula:
\[n = \frac{2 \cdot f(\alpha, \beta/2) \cdot \pi \cdot (100 – \pi)}{d^2}\]
Where π stands for the success rate in both groups. \( f(\alpha, \beta/2) \) refers to the Z values, which are determined by the significance level and the power. This formula ensures a precise calculation of the sample size in order to achieve meaningful results in an equivalence study.