A Binary Outcome Superiority Trial is a clinical trial method that aims to show that a treatment is superior to another treatment in terms of a binary outcome. A binary outcome refers to categories such as “success” vs. “failure” or “disease” vs. “health”.
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Goal and concept
The main aim of such a study is to prove that the new treatment offers a statistically significant advantage over the existing treatment. In contrast to equivalence or non-inferiority studies, the focus here is on demonstrating superiority. This means that the results of the new treatment must be clearly better than those of the control group.
Free online calculator to calculate the sample size
Use our online calculator to calculate the required sample size for your superiority study quickly and easily.
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Calculation of the sample size
Sample size calculation is crucial to ensure that the study has sufficient statistical power to detect a real difference between the groups. This involves determining an expected difference between the two groups that is considered clinically significant. Our special calculator helps you to determine this difference and the required sample size.
Application and requirements
An example of a binary outcome superiority trial would be the comparison of a new drug treatment with an existing standard treatment for lowering blood pressure. If the aim is to significantly improve the cure rate of the new treatment, e.g. from 60% to 75%, then the trial demonstrates superiority if this difference is statistically and clinically significant.
Conducting such a trial requires a clear hypothesis, careful definition of the primary endpoint and detailed planning to minimize bias or random error.
Notes on sample size calculation for superiority studies with binary outcomes
The calculation of the sample size for a binary outcome superiority trial is based on the expected difference between the groups, the significance level and the statistical power. These parameters ensure that the study is robust enough to test the hypothesis of superiority.
Significance level (alpha)
The significance level, also known as alpha (α), defines the probability of finding a difference when in reality none exists. Typically, an alpha of 0.05 is used, which corresponds to a 5% risk of an error of the first kind.
Power (1-Beta)
The power (1-β) indicates how likely it is that the study will detect a real difference between the groups. A typical power of 80% means that the risk of a second type error (β) is 20%.
Percentage success rates in both groups
The success rate describes the proportion of patients in each group who achieve the desired result. In superiority studies, a significantly higher success rate is expected in the experimental group.
Expected difference (d)
The expected difference (d) indicates the minimum difference between the success rates of the groups that is considered clinically significant. For example, a value of 15% (d = 15) means that the new treatment must improve the success rate by at least 15% to be considered superior.
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 for significance level and power. This formula ensures a precise sample size calculation and helps you to achieve reliable results in your superiority study.