A Continuous Outcome Equivalence Trial is a clinical trial method that aims to show that two treatments can be considered equivalent in terms of a continuous outcome. Continuous results such as blood pressure, cholesterol levels or pain scale scores are precisely recorded on a scale.
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Goal and concept
The aim of an equivalence trial is to prove that the difference between the two treatment groups is within a predefined equivalence limit. In contrast to superiority trials, which are designed to show the superior efficacy of a new treatment, and non-inferiority trials, which test for acceptable inferiority, this study examines whether the treatments are clinically comparable. The aim is to find no relevant advantage or disadvantage between the treatments.
Free online calculator to calculate the sample size
Use our online calculator to quickly and easily calculate the required sample size for your equivalence study with continuous results.
Calculation of the sample size
Calculating the sample size is a crucial step to ensure sufficient statistical power. The equivalence limit is defined, which indicates the maximum acceptable difference between the groups. You can use our online calculator to determine the sample size quickly and precisely in order to achieve valid and reliable results.
Application and requirements
A typical example of a Continuous Outcome Equivalence Trial is the comparison of two drugs for lowering blood pressure, in which the mean reduction in systolic blood pressure is examined. If the difference between the drugs is within 3 mmHg, the study proves equivalence.
Conducting such a study requires careful planning, especially when determining the equivalence limits. In addition, a sound statistical analysis is necessary in order to avoid distortions and misinterpretations.
Notes on calculating the sample size for equivalence studies with continuous results
The calculation of the sample size is based on the standard deviation of the results, the equivalence limits, the significance level and the statistical power. These factors ensure that the study delivers meaningful results.
Significance level (alpha)
The significance level (α) indicates the probability with which a difference between the groups is falsely recognized as significant; usually an alpha of 0.05 is used, which means a 5% risk of a first type error.
Power (1-Beta)
The power (1-β) of a study indicates how likely it is that the equivalence will be correctly established. A power of 90% ensures that the probability of a second type of error is low.
Standard deviation (σ)
The standard deviation (σσ) indicates the variability of the measured values within each group. A high dispersion of results requires a larger sample in order to achieve valid results.
Equivalence limit (Δ)
The equivalence limit (ΔΔ) defines the maximum acceptable difference between the two groups. For example, a difference of ±3 mmHg in blood pressure could be considered equivalent.
Formula for calculation
The sample size is calculated using the following formula:
n=2⋅f(α,β/2)⋅σ2Δ2n = \frac{2 \cdot f(\alpha, \beta/2) \cdot \sigma^2}{\Delta^2}
Here, f(α,β/2)f(\alpha, \beta/2) stands for the Z values, which are determined by the significance level and the power, σ\sigma for the standard deviation of the results and Δ\Delta for the equivalence limit. This formula ensures that the sample size is large enough to prove the equivalence of the treatments with a high degree of statistical certainty.