Equivalence and non-inferiority Calculator
When two groups are compared, one is usually interested in whether there is
- a difference,
- a superiority or
- an inferiority.
These tests take place in classical randomized controlled clinical trials (RCT), where the aim is to evaluate a difference between two treatments. The aim of these tests is to prove the superiority of the new drug over the standard drug.
Especially in medical statistics, however, it often happens that one wants to test for equivalence or non-inferiority. This is the case, for example, when a new drug has fewer side effects than the already established drug. Now a clinical study is to prove that the new drug is at least not worse than the established drug.
Equivalence Study
An equivalence study is conducted when equivalence of two therapies is to be demonstrated. An equivalence test is therefore carried out when it is to be shown that there are no or no significant differences in efficacy between two treatments.
To define what no substantial differences means, the equivalence limit δ must first be defined. This then determines which differences can be tolerated as clinically irrelevant
.
The limits of equivalence must be set so that they are clinically appropriate. Depending on the severity of the condition under investigation, more or less stringent limits of equivalence are required.
equivalence Vs difference
Important: A non-significant test result in a bilateral t-test is not sufficient to demonstrate equivalence.
It should also be noted that the calculated sample size tends to be larger for equivalence studies than for superiority trials.
Non-inferiority Study
In clinical research, the aim is to use a test for non-inferiority it can be shown that a new therapy is "not significantly worse" than the standard therapy. The null and alternative hypothesis results with
where μnew is the expected value of the new, μst the expected value of the standard therapy and δ the constant for the equivalence barrier.
The equivalence barrier must be defined in advance and often results from the literature. It is the value that is just about accepted from the point of view of the clinical question.
If the null hypothesis is rejected and thus the alternative hypothesis is accepted, this can mean that the new therapy is
- better,
- just as well or
- worse within the tolerable range δ.
Non-inferiority test VS superiority test
Important: A non-significant test result in a superiority test with a one tailed t-test is not sufficient to Non-inferiority detection.
A non-inferiority trial is a special case of an equivalence trial; it is only intended to determine whether a new treatment is not worse than an existing treatment. A non-inferiority study is thus always one-sided.
Calculate Equivalence and non-inferiority
A fictitious example is used to calculate a non-inferiority test. In this example, we will investigate whether a new drug is not inferior to the already established drug. Thus, a clinical trial is to show that the new drug is at least not inferior to the established drug.
The following 10 unpaired values result from the clinical study, whereby a high value indicates good therapeutic success.
| new drug | established drug |
|---|---|
| 62 | 61 |
| 70 | 71 |
| 50 | 48 |
| 51 | 49 |
| 60 | 58 |
| 60 | 53 |
| 45 | 55 |
| 55 | 56 |
| 59 | 58 |
| 65 | 68 |
After the upper table has been copied to the Equivalence and Non-inferiority calculator , you only have to click on the two variables, select Non-inferiority as the calculation type and choose the constant δ for the equivalence limit. Since this is a fictitious example, simply choose -5 for the equivalence barrier, this value is made up and must of course be adapted to the respective clinical trial.
After all settings have been made to calculate a non-inferiority study, DATAtab first outputs the descriptive statistics and the levene test of variance equality. The levene test of variance equality yields a significance of 0.817 which is greater than 0.05, thus maintaining the null hypothesis and assuming variance equality.
After the descriptive statistics you will then receive the results for the non-inferiority study. The confidence interval cuts the equivalence barrier of -5, so that no non-inferiority can be demonstrated with these data and the established drug must continue to be preferred.
The graphical representation also clearly shows that the confidence interval intersects the lower limit (equivalence limit) marked in red. If the confidence interval were to lie completely to the right of the red line, non-inferiority would be proven for these data.
Calculate Equivalence and non-inferiority Trials
To calculate an equivalence or non-inferiority test, simply copy your data into the upper table and select the desired data. Then you can select whether an equivalence or non-inferiority test should be calculated and specify the bounds.
Afterwards you will already get the results.
Equivalence and non-inferiority studies are increasingly used in clinical trials. Clinical studies aimed at demonstrating that there are no relevant differences between two treatments are becoming increasingly common.