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In a clinical trial, the usual analysis is to conclude that there is a “difference” if the p-value is smaller than 0.05 and to conclude that there is no difference if the p-value is greater than 0.05.
In the previous issue (vol. 8), we introduced that if the null hypothesis could not be rejected, it did not mean that it was positively proven that the two drugs are equally effective, and the correct interpretation is that “there was no significant difference” or “it was not known whether there was an effect. So what should we do if we want to clarify that the effects of two drugs are equal?
In this issue, we will explain what kind of analysis should be performed to demonstrate equivalence.
How can we show equivalence?
Example: In a clinical trial in which new antipyretic drug Y and conventional drug X were assigned, the mean decreased body temperature before and after drug administration was 1.0°C for new drug Y and 0.7°C for conventional drug X.
Below are two clinical trials A (Table 1) and B (Table 2).
Both A and B had the same mean lower body temperature, p=1.00>0.05.
From this, the null hypothesis cannot be rejected in both cases, and it cannot be said that there is a difference between Y and X in the mean value of decreasing body temperature. Nor can we conclude from these results that Y and X are equivalent.
[Table1] Clinical Trial Results A
[Table2] Clinical Trial Results B
Equivalence cannot be ascertained by the p-value, but equivalence can be estimated using a confidence interval.
The confidence interval for A is -0.55 to 0.55.
The confidence interval for B is -0.09 to 0.09.
Even though the p-values are the same, the confidence interval is narrower for B than for A. Contrastingly, A is too wide to be considered equivalent to Y and X, while B is narrow enough to be considered equivalent.
If the confidence interval for B is as narrow as -0.09 to 0.09, and it can be judged that they can be considered clinically equivalent, then Y and X can be considered equivalent. However, the acceptable range of equivalence, the criterion for this judgment, must be determined before starting a research study and stated in the research protocol.
This acceptable range is called the “equivalence margin.”
[Figure] Confidence interval and equivalence margin
As shown in the figure, B is within the equivalence margin, so we can say that there is equivalence.
Therefore, when reading an article, we must look carefully at what the data indicate, the test method, the range of equivalence margins, and the n number (sample size).
Thus, when equivalence is indicated, both the upper and lower limits of the confidence interval must fall within the range of the equivalence margin. To achieve this, the n number (sample size) must be set before the test so that the confidence interval is quite small, and the test must be conducted with a sufficient n number. Therefore, non-inferiority testing is often used to solve this problem.
The Ministry of Health, Labour and Welfare (MHLW) has issued guidelines for bioequivalence studies that should be included in applications for generic drugs and other products. The guidelines specify in detail the test method, equivalence evaluation parameters, acceptable range of bioequivalence (equivalence margin), statistical analysis, how equivalence should be determined, etc. (Reference: Guidelines for Bioequivalence Studies of Generic Drugs).
In the next issue, we will discuss non-inferiority studies.
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