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Application: This procedure is used to test the following hypotheses:
The test drug is concluded to be equivalent to the control in average if the null hypothesis is rejected at significance level α.
a) value of α, the probability of type I error
b) value of β, the probability of type II error
c) value of allowable difference
d) value of Population variance
e) value of δ>0, the equivalence limit.
Formula: <![if !vml]><![endif]> (*)
α: The probability of type I error is the Probability of rejecting the null hypothesis when null hypothesis is true. The null hypothesis is the two mean values are not equivalent.
β: The probability of type II error is the Probability of failing to reject the null hypothesis when null hypothesis is false.
δ: The largest change from the reference value (baseline) that is considered to be trivial.
μ2 – μ1: Value of allowable difference is the true mean difference between a test drug (μ2) and a placebo control or active control agent (μ1).
Example 1: Suppose the true difference is 1% (i.e., μ2–μ1=1%) and the equivalence limit is 5% (i.e., δ=0.05). Thus, by using (*), with the standard deviation is 10% (i.e., population variance is 0.01), the required sample size to achieve an 80% power (β=0.2) at α=0.05 for correctly detecting such difference of 0.05 change obtained by normal approximation as n=108.
Reference: Chow, Shao and Wang, Sample Size Calculations In