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Sample Size Calculation using StudySize 1.0. Non-inferiority
for proportions A clinical trial is planned to compare the effect of a new treatment with the existing treatment. The plan is to show that the new treatment is clinically at least as good as the existing. Since the new treatment is thought to have fewer adverse events, it is considered sufficient to show that the true percentage of patients responding to the new treatment is not less than 5% compared to the old one. From previous experience one knows that the percentage of responders with the existing treatment is approximately 60%. The study will be a randomized double blind parallel group study with equal number of patients in the two groups. The objective is to conclude that the true percentage of responders with the new treatment is at most 5% less than for the existing. Thus the difference in percentage of responders, the new treatment minus the existing treatment, should be greater than - 5%. If this is the case, the new treatment is considered as non-inferior to the existing treatment with respect to the percentage of responders. The intention is to perform a one-sided test based on the binomial distribution and conclude that the new treatment is non-inferior if the calculated one-sided p-value is less than 0.05 (significance level), i.e. a statistical significant result. Moreover, if the true difference between the new treatment and the old treatment is exactly 0%, then the test should give a p-value less than 0.05 with a probability of 0.80. In other words, we should conclude non-inferiority with a probability of 0.80 (power). Since we want to conclude that the difference in responders, new treatment minus existing treatment, is greater than - 5%, we choose as the null hypothesis H0: the true difference in proportions is less than or equal to - 0.05 and the alternative hypothesis H1: the true difference in proportions is greater than - 0.05. The null hypothesis is rejected if the calculated difference in proportions is large enough. The sample size calculation is performed as follows;
Choose the option
button One-sided, and among the Interchangeable Parameters options Prop.
2 - Prop. 1 and Size 2 / Size 1, and press OK.
Assume that the
number of patients is considered too many and therefore a discussion
has been initiated if it might be possible to choose a lower limit for
non-inferiority than the proposed - 0.05. Moreover, one also thinks
that the power perhaps should be higher than 0.80. Hence, we would like
to see how the value of the difference in proportions under H0 varies
for different values of the sample size and power. The previous options
for the binomial distribution will show up. Set the parameter values shown below and press OK
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