Now Playing: Non-Inferiority Tests for the Difference Between Two Proportions (3:20)
A study is being designed to establish the non-inferiority of a new treatment compared to the current treatment. Historically, the current treatment has enjoyed a 63% cure rate. The new treatment substantially reduces the seriousness of certain side effects that occur with the current treatment. Thus, the new treatment will be adopted even if it is slightly less effective than the current treatment. The researchers will recommend adoption of the new treatment if it has a cure rate that is 5% lower than the current treatment, or higher.
When the data has been obtained, the researchers plan to use the Unpooled Z-test to analyze the data. They want to estimate the sample size needed to achieve 90% power when the actual cure rate of the new treatment ranges from 60% to 70%. Alpha will be 0.025.
The sample size plot shows that the sample size decreases dramatically as the assumed cure rate of the new treatment increases.
The researchers then wish to see the effect if the current treatment cure rate is different from 63%.
The plot shows that the change in sample size is minor.
Users sometimes ask about the power calculation method, which shouldn’t be confused with the assumed test type. The choice for the power calculation method is only concerned with how the power is calculated, not the test statistic that will be used.
When Binomial Enumeration is selected for the power calculation method, the power is computed using binomial enumeration of all possible outcomes. Binomial enumeration of all outcomes is possible because the responses are discrete 0’s and 1’s.
When Normal Approximation is chosen, approximate power is computed using the normal approximation to the binomial distribution.
When the sample sizes are reasonably large (maybe greater than 50) and the proportions are between 0.2 and 0.8, the two methods will give similar results. For smaller sample sizes and more extreme proportions, the normal approximation is not as accurate, so the binomial calculations may be more appropriate.