86 CHAPTER 6 Hypothesis Testingway to do the test is to construct a two - sided confi dence interval for
the mean difference, and if δ lies outside the interval, you reject non-
equivalence. To ensure that the two one - sided tests each have level α ,
you must choose a symmetric 100(1 − 2 α ) % confi dence interval. This
is a little counterintuitive, because for example, it is a 90% confi dence
interval that is used to construct a test at the 5% signifi cance level.
However, this is right, because we must reject both t - tests to claim
equivalence.
6.11.3 Noninferiority Tests
Noninferiority is a one - sided test that a new treatment is not clinically
signifi cantly worse than a particular established treatment. Signifi cantly
worse is defi ned by a chosen δ just as was needed to demonstrate
equivalence.
Steps in Noninferiority Testing
- Select a clinically important difference δ.
- State as the null hypothesis H 0 : d ≥ δ , where d = M n − M s , and
M n is the mean for the new treatment, and M s is the mean for
the old one. Then the alternative hypothesis H 1 is that d < δ. - Choose a signifi cance level α.
- Determine the critical value for the appropriate test.
- Calculate the test statistic (d or a scaled version of it).
- Reject H 0 if the test statistic exceeds the critical value.
6.12 REPEATED MEASURES ANALYSIS OF
VARIANCE AND LONGITUDINAL DATA ANALYSIS
In clinical trials, measurements are taken on key variables at several
patient visits to the site. If a change from baseline at the end of the trial
is all that is of interest, conventional analysis of variance (ANOVA) or
covariance can be used. However, if one is interested in how the results
change over several visit (i.e., are interested in trends), then the multiple
measurements on the same subject at different time points introduces
correlations that conventional methods do not account for. When we