Introduction to Power and Sample Size Analysis: Equivalence and Noninferiority

Equivalence and Noninferiority

Whereas the standard two-sided hypothesis test for a parameter $\text{[math]}$ (such as a mean difference) aims to demonstrate that it is significantly different than a null value $\text{[math]}$ :

	$\text{[math]}$	$\text{[math]}$
	$\text{[math]}$	$\text{[math]}$

an equivalence test instead aims to demonstrate that it is significantly similar to some value, expressed in terms of a range $\text{[math]}$ around that value:

	$\text{[math]}$	$\text{[math]}$
	$\text{[math]}$	$\text{[math]}$

Whereas the standard one-sided hypothesis test for $\text{[math]}$ (say, the upper one-sided test) aims to demonstrate that it is significantly greater than $\text{[math]}$ :

	$\text{[math]}$	$\text{[math]}$
	$\text{[math]}$	$\text{[math]}$

a corresponding noninferiority test aims to demonstrate that it is not significantly less than $\text{[math]}$ , expressed in terms of a margin $\text{[math]}$ :

	$\text{[math]}$	$\text{[math]}$
	$\text{[math]}$	$\text{[math]}$

Corresponding forms of these hypotheses with the inequalities reversed apply to lower one-sided noninferiority tests (sometimes called nonsuperiority tests).

The POWER procedure performs power analyses for equivalence tests for one-sample, paired, and two-sample tests of normal and lognormal mean differences and ratios. It also supports noninferiority tests for a variety of analyses of means, proportions, and correlation, both directly (with a MARGIN= option representing $\text{[math]}$ ) and indirectly (with an option for a custom null value representing the sum or difference of $\text{[math]}$ and $\text{[math]}$ ).