**Help Aids** Top

**Application:
**This procedure is used when the test object (i.e.,
drug) is concluded to be equivalent to a gold standard on average under an
acceptable superiority margin. The following hypotheses are usually considered:.

**When δ>0,
the rejection of the null hypothesis indicates superiority over the reference value.
**

**When δ<0, the rejection of the null hypothesis implies non-inferiority against the
reference value.
**

**Procedure**:

- Enter

a)
value
of ** α**,
the probability of type I error

b)
value
of ** β**,
the probability of type II error

c)**
**value of

d) value of *population
variance*

e)
value
of ** δ**>0,
the superiority margin or value of

- Click the button “Calculate” to obtain result sample size N.

**Formula:
**_{}** (*)**

**Notations:**

**α****:** The
probability of type I error (significance level) is the *probability of rejecting the true null
hypothesis. *

**β****:** The
probability of type II error (1 – power of the test) is the *probability of
failing to reject the false null hypothesis.*

**δ****:** Clinically meaningful difference. The largest *change from the reference value (baseline) that is considered to be trivial.
*

**μ – μ _{0}:**
The value of

**Examples**

**Example 1: **A pharmaceutical company
is studying for prevention of progression from osteopenia to osteoporosis they wish to show that the mean
bone density post-treatment is no less than pre-treatment by a clinically
meaningful (i.e., reduce AMBD) difference ** δ=-0.5 **to test non-inferiority. The difference of mean bone density between
before and after treatment is expected to be

**Reference**: Chow, Shao and Wang, *Sample Size Calculations In
Clinical Research*,