ingful maximum tolerated error for estimation of the coe‰cient of correlation.
Instead of controlling the width of a desired confidence interval, the sample size
determination ia approached in terms of controlling the risk of making a type
II error. The decision is concerned with testing a null hypothesis,
H 0 :r¼ 0
against an alternative hypothesis,
HA:r¼rA
in whichrAis the investigator’s hypothesized value for the coe‰cient of corre-
lationrof interest. With a given level of significancea(usually, 0.05) and a
desired statistical power (1b;bis the size of type II error associated with the
alternativeHA), the required sample size is given by
ffiffiffiffiffiffiffiffiffiffiffi
n 3
p
FðrAÞ¼z 1 aþz 1 b
where
FðrÞ¼
1
2
ln
1 þr
1 r
The transformation fromrtoFðrÞis often referred to asFisher’s transforma-
tion, the same transformation used in forming confidence intervals in Chapter
- Obviously, to detect a true correlationrAgreater than 0.5, a small sample
size would su‰ce, which is suitable in the context of phase II trials.
Example 12.3 Suppose that we decide to preseta¼ 0 :05. To design a study
such that its power to detect a true correlationrA¼ 0 :6 is 90% (orb¼ 0 :10),
we would need only
FðrAÞ¼
1
2
ln
1 þrA
1 rA
¼
1
2
ln
1 : 6
0 : 4
¼ 0 : 693
ffiffiffiffiffiffiffiffiffiffiffi
n 3
p
FðrAÞ¼z 1 aþz 1 b
ffiffiffiffiffiffiffiffiffiffiffi
n 3
p
ð 0 : 693 Þ¼ 1 : 96 þ 1 : 28
orn¼25 subjects.
SAMPLE SIZES FOR OTHER PHASE II TRIALS 455