Introductory Biostatistics

We can set the maximum tolerated error at a very low level, resulting in very
short confidence intervals.

Example 12.2 Suppose that a study is to be conducted to estimate the smok-
ing rate among N.O.W. (National Organization for Women) members. Sup-
pose also that we want to estimate this proportion to within 3% (i.e.,d¼ 0 :03)
with 95% confidence.

(a) Since the current smoking rate among women in general is about 27%

(0.27), we can use this figure in calculating the required sample size. This

results in

n¼

ð 1 : 96 Þ^2 ð 0 : 27 Þð 0 : 73 Þ

ð 0 : 03 Þ^2

¼ 841 : 3

or a sample of size 842 is needed.

(b) If we do not want or have the figure of 27%, we still can conservatively

take

nmax¼

ð 1 : 96 Þ^2 ð 0 : 25 Þ

ð 0 : 03 Þ^2

¼ 1067 : 1

(i.e., we can sample 1068 members of N.O.W.). Note that this con-

servative sample size is adequate regardless of the true valuepof the

unknown population proportion; values ofnandnmaxare closer whenp

is near 0.5.

12.5 SAMPLE SIZES FOR OTHER PHASE II TRIALS

As pointed out in previous sections, most phase II trials are single-arm studies
where we are seeking the antitumor activitity of a drug measured by response
rate. But there are also a variety of other phase II trials.
Some phase II trials are randomized comparative studies. These are most
likely to be cases where we have established activity for a given drug (from a
previous one-arm nonrandomized trial) and wish to add another drug to that
regimen. In these randomized phase II trials, the goal is toselectthebetter
treatment (the sample sizes for these phase II trials are covered in Section 12.7).
Some phase II trials deal with assessing the activity of a biologic agent where
tumor response is not the main endpoint of interest. We may be attempting to

SAMPLE SIZES FOR OTHER PHASE II TRIALS 453