Introductory Biostatistics

tigators hope to increase this to at least 70% using intravesical chemotherapy
(treatment by drug) immediately after surgery at the time of cystoscopy. This
alternative hypothesis is equivalent to a hypothesized hazards ratio of

y¼

lnð 0 : 5 Þ

lnð 0 : 7 Þ

¼ 1 : 94

Suppose also that we decide to preseta¼ 0 :05 (two-sided) and want the power
to be about 90% (i.e.,b¼ 0 :10). In other words, we use

z 1 a¼ 1 : 96

z 1 b¼ 1 : 28

From this information, the required total sample size is

d¼ðz 1 aþz 1 bÞ^2

1 þy

1 y

 2

¼ð 1 : 96 þ 1 : 28 Þ^2

1 þ 1 : 94

1  1 : 94

 2

¼103 events

N¼

2 d

2 P 1 P 2

¼

ð 2 Þð 103 Þ

2  0 : 5  0 : 7

¼258 patients;129 in each group

Example 12.13 In the example above, suppose that the study was under-
enrolled and was actually conducted with only 200 patients, 100 randomized to
each of the two treatment arms. Then we have

d¼

ðNÞð 2 P 1 P 2 Þ

2

¼80 events

ðz 1 aþz 1 bÞ^2 ¼

d

½ð 1 þyÞ=ð 1 yފ^2

¼ 8 : 178

z 1 b¼

ffiffiffiffiffiffiffiffiffiffiffi

8 : 178

p

 1 : 96

¼ 0 : 90

corresponding to a power of approximately 84%.

468 STUDY DESIGNS