Introductory Biostatistics

leading to the required minimum sample size:

n¼

ð 1 : 96 Þ^2 pð 1 pÞ

d^2

(rounded up to the next integer). This required sample size is a¤ected by three
factors:

1. The degree of confidence (i.e., 95% which yields the coe‰cient 1.96)


2. The maximum tolerated error or upper bound for the margin of error,d,
   determined by the investigator(s)


3. The proportionpitself

This third factor is unsettling. To findnso as to obtain an accurate value of
the proportion, we need the proportion itself. There is no perfect, exact solution
for this. Usually, we can use information from similar studies, past studies, or
studies on similar populations. If no good prior knowledge about the propor-
tion is available, we can replacepð 1 pÞby 0.25 and use a conservative sample
size estimate:

nmax¼

ð 1 : 96 Þ^2 ð 0 : 25 Þ

d^2

becausenmaxbnregardless of the value ofp. Most phase II trials are small;
investigators often set the maximum tolerated error or upper bound for the
margin of error,d, at 10% (0.10) or 15%; some even set it at 20%.

Example 12.1 If we set the maximum tolerated errordat 10%, the required
minimum sample size is

nmax¼

ð 1 : 96 Þ^2 ð 0 : 25 Þ

ð 0 : 1 Þ^2

or 97 patients, which is usually too high for a small phase II trial, especially in
the field of cancer research, where very few patients are available. If we set the
maximum tolerated errordat 15%, the required minimum sample size is

nmax¼

ð 1 : 96 Þ^2 ð 0 : 25 Þ

ð 0 : 15 Þ^2

or 43 patients.

The same method for sample size determination as above applies to surveys
as well, except that for surveys we can a¤ord to use much larger sample sizes.

452 STUDY DESIGNS