Introductory Biostatistics

Example 12.11 A new vaccine will be tested in which subjects are to be
randomized into two groups of equal size: a control (unimmunized) group and
an experimental (immunized) group. Based on prior knowledge about the vac-
cine through small pilot studies, the following assumptions are made:

1. The infection of the control group (when challenged by a certain type of
   bacteria) is expected to be about 50%:

p 2 ¼ 0 : 50

2. About 80% of the experimental group is expected to develop adequate
   antibodies (i.e., at least a twofold increase). If antibodies are inadequate,
   the infection rate is about the same as for a control subject. But if an
   experimental subject has adequate antibodies, the vaccine is expected to
   be about 85% e¤ective (which corresponds to a 15% infection rate against
   the challenged bacteria).

Putting these assumptions together, we obtain an expected value ofp 1 :

p 1 ¼ð 0 : 80 Þð 0 : 15 Þþð 0 : 20 Þð 0 : 50 Þ

¼ 0 : 22

Suppose also that we decide to preseta¼ 0 :05 and want the power to be about
95% (i.e.,b¼ 0 :05). In other words, we use

z 1 a¼ 1 : 96

z 1 b¼ 1 : 65

From this information, the total sample size required is

N¼ð 4 Þð 1 : 96 þ 1 : 65 Þ^2

ð 0 : 36 Þð 0 : 64 Þ

ð 0 : 50  0 : 22 Þ^2

F 154

so that each group will have 77 subjects. In this solution we use

p¼ 0 : 36

the average of 22% and 50%.

12.9.3 Survival Time as the Endpoint

When patients’ survivorship is considered as the endpoint of a trial, the prob-
lem may look similar to that of comparing two proportions. For example, one
can focus on a conventional time span, say five years, and compare the two

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