Introductory Biostatistics

a¼ 0 : 05 !z 1 a¼ 1 : 96 ðtwo-sided testÞ

b¼ 0 : 10 !z 1 b¼ 1 : 28

The number of discordant pairs is given by

P¼

y

1 þy

¼ 0 : 80

m¼

½ðz 1 a= 2 Þþz 1 b

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

Pð 1 PÞ

p

Š^2

ðP 0 : 5 Þ^2

¼

½ð 1 : 96 = 2 Þþ 1 : 28

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

ð 0 : 80 Þð 0 : 20 Þ

p

Š^2

0 : 302

F 25

M¼

m

p 0 ð 1 p 1 Þþp 1 ð 1 p 0 Þ

¼

38

ð 0 : 4 Þð 0 : 2627 Þþð 0 : 7373 Þð 0 : 6 Þ

F 46

that is pairs, 46 cases and 46 matching controls.

12.10.3 Unmatched Designs for a Continuous Exposure

When the risk factor under investigation in a case–control study is measured
on a continuous scale, the problem is similar to that of a phase III trial where
we want to compare two population means as seen in Section 12.7.1. Recall
that in a comparison of two population means,m 1 versusm 2 , the required min-
imum total sample size is calculated from

N¼ 4 ðz 1 aþz 1 bÞ^2

s^2

d^2

assuming that we conduct a balanced study with each group consisting of
n¼N=2 subjects. Besides the level of significanceaand the desired power
ð 1 bÞ, this required total sample size is a¤ected by the variances^2 of the
population and the quantity

d¼jm 1 m 0 j

which is the magnitude of the di¤erence betweenm 1 , the mean for the cases,
andm 0 , the mean for the controls, that is deemed to be important. To put it in a

SAMPLE SIZE DETERMINATION FOR CASE–CONTROL STUDIES 473