Introductory Biostatistics

statistic,

z¼

n 10 n 01

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

n 10 þn 01

p

is compared to percentiles of the standard normal distribution. The corre-
sponding two-tailed procedure based on

X^2 ¼

ðn 10 n 01 Þ^2

n 10 þn 01

is often called McNemar’s chi-square test (1 df) (introduced in Section 6.2). It
is interesting to note that if we treat a matched pair as a group or a level of a
confounder, and present the data in the form of a 22 table (Table 11.8), the
Mantel–Haenszel method of Section 1.3.4 would yield the same estimate for
the odds ratio:

dORMH¼

dOROR

¼

n 10

n 01

As for the task of forming a 95% confidence interval, an alternative to the
preceding formula is first to estimate the odds ratio on a log scale with esti-
mated variance

VarVardðlogðdORORÞÞ¼^1

n 10

þ

1

n 01

leading to a 95% confidence interval of

n 10

n 01

exp G 1 : 96

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

1

n 10

þ

1

n 01

!s

Example 11.7 In a study of endometrial cancer in which the investigators
identified 63 cases occurring in a retirement community near Los Angeles,

TABLE 11.8

Disease Classification

Exposure Cases Controls Total

Yes ai bi aiþbi
No ci di ciþdi

Total 1 1 2

408 ANALYSIS OF SURVIVAL DATA