Introductory Biostatistics

The result turns out to be, quite simply,

dORMH¼

P

ðMmþ 1 Þn 1 ;m 1

P

mn 0 ;m

and the Mantel–Haenszel estimate has been used widely in the analysis of
case–control studies with multiple matching.

11.6.3 Testing for Exposure E¤ect

From the same likelihood function as seen above, a test for

H 0 :OR¼ 1

was derived and is given by:

w^2 ES¼

f

PM

m¼ 1 ½n^1 ;m^1 mnm=ðMþ^1 ފg

2

½ 1 =ðMþ 1 Þ^2 Š

PM

m¼ 1 mnmðMmþ^1 Þ

a chi-square test with 1 degree of freedom.

Example 11.8 In a study on endometrial cancer, the investigators identified 63
cases of endometrial cancer occurring in a retirement community near Los
Angeles, California from 1971 to 1975. Each diseased person was matched with
R¼4 controls who were alive and living in the community at the time the case
was diagnosed, who were born within one year of the case, who had the same
marital status, and who had entered the community at approximately the same
time. The risk factor was previous use of estrogen (yes/no), and the data in
Example 11.7 involve only the first-found matched control. We are now able to
analyze the complete data set by 4:1 matching (Table 11.11). Using these 52
sets with four matched controls, we have

w^2 ES

¼

ð 25 Þf½ 4 ð 1  10 Þ= 5 Šþ½ 17 ð 2  20 Þ= 5 Šþ½ 11 ð 3  12 Þ= 5 Šþ½ 9 ð 4  10 Þ= 5 Šg^2

ð 1  10  4 Þþð 2  20  3 Þþð 3  12  2 Þþð 4  10  1 Þ

¼ 22 : 95

TABLE 11.10

Disease Classification

Exposure Cases Controls Total

Yes abaþb
No cdcþd

Total 1 MMþ 1

MULTIPLE MATCHING 411