Introductory Biostatistics

The Mantel–Haenszel estimate for the odds ratio is

dORMH¼

ð 4 Þð 4 Þþð 3 Þð 17 Þþð 2 Þð 11 Þþð 1 Þð 9 Þ

ð 1 Þð 6 Þþð 2 Þð 3 Þþð 3 Þð 1 Þþð 4 Þð 1 Þ

¼ 5 : 16

When the number of controls matched to a case,M, is variable (due pri-
marily to missing data), the test for exposure e¤ects should incorporate data
from all strata:

w^2 ES¼

f

P

M

PM

m¼ 1 ½n^1 ;m^1 mnm=ðMþ^1 ފg

2

P

M

PM

m¼ 1 ðmnmðMmþ^1 Þ=ðMþ^1 ÞÞ

The corresponding Mantel–Haenszel estimate for the odds ratio is

dORMH¼

P

M

P

ðMmþ 1 Þn 1 ;m 1

P

M

P

mn 0 ;m

Example 11.9 Refer to the data on endometrial cancer in Table 11.11; due to
missing data, we have some cases matching to four controls and some matching
to three controls. In addition to 4:1 matching, we have 3:1 matching (Table
11.12). With the inclusion of the four sets having three matched controls, the
result becomes

TABLE 11.12

Number of Exposed Persons in Each Matched Set

Case 1 2 3

Exposed 1 3 0
Unexposed 0 0 0

Total 1 3 0

TABLE 11.11

Number of Exposed Persons in Each Matched Set

Case 1 2 3 4

Exposed 4 17 11 9
Unexposed 6 3 1 1

Total 10 20 12 10

412 ANALYSIS OF SURVIVAL DATA