(a) Among smokers, whether or not shipbuilding and lung cancer are
related
(b) Among nonsmokers, whether or not shipbuilding and lung cancer are
relatedIn fact, the original data were tabulated separately for three smoking levels
(nonsmoking, moderate smoking, and heavy smoking); in Example 1.2, the last
two tables were combined and presented together for simplicity. Assuming that
the confounder, smoking, is not an e¤ect modifier (i.e., smoking does not alter
the relationship between lung cancer and shipbuilding), however, we do not
want to reach separate conclusions, one at each level of smoking. In those
cases, we want to pool data for a combined decision. When both the disease
and the exposure are binary, a popular method used to achieve this task is the
Mantel–Haenszel method. This method provides one single estimate for the
common odds ratio and can be summarized as follows:
- We form 22 tables, one at each level of the confounder.
- At a level of the confounder, we have the data listed in Table 1.17.
Since we assume that the confounder is not an e¤ect modifier, the odds ratio
is constant across its levels. The odds ratio at each level is estimated byad=bc;
the Mantel–Haenszel procedure pools data across levels of the confounder to
obtain a combined estimate (some kind of weighted average of level-specific
odds ratios):
ORMH¼
P
ad=n
P
bc=nExample 1.18 A case–control study was conducted to identify reasons for the
exceptionally high rate of lung cancer among male residents of coastal Georgia
as first presented in Example 1.2. The primary risk factor under investigation
was employment in shipyards during World War II, and data are tabulated
separately for three levels of smoking (Table 1.18).
There are three 22 tables, one for each level of smoking. We begin with
the 22 table for nonsmokers (Table 1.19). We have for the nonsmokers
TABLE 1.17
Disease ClassificationExposure þTotal
þ ab r 1
cd r 2
Total c 1 c 2 n
RATIOS 27