It can be seen that the proportion of smokers among the cases (71.7%) was
higher than that for the controls (37.7%) and the di¤erence is highly statistically
significant (p< 0 :001).
6.4 MANTEL–HAENSZEL METHOD
We are often interested only in investigating the relationship between two
binary variables (e.g., a disease and an exposure); however, we have to control
for confounders. A confounding variable is a variable that may be associated
with either the disease or exposure or both. For example, in Example 1.2, a
case–control study was undertaken to investigate the relationship between lung
cancer and employment in shipyards during World War II among male resi-
dents of coastal Georgia. In this case, smoking is a confounder; it has been
found to be associated with lung cancer and it may be associated with em-
ployment because construction workers are likely to be smokers. Specifically,
we want to know:
Among smokers, whether or not shipbuilding and lung cancer are related
Among nonsmokers, whether or not shipbuilding and lung cancer are
relatedThe underlying question is the question concerning conditional indepen-
dence between lung cancer and shipbuilding; however, we do not want to reach
separate conclusions, one at each level of smoking. Assuming that the con-
founder, smoking, is not an e¤ect modifier (i.e., smoking does not alter the
relationship between lung cancer and shipbuilding), we want to pool data for a
combined decision. When both the disease and the exposure are binary, a pop-
ular method to achieve this task is the Mantel–Haenszel method. The process
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 frequencies as shown in Table
6.8.
TABLE 6.8
Disease ClassificationExposure þTotal
þ ab r 1
cd r 2
Total c 1 c 2 n
218 COMPARISON OF POPULATION PROPORTIONS