3. general considerations for the analysis of case-control ... - IARC

98 BRESLOW & DAY
The confounding effects of C1 and C2 have been eliminated, and we can estimate the
independent association of E with disease. Methods for constructing summary estimates
of the relative risk associated with E, and summary significance tests, are given in the
next chapter. Continuous variables can be incorporated into this approach by dividing
up the scale of measurement and treating them as ordered categorical variables.
When the confounding variables take more than two levels, the criteria we discussed
for assessing when a dichotomous variable might confound an exposure/disease association
need to be slightly relaxed. For dichotomous variables, a factor confounds an
association if, and only if, it is associated both with disease and exposure. The "only if"
part of this criterion holds for all potentially confounding variables, but with polytomous
factors we can construct examples in which a factor is related both to disease and to exposure,
but does not confound the disease-exposure association (Whittemore, 1978).
There also needs to be some modification of criteria for assessing confounding when
more than one confounding variable is present. In the following example, from Fisher
and Patil (1974), we have two confounding variables, C1 and C2. Neither one alone
confounds the association of E with disease, but the two jointly do confound the association.
Stratifying by each of the two possible confounders, in turn, we have:
Stratification by C1
Stratification by C2
No stratifi- Factor Cl+ Factor Cl- Factor C2+ Factor C2-
cation
Exposure E Exposure E Exposure E Exposure E Exposure E
+ - + - + - + - + -
Case
Control
Odds ratio 2.2 2.2 2.2 2.2
Case
But, when we stratify by both confounders jointly we have:
Joint stratification by C1 and C2
Factor Factor Factor Factor
C, + C2+ C, + C2- C1-C2+ C1-C2-
Exposure E Exposure E Exposure E Exposure E
+ - + - + - + -
Control
Odds ratio