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

136 BRESLOW & DAY
and variance of
and
with fitted frequencies
A(vu) = A(8.07) = 107.48
and variance of
It is instructive to verify that the empirical odds ratios calculated from the fitted frequencies satisfy
and
respectively. The actual range of possible values for a is max(0,205-775) to min(200,205), i.e., (0,200).
This is much broader than the intervals including two standard deviations on both sides of the fitted
means 84.22 + 2qm = (72.7, 95.7) and 107.48 k 2 m 0 = (96.3, 118.7). Hence there is little doubt
about the accuracy of the normal approximation for these data.
4.4 Combination of results from a series of 2 x 2 tables; control of confounding
The previous two sections dealt with a special situation which rarely occurs in practice.
We have devoted so much attention to it in order to introduce, in a simplified setting,
the basic concepts needed to solve more realistic problems, such as those posed by the
presence of nuisance or confounding factors. Historically one of the most important
methods for control of confounding has been to divide the sample into a series of
strata which were internally homogeneous with respect to the confounding factors.
Separate relative risks calculated within each stratum are free of bias arising from
confounding (5 3.4).
In such situations one first needs to know whether the association between exposure
and disease is reasonably constant from stratum to stratum. If so, a summary measure
of relative risk is required together with associated confidence intervals and tests of
significance. If not, it is important to describe how the relative risk varies according
to changes in the levels of the factors used for stratum formation. In this chapter we
emphasize the calculation of summary measures of relative risk and tests of the
hypothesis that it remains constant from stratum to stratum. Statistical models which