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

GENERAL CONSIDERATIONS 11 1
confined to those first employed before 1930. Changes in the operation of the refinery
at that time could, quite plausibly, have removed the carcinogenic agents, and the
change in risk assists in identifying what those agents may have been.
3.6 Modelling risk
The use of stratification and cross-tabulation to investigate the joint effect on risk
of two variables, in terms of how the two factors mutually confound each other and
interact, is reasonably straightforward. However, even with two variables, as the number
of values each variable can take increases, the control of confounding by means of
stratification can lead to substantial losses of information, and tests for interaction will
lack power. As the complexity of the problem increases, the approach via stratification
becomes not only unwieldy but increasingly wasteful of information. The different
effects associated with different levels of a variable will not normally be unrelated, and
can be expected to change smoothly. For example, for a quantitative variable, risk will
usually vary in a manner which can be described by a simple family of curves. It would
be rare to need more than second degree terms, after perhaps some initial transformation
of the scale.
Similarly, interactive effects between several variables will not normally vary in a
structureless way, and general experience has been that most situations are well described
by some simple structure of the interactions. These considerations lead to the
use of regression methods, in which the risk associated with each variable is expressed
as some explicit function, and interaction effects are described in terms of the specific
parameters of interest. Chapters 6 and 7 are devoted to the development of these
methods, which will not be further discussed here except to outline briefly their advantages.
These can be summarized as follows:
1. One can study the joint effect of several exposures simultaneously. The stratification
approach we considered earlier places the emphasis on one specific exposure.
Study of the combined risk associated with several exposures is an important complement
of the single exposure analysis.
2. When the number of levels of the confounding variables increases, one can remove
their effect as fully as by fine stratification but with less loss of information.
3. One can test for specific interaction effects of interest with the considerable increase
in power this provides. One also obtains a parametric description of the interaction.
4. The risk associated with different levels of a quantitative variable can be expressed
in simple and descriptive terms.
In studies where controls are individually matched to cases, these advantages are
accentuated, as Chapters 5 and 7 make apparent. But regression methods should not
replace analyses based on cross-tabulation, rather they should complement and extend
them, as we illustrate in Chapter 6.
3.7 Comparisons between more than two groups
So far, we have considered methods of analysis appropriate for comparisons between
one case group and one control group. Situations occur, however, when comparisons
among more than two groups are required. One may want to test whether the relative