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

236 BRESLOW & DAY
equation. If such a judgement cannot be made, one must simply admit that precise
identification of the factor responsible for the effect is impossible. To quote from
Mosteller and Tukey (1977): "We must be prepared for one variable to serve as a
proxy for another and worry about the possible consequences, in particular, whether the
proxy's coefficient siphons off some of the coefficient we would like to have on the
proper variable, or whether a variable serves well only because it is a proxy. In either
case, interpretation of the regression coefficient requires very considerable care."
Much of the discussion in 5 3.4 on whether or not one should adjust for apparent confounding
variables is relevant here.
6.11 Transforming continuous risk variables
One of the more perplexing issues facing the analyst who uses quantitative regression
methods is the choice of appropriate scales on which to express continuous risk
variables. He must decide between original measurements, as recorded by machine or
interviewer, and such transforms as logs, square roots, reciprocals, or any number of
other possibilities. Since the object is to achieve a near-linear relationship between the
quantitative regression variable and log risk, it usually helps to make some plots of
relative risks for grouped data as we did in Figures 6.1 to 6.4. If the data are sufficiently
extensive, so that a regular pattern emerges, one can at least rule out some of the
possible choices on the grounds of lack of fit. For example it was fairly clear from both
graphical and quantitative analysis of the Ille-et-Vilaine data that the effects of alcohol
were best expressed on the original linear scale, while for tobacco a log transform was
required.
However epidemiological data are rarely sufficient to enable fine distinctions to be
made between rather similar functional forms for the dose-response relationship on
statistical grounds alone. Accurate measurements of human exposure to potential risk
factors are not often available. Hence recourse is made to animal experimentation for
elucidating fundamental aspects of the carcinogenic process. Such experiments allow
one to control fairly strictly the amounts of carcinogen administered to homogenous
subgroups of animals, and data derived from them are more amenable to precise quantitative
analysis than are data from observational studies of human populations.
Example: One animal model which has been used to suggest relationships for human epithelial tumours
is that of skin-painting experiments in mice. In an experiment reported by Lee and O'Neill (1971), mice
were randomly assigned to four dosage groups each containing 300 animals. Starting at about three weeks
of age, benzo[alpyrene (BP) was painted on their shaved backs in the following dosages:
Group 1 6pg BP/week
Group 2 12pg BP/week
Group 3 24 pg BP/week
Group 4 48pg BPlweek
The animals were examined regularly, and the week of tumour occurrence was taken to be the first week
that a skin tumour was observed. Age-specific incidence rates of skin tumours were estimated for each
dosage group according to the methods of § 2.1. The number of animals developing a skin tumour for the
first time during any one week was divided by the number still alive and free of skin tumours at the middle
of that week. Since few new tumours would arise in any given week, these age-specific estimates tended
to be highly unstable. Consequently, the four dosage groups were compared in terms of the age-specific
cumulative incidence rates (5 2.3).