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