Page 199 - 20dynamics of cancer

184 CHAPTER 9

I discuss two alternative formulations. First, most prior explanations
fit the observations by positing that carcinogens in smoke affect only one
or two stages in progression, leaving the other stages mostly unaffected.
Second, I show that the standard multistage model of progression
also fits the observations very well. Previous authors rejected that stan-
dard model because they used the common approximation for incidence
given by Armitage and Doll (1954), which in fact does not apply well to
the problem of carcinogen exposure followed by cessation.

CARCINOGENS AFFECT SOME STAGES BUT NOT OTHERS
This idea was stated most clearly and perhaps originally by Armitage
in the published discussion following Doll (1971). I quote from Armitage
at length, because his words set the line of thinking that has dominated
the subject. Note that, at the time, the dose-response curve was thought
to be linear. Later work suggested that the response may in fact fit a
curve that rises with the square of dose (Doll and Peto 1978). Here is
what Armitage said:
The dose-response relationship seems to be linear, which suggests
that the carcinogen affects the rate of occurrence of critical events
at one stage, and one only, in the induction period. (If it affected
two stages, one might have expected a quadratic relationship, and
so on.) Does this crucial event happen early or late in the induction
period? For example, in a six-stage process, are we thinking of an
early stage, the first or second, or a late stage, the fifth or sixth?
The evidence here seems to conflict. One argument would sug-
gest that a very early stage is involved. I am thinking of the de-
lay of a generation or so between the increase in smoking in men
around the First World War, and the rise in lung cancer mortality
rates which was so marked 20 or 30 years later; and similarly the
increase in cigarette smoking among women about the time of the
Second World War, and the rise in lung cancer rates for females
which has become so noticeable in the last few years. This long
delay is what one would expect if a very early part of the process
were involved rather than a very recent one.
On the other hand, the halt in the rise in risk quite soon after
smoking stops suggests that a late stage is involved. Professor
Doll’s very ingenious treatment of the data on ex-smokers, in Tables
13 and 14, confirms the latter view. In a multi-stage process, if the
first stage were involved, the rate after stopping smoking would
continue to rise in the same way as for continuing smokers. If,