Understanding the Fundamentals of Epidemiology an evolving text

Age standardized lung cancer rates by smoking and asbestos exposure
(per 100,000 person years)
Smokers Nonsmokers
Exposed to asbestos 602 58
Not exposed to asbestos 123 11
When we calculate the disease rates that correspond to each of the four causal pathways in the lower
configuration of causal "pies" above, the two leftmost pathways have the same rates as in the upper
configuration. The rate corresponding to the rightmost pathway (Asbestos|{B3}) is 58-11 =
47/100,000 py. The rate that corresponds to the third causal pathway (Smk|Asb|{B2}) is now
reduced since some of cases with both exposures could be due to the effect of asbestos. So the rate
that corresponds to the third pathway is now (602-112-11-47)/100,000 py = 410/100,000 py.
We might take these rates and reason as follows:
Increase due to smoking 123 - 11 = 112
Increase due to asbestos 58 - 11 = 47
Total increase expected due to both 112 + 47 = 159
Total observed increase 602 - 11 = 591 !
Since the increase due to the combined effect greatly exceeds that expected from our (additive)
model, we would conclude that the effect is synergistic.
Alternatively, we might reason in relative terms:
Relative increase due to smoking 123 / 11 = 11.2
Relative increase due to asbestos 58 / 11 = 5.3
Total increase expected due to both 11.2 x 5.3 = 59.4
Total observed increase 602 / 11 = 54.7
This time the observed increase and that expected from our (multiplicative) model are quite close, so
we conclude that there is no effect modification. We are thus faced with a situation where the
decision about effect modification depends upon what model we employ to arrive at an expected
joint effect to compare with the observed joint effect (or equivalently, upon the scale of
measurement, hence the term "effect measure modification").
Before pondering this dilemma further, we should first state the additive and multiplicative models
explicitly. To do so we introduce a notation in which "1" indicates presence of a factor, a "0"
indicates absence of a factor, the first subscript represents the first risk factor, and the second
subscript represents the second risk factor (see below).
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www.epidemiolog.net, © Victor J. Schoenbach 12. Multicausality: Effect modification - 399
rev. 11/5/2000, 11/9/2000, 5/11/2001