per unit dose.* Further, the risk for a truly unexposed nonsmoker, i.e., γ0(t,s), is assumed to be the same for men and women. This assumption is supported, in part, by the results given in Chapter 12 and, in part, by earlier studies of Garfinkel (1981) and Friedman et al. (1984). Doll (1984), however, gives different risks for men and women of lung cancer mortality in nonsmokers.
If dE is actual dose in the “exposed” persons and dN is the actual dose in persons who believe themselves to be “unexposed,” then we have, from Equation 1:
The relative risk for a person identified as “exposed” compared to a person identified as “unexposed” [RR(dE)] is given by Equation 2A divided by 2B:
which, from Chapter 12, is 1.34, the relative risk estimated from the epidemiologic studies.
From the studies that measured cotinine in “exposed” and “unexposed” persons, we assume that the operative dose level, dE, among “exposed” individuals is 3 times as high as the dose level in the self-reported “unexposed” persons, dN, and that the ratio of 3:1 is proportional to a lifetime dose difference. Therefore, Equation 3 may be rewritten as:
Equation 4 can be solved for βdN, which is the increase in risk for persons called “unexposed,” but who, in fact, have been exposed
Work by Doll and Peto (1978) shows that the relative risk for direct smokers increases as a linear-quadratic function of dose, rather than the simple linear form shown here. A more sophisticated model would take into account the several stages at which cigarette smoke operates in the multistage development of cancer. At low doses the linear-quadratic is well approximated by the linear, i.e., 1+β1d+β2d2 is close to 1+βd because the d2 term approaches zero.