smoked one pack per day from age 18 to 45 and was moderately exposed to other people’s cigarette smoke lies between 520 and 2,030 per 100,000.
The first method for estimating the true relative risk relies on two assumptions:
The excess relative risk in a nonsmoker is proportional to the lifetime dose of ETS. That is, if an individual’s dose of ETS (at all ages) were doubled, his excess relative risk would be doubled.
At every age, “exposed” subjects have been exposed to ETS at a rate 3 times that of “unexposed” subjects. A factor of 3 was selected to reflect the empirical observation that the concentration of cotinine in the urine of nonsmokers with smoking spouses is about 3 times that of nonsmokers without smoking spouses (Wald and Ritchie, 1984).
These two assumptions imply that the excess (true) relative risk in “exposed” individuals is 3 times that of “unexposed” individuals. Hence, in the absence of bias, the summary rate ratio of 1.3 equals the ratio of the true relative risk in “exposed” individuals to that in “unexposed” individuals. Therefore,
where x and 3x are the excess true relative risks in “unexposed” and “exposed” individuals, respectively. Solving for x gives x= 0.18 and, thus, the true relative risk in “exposed” and “unexposed” individuals of 1.54 and 1.18, respectively. If we used the summary rate ratio of 1.14 from only the U.S. studies (see Chapter 12), we estimate the true relative risk in “exposed” and “unexposed” individuals to be 1.23 and 1.08, respectively.
It is likely that the second assumption above may be inappropriate (see Remark 4 in the Technical Discussion). For instance, it is unlikely that the ETS exposure in childhood is 3 times greater in subjects who later married smokers, i.e., “exposed” subjects, than in subjects who later married nonsmokers, i.e., “unexposed” subjects. If it is not appropriate, then another approach is necessary. This approach is outlined in Method 2, which follows.