Table 7.6 is based on a study involving British doctors.

Table 7.6 Data for Exercise 7.36 on Coronary Death Rates Person-Years Coronary Deaths Age Nonsmokers Smokers Nonsmokers Smokers 35–44 18,793 52,407 2 32 45–54 10,673 43,248 12 104 55–64 5710 28,612 28 206 65–74 2585 12,663 28 186 75–84 1462 5317 31 102 Source: Doll R. and A. Bradford Hill. 1966. Natl. Cancer Inst. Monogr. 19: 205–268.

a. Fit a main-effects model for the log rates using age and smoking as factors.

In discussing lack of fit, show that this model assumes a constant ratio of nonsmokers’ to smokers’ coronary death rates over age, and evaluate how the sample ratio depends on age.

b. Explain why it is sensible to add a quantitative interaction of age and smoking. For this model, show that the log ratio of coronary death rates changes linearly with age. Assign scores to age, fit the model, and interpret.