Table 4.9, based on a study with British doctors conducted by R. Doll and A. B. Hill, was analyzed by N. R. Breslow in A Celebration of Statistics, A. C. Atkinson and S. E. Fienberg, eds. (Berlin: Springer-Verlag, 1985).

a. For each age, compute the sample coronary death rates per 1000 person- years, for nonsmokers and smokers. To compare them, take their ratio and describe its dependence on age.

b. Fit a main-effects model for the log rates having four parameters for age and one for smoking. In discussing lack of fit, show that this model assumes a constant ratio of nonsmokers' to smokers' coronary death rates over levels of age.

c. Based on (a), explain why it is sensible to add a quantitative interaction of age and smoking. Assign scores to the levels of age, and add a term based on the product of age and smoking. For this model, show that the log of the ratio of coronary death rates changes linearly with age. Fit the model, and interpret.

Table 4.9 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 5,710 28,612 28 206 65-74 2,585 12,663 28 186 1,462 75-84 Source: R. Doll and A. B. Hill, Natl. Cancer Inst. Monogr., 19: 205-268 (1966). 5,317 31 102