Table 3.9, based on a study with British doctors conducted by R. Doll and A. Bradford Hill, was analyzed by N. R. Breslow in A Celebration of Statistics, Berlin: Springer, 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. Specify a main-effects Poisson model for the log rates having four parameters for age and one for smoking. Explain why this model assumes a constant ratio of nonsmokers’ to smokers’ coronary death rates over levels of age. Based on (a), would you expect this model to be appropriate?
c. Based on (a), explain why it is sensible to add a quantitative interaction of age and smoking. Specify this model, and show that the log of the ratio of coronary death rates changes linearly with age.
d. Fit the model in (b). Assign scores to the levels of age for a product interaction term between age and smoking, and fit the model in (c). Compare the fits by comparing the deviances. Interpret.