For the nonmelanoma skin cancer data considered in this chapter, consider the following additional model that was fit to these data:
Model 5: In λij = a + 0 In Ti + βE + δE(In Ti)
where Ti{is defined as
Ti = [Midpoint of the ith age interval] – 15/i = 1, 2,..., 8
and E denotes city (1 = Dallas-Ft. Worth, 0 = Minneapolis-St. Paul).
a. Using the available edited computer output, calculate the estimated rate ratio comparing the two cities for the following two age-groups:
(i) 15-24
(ii) 45-54.
(For the 15-24 age-group, Ti, = 1/7; for the 45-54 age-group, Ti = 1.)
b. What do your results in part (a) suggest about interaction?
c. Carry out both a Wald test and an LR test for the significance of the coefficient of the product term E(In Tj). [To carry out the LR test, use the deviance statistic D(β) given in Table 24.3 for model 4].
d. Do the results from part (c) support the conclusion that the product term E(In Ti)) needs to remain in the model?
e. Are the tests conducted in part (c) equivalent to testing whether either model 4 or model 5 fits the data?
f. Which model appears to be the best model among models 3, 4, and 5? Briefly justify any answer.