Table 4.18 shows estimated effects for a fitted logistic regression model with squamous cell esophageal cancer (1 = yes, 0 = no) as the response variable Y . Smoking status (S) equals 1 for at least one pack per day and 0 otherwise, alcohol consumption (A) equals the average number of alcoholic drinks consumed per day, and race (R) equals 1 for blacks and 0 for whites.

a. To describe the race-by-smoking interaction, construct the prediction equation when R = 1 and again when R = 0. Find the fittedYS conditional odds ratio for each case. Similarly, construct the prediction equation when S = 1 and again when S = 0. Find the fitted YR conditional odds ratio for each case. Note that, for each association, the coefficient of the cross-product term is the difference between the log odds ratios at the two fixed levels for the other variable.

b. In Table 4.18, explain what the coefficients of R and S represent, for the coding as given above. What hypotheses do the P-values refer to for these variables?

c. Suppose the model also contained an A × R interaction term, with coefficient 0.04. In the prediction equation, show that this represents the difference between the effect of A for blacks and for whites.