For Table 7.8, in fitting marginal models to describe main effects of race, gender, and substance type on whether a subject had used that substance, we find evidence of an interaction between gender and substance type. Using GEE with exchangeable working correlation, the estimated probability πˆ of using a particular substance satisfies logit(ˆπ) = − 0.57 + 1.93s1 + 0.86s2 + 0.38r − 0.20g + 0.37g × s1 + 0.22g × s2,

where r, g, s1, s2 are indicator variables for race (1 = white, 0 = nonwhite), gender (1 = female, 0 = male), and substance type (s1 = 1, s2 = 0 for alcohol; s1 = 0, s2 = 1 for cigarettes; s1 = s2 = 0 for marijuana). Show that:

a. The group with the highest estimated probability of use of marijuana is white males. What group is it for use of alcohol? cigarettes?

b. Given gender, the estimated odds a white subject used a given substance are 1.46 times the estimated odds for a nonwhite subject.

c. Given race, the estimated odds that a female used (alcohol, cigarettes, marijuana)
are (1.19, 1.02, 0.82) times the estimated odds for males.

d. Given race, the estimated odds that a female used (alcohol, cigarettes) are (9.97, 2.94) times the estimated odds she used marijuana.

e. Given race, the estimated odds that a male used (alcohol, cigarettes) are (6.89, 2.36) times the estimated odds he used marijuana.