Multicausality: Confounding - Assignment solutions

1. a. Reserpine is a risk factor. Overall, the incidence of breast cancer is 10.47 per 100,000 women-years in reserpine users and 6.14 per 100,000 women-years in nonusers. Moreover, among the non-obese, the rate ratio is: 6.40/4.10 = 1.6. Looking in the non-obese women avoids potential confounding by obesity if it is a risk factor. b. Obesity is also a risk factor. The overall incidence rates for obese and non-obese women, respectively, are 8.72/100,000 women-years and 4.22/100,000 women-years. Among the women who did not take reserpine, the rate ratio is 8.30/4.10 = 2.0. Looking in the group of reserpine non-users avoids potential confounding by reserpine. c. Reserpine use is associated with obesity, though that fact cannot be deduced from the stratum-specific breast cancer rates alone. The direct approach is to remember that the crude rates are weighted averages of stratum-specific rates, with the weights consisting of the population prevalence of the risk factors. So: where P RO is the prevalence of reserpine use in obese subjects, and _ P RO is the prevalence of reserpine use in nonobese subjects. _ Solving these two equations gives P RO = 0.1 and P RO = 0.05, so reserpine use is more prevalent in obese women (presumably because they are more likely to have hypertension). The relative prevalence is 2.0; the odds ratio of association between obesity and reserpine use is [(.1)(.95)]/[(.9)(.05)] = 2.1. Such an association might be characterized as "moderate." Note that the above procedure involving weighted averages can be equally well carried out on the basis of the column rates, rather than the row rates. The odds ratio will be effectively the same. d. The association between reserpine and breast cancer is not attributable to obesity (in the data for this problem). The most relevant rates to demonstrate that the association is not