Different disease rates in two populations: how much is due to differences in risk factors?

Two populations with different disease rates may differ in their risk factors for the disease. If so, it is desirable to know what proportion of the disease excess in the high-risk population is attributable to its greater exposure to the risk factors. This proportion has been called the relative attributable risk (RAR). A related measure is the adjusted relative risk (ARR), defined as the ratio of rates in high-risk to low-risk populations that would be observed if the distribution of risk factors in the high-risk population equalled that of the low-risk population. We present methods for obtaining consistent estimates and asymptotic confidence intervals for both the RAR and the ARR using data from case-control studies in the two populations. The methods are applied to the problem of estimating the differences in ovarian cancer incidence between U.S. white women (high-risk) and U.S. black women (low-risk) attributable to differences in reproductive risk factors. Simulations show that the methods perform well; however, when the true RAR is close to 0 or 1 or when sample sizes are small, RAR estimates may fall outside the unit interval. We discuss circumstances when the true RAR lies outside the unit interval; in such circumstances the ARR is easier to interpret.