Estimating the generalized impact fraction from case-control data

The generalized impact fraction (also called the generalized attributable fraction) was introduced by Waiter (1980, American Journal of Epidemiology 112, 409-416) and Morgenstern and Bursic (1982, Journal of Community Health 7, 292-309) is a measure that generalizes the population attributable fraction (attributable risk). It is defined as the fractional reduction of a disease resulting from changing the current distribution of a risk factor to some modified distribution. We show that the point and variance estimator derived by Greenland and Drescher (1993, Biometrics 49, 865-872) for fixed shift functions can be extended to situations where the shift is a probabilistic function of the actual exposure value. The formulas are applicable for case-control designs where the cases are simply randomly selected and the controls are chosen in one of three ways: simple random sampling, stratified random sampling, and frequency matching.