Harvard University - Department of Goverment & Center for Basic Research in the Social Sciences
We address a disagreement between epidemiologists and econometricians (and also among several camps within the medical, epidemiological, and public health literatures) about inference from the simplest type of case-control samples. To estimate the conditional probability of disease, the relative risk, or the risk difference in these data, some assumption about the population fraction of "cases" is necessary. This population fraction is assumed to be effectively zero by epidemiologists and known exactly, but not necessarily zero, by econometricians. Since the population fraction is usually not known exactly, more recent econometric literature assumes complete ignorance. Methods based on this ignorance assumption produce bounds on the quantities of interest that, unfortunately, are often wide and always encompass a conclusion of no treatment effect (relative risks of one or risk differences of zero) no matter how strong the true effect is. We simplify the existing bounds for risk differences, making them easier to estimate, and then suggest a resolution of the disagreement by providing a method that allows researchers to include easily available information (e.g., that the fraction of cases in the population falls within [.2,.3]); this method avoids unrealistic assumptions and considerably narrows the bounds and hence confidence intervals on all quantities of interest. We also offer public-domain software for all methods introduced, and discuss implications for reporting standards in applied research.