1 We thank Sander Greenland for his generosity, insight, and wisdom about the epidemiologic.pdf

Estimating Risk and Rate Levels, Ratios, and Differences in Case-Control Studies1 Gary King2 Langche Zeng3 May 5, 2001 1We thank Sander Greenland for his generosity, insight, and wisdom about the epidemiological literature, Norm Breslow and Ken Rothman for many helpful explanations, and Chuck Manski for his suggestions, provocative econometric work, and other discussions. Thanks also to Neal Beck, Rebecca Betensky, Josue? Guzma?n, Bryan Langholz, Meghan Murray, Adrain Raferty, Ted Thomp- son, Jon Wakefield, Clarice Weinberg, David Williamson for helpful discussions, Ethan Katz for research assistance, and Mike Tomz for spotting an error in an earlier version. Thanks to the National Science Foundation (IIS-9874747), the Centers for Disease Control and Prevention (Di- vision of Diabetes Translation), the National Institutes of Aging (P01 AG17625-01), the World Health Organization, and the Center for Basic Research in the Social Sciences for research sup- port. Software to implement the methods in this paper is available for Stata and for Gauss from http://GKing.Harvard.Edu. 2Department of Government, Harvard University and Global Programme on Evidence for Health Policy, World Health Organization (Center for Basic Research in the Social Sciences, 34 Kirkland Street, Harvard University, Cambridge MA 02138; http://GKing.Harvard.Edu, King@Harvard.Edu, (617) 495-2027). 3Department of Political Science, George Washington University, 2201 G Street NW, Washing- ton, DC 20052, lzeng@. Abstract Classic (or “cumulative”) case-control sampling designs do not admit inferences about quantities of interest other than risk ratios, and then only by making the rare events as- sumption. Probabilities, risk differences, and other quantities cannot be computed with- out knowledge of the population incidence fraction. Similarly, density (or “risk set”) case-control sampling designs do not allow inferences about quantities other than the rate ratio. Rates, rate differences, cumulative rates