Gary King and Langche Zeng. "Inference
in Case-Control Studies," in Shein-Chung Chow, ed.,
Encyclopedia of Biopharmaceutical Statistics, 2nd
edition. New York: Marcel Dekker, 2004, copy at http://gking.harvard.edu/files/abs/1s-enc-abs.shtml. (Article: PDF)
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 assumption. Probabilities, risk differences, and other quantities
cannot be computed without 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, risks, and other quantities cannot be estimated unless auxiliary information
about the underlying cohort such as the number of controls in each full risk set
is available. Most scholars who have considered the issue recommend reporting
more than just the relative risks and rates, but auxiliary population information
needed to do this is not usually available. We address this problem by developing
methods that allow valid inferences about all relevant quantities of interest
from either type of case-control study when completely ignorant of or only partially
knowledgeable about relevant auxiliary population information.
This is a somewhat revised and extended version of Gary King and Langche Zeng.
2002. "Estimating Risk and Rate Levels, Ratios, and Differences in Case-Control
Studies," Statistics in Medicine, 21: 1409-1427. (Article:
PDF | Abstract: HTML) You may also be interested in our
related work in other fields, such as in international relations, Gary King
and Langche Zeng. "Explaining Rare Events in International Relations," International
Organization, 55, 3 (Spring, 2001): 693-715, and in political methodology,
Gary King and Langche Zeng, (Article: PDF | Abstract:
HTML). "Logistic Regression in Rare
Events Data," Political Analysis, Vol. 9, No. 2, (Spring, 2001): Pp.
137--63. (Article: PDF | Abstract:
HTML). Also see related research.
Software that implements the ideas in this paper is also
available. (Software:
Stata, Zelig and R)