Abstract: The problem of drawing causal inferences from retrospective case-control studies is considered. A model for causal inference in prospective studies is reviewed and then applied to retrospective studies. The limitations of case-control studies are formulated in terms of the level of causally relevant parameters that can be estimated in such studies. An example using data from a large retrospective study of coffee-drinking and myocardial infarctions is used to illustrate the ideas of the article.

Philosophical discussions of causality often emphasize the meaning of causation. Scientists are usually concerned with understanding causal mechanisms. Purely statistical discussions of causality are substantially more limited in scope, because the unique contribution of statistics is to the measuring of causal effects and not to the understanding of causal mechanisms or to the meaning of causation. This distinction is sometimes expressed as “statistics can establish correlation, but not causation.” We feel our emphasis on measurement is more appropriate, because it focuses on what statistical theory can contribute to discussions of causality. Measuring causal effects accurately without any understanding whatsoever of the causal mechanisms involved or of the meaning of causation is not only possible but is, of course, a commonplace experience of everyday life; that is, people are quite capable of using automobiles, ovens, calculators, and typewriters safely and effectively without any knowledge of how these devices work. Of course, careful measurements of causal effects often lead to a better understanding of the causal mechanisms involved.