The "numerical method" in medicine goes back to Pierre Louis' study of pneumonia (1835), and John Snow's book on the epidemiology of cholera (1855). Snow took advantage of natural experiments and used convergent lines of evidence to demonstrate that cholera is a waterborne infectious disease. More recently, investigators in the social and life sciences have used statistical models and significance tests to deduce cause-and-effect relationships from patterns of association; an early example is Yule's study on the causes of poverty (1899). In my view, this modeling enterprise has not been successful. Investigators tend to neglect the difficulties in establishing causal relations, and the mathematical complexities obscure rather than clarify the assumptions on which the analysis is based.

Formal statistical inference is, by its nature, conditional. If maintained hypotheses A, B, C, ... hold, then H can be tested against the data. However, if A, B, C, ... remain in doubt, so must inferences about H. Careful scrutiny of maintained hypotheses should therefore be a critical part of empirical work--a principle honored more often in the breach than the observance. Snow' work on cholera will be contrasted with modern studies that depend on statistical models and tests of significance. The examples may help to clarify the limits of current statistical techniques for making causal inferences from patterns of association.

Cancer clusters present analytic problems of their own. There are many routes of exposure, and many forms of pathology. Distinguishing between real associations and patterns created by chance may be especially difficult in that context. Epidemiology has made enormous contributions to the control of disease, but remains an inexact science where judgment matters more than statistical technique. There is ample room for differences of opinion.