The “numerical method” in medicine goes back to Pierre
Louis’ 1835 study of pneumonia and John Snow’s 1855 book on the
epidemiology of cholera. 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
causeandeffect relationships from patterns of association; an
early example is Yule's 1899 study on the causes of poverty. 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’s 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.