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.
"From association to causation: some remarks on the history of statistics." Statist. Sci. 14 (3) 243 - 258, August 1999. https://doi.org/10.1214/ss/1009212409