Statistical Science

From association to causation: some remarks on the history of statistics

David Freedman

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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.

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Statist. Sci., Volume 14, Number 3 (1999), 243-258.

First available in Project Euclid: 24 December 2001

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Association causation regression history of statistics modeling significance epidemiology


Freedman, David. From association to causation: some remarks on the history of statistics. Statist. Sci. 14 (1999), no. 3, 243--258. doi:10.1214/ss/1009212409.

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  • Abbott, A. (1997). Of time and space: the contemporary relevance of the Chicago school. Social Forces 75 1149-1182. Alberts, B., Bray, D., Lewis, J., Raff, M., Roberts, K. and
  • Watson, J. D. (1994). Molecular Biology of the Cell, 3rd ed. Garland, New York.
  • American Cancer Society (1997). Cancer Facts & Figures1997. American Cancer Society, Atlanta, GA.
  • Angrist, J. D., Imbens, G. W. and Rubin, D. B. (1996). Identification of causal effects using instrumental variables. J. Amer. Statist. Assoc. 91 444-472. Aurelian, L., Schumann, B., Marcus, R. L. and Davis, H. J.
  • (1973). Antibody to HSV-2 induced tumor specific antigens in serums from patients with with cervical carcinoma. Science 181 161-164.
  • Berkson, J. (1955). The statistical study of association between smoking and lung cancer. Proceedings of the Mayo Clinic 30 319-348.
  • Blau, P. M. and Duncan, O. D. (1967). The American Occupational Structure Chapter 5. Wiley, New York.
  • Breslow, N. and Day, N. E. (1980). Statistical Methods in Cancer Research 1. Sci. Publ. 32, International Agency for Research on Cancer, Lyon. (Distributed by Oxford Univ. Press.)
  • Breslow, N. and Day, N. E. (1987). Statistical Methods in Cancer Research 2. Sci. Publ. 82, International Agency for Research on Cancer, Lyon. (Distributed by Oxford Univ. Press.)
  • Bross, I. D. J. (1960). Statistical criticism. Cancer 13 394-400.
  • Buck, C., Llopis, A., N´ajera, E. and Terris, M., eds. (1989). The Challenge of Epidemiology: Issues and Selected Readings. Sci. Publ. 505, World Health Organization, Geneva.
  • Cannistra, S. A. and Niloff, J. M. (1996). Cancer of the uterine cervix. New England Journal of Medicine 334 1030-1038.
  • Carmelli, D. and Page, W. F. (1996). Twenty-four year mortality in World War II US male veteran twins discordant for cigarette smoking. Internat. J. Epidemiology 25 554-559.
  • Carpenter, K. J. (1981). Pellagra. Academic Press, New York.
  • Colwell, R. R. (1996). Global climate and infectious disease: the cholera paradigm. Science 274 2025-2031.
  • Cook, D. (1980). Smoking and lung cancer. R. A. Fisher, An Appreciation. Lecture Notes in Statist. 1 182-191. Springer, New York.
  • Copas, J. B. and Li, H. G. (1997). Inference for non-random samples. J. Roy. Statist. Soc. Ser. B 59 55-77.
  • Cornfield, J. (1951). A method for estimating comparative rates from clinical data. Applications to cancer of the lung, breast and cervix. Journal of the National Cancer Institute 11 1269- 1275. Cornfield, J., Haenszel, W., Hammond, E. C., Lilienfeld,
  • A. M., Shimkin, M. B. and Wynder, E. L. (1959). Smoking and lung cancer: recent evidence and a discussion of some questions. Journal of the National Cancer Institute 22 173-203.
  • Cox, D. (1977). The role of significance tests. Scand. J. Statist. 4 49-70.
  • Desrosi eres, A. (1993). La Politique des Grands Nombres: Histoire de la Raison Statistique. Editions La D´ecouverte, Paris. [English translation by C. Naish (1998) The Politics of Large Numbers: A History of Statistical Reasoning. Harvard Univ. Press.]
  • Dickersin, K. (1997). How important is publication bias? A synthesis of available data. AIDS Education and Prevention Suppl. A 9 15-21.
  • Dijkstra, T. K., ed. (1988). On Model Uncertainty and Its Statistical Implications. Lecture Notes in Econom. and Math. Systems 307 Springer, New York.
  • Doll, R. (1987). Major epidemics of the 20th century: from coronary thrombosis to AIDS. J. Roy. Statist. Soc. Ser. A 150 373-395.
  • Doll, R., Evans, H. J. and Darby, S. C. (1994). Paternal exposure not to blame. Nature 367 678-680.
  • Doll, R. and Hill, A. B. (1950). Smoking and carcinoma of the lung: preliminary report. British Medical Journal ii 739- 748.
  • Doll, R. and Hill, A. B. (1952). A study of the aetiology of carcinoma of the lung. British Medical Journal ii 1271-86.
  • Doll, R. and Hill, A. B. (1954). The mortality of doctors in relation to their smoking habit: a preliminary report. British Medical Journal i 1451-1455.
  • Dubos, R. (1988). Pasteur and Modern Science. Springer, New York.
  • Ehrenberg, A. S. C. and Bound, J. A. (1993). Predictability and prediction (with discussion). J. Roy. Statist. Soc. Ser. A 156 (Part 2) 167-206.
  • Evans, A. S. (1993). Causation and Disease: A Chronological Journey. Plenum, New York.
  • Evans, R. J. (1987). Death in Hamburg: Society and Politics in the Cholera Years. Oxford Univ. Press.
  • Finlay, B. B., Heffron, F. and Fialkow, S. (1989). Epithelial cell surfaces induce Salmonella proteins required for bacterial adherence and invasion. Science 243 940-942.
  • Fisher, R. A. (1959). Smoking: The Cancer Controversy. Oliver and Boyd, Edinburgh.
  • Freedman, D. (1983). A note on screening regression equations. Amer. Statist. 37 152-155.
  • Freedman, D. (1987). As others see us: a case study in path analysis. Journal of Educational Statistics 12 101-223.
  • Freedman, D. (1991). Statistical models and shoe leather. In Sociological Methodology (P. Marsden, ed.) American Sociological Association, Washington, DC.
  • Freedman, D. (1995). Some issues in the foundation of statistics. Foundations of Science 1 19-83.
  • Freedman, D. (1997). From association to causation via regression. Adv. in Appl. Math. 18 59-110.
  • Freedman, D., Gold, L. S. and Lin, T. H. (1996). Concordance between rats and mice in bioassays for carcinogenesis. Journal of Regulatory Toxicology and Pharmacology 23 225-232.
  • Freedman, D. and Navidi, W. (1989). On the multistage model for carcinogenesis. Environmental Health Perspectives 81 169-188.
  • Freedman, D. and Navidi, W. (1990). Ex-smokers and the multistage model for lung cancer. Epidemiology 1 21-29.
  • Freedman, D., Pisani, R. and Purves, R. (1997). Statistics, 3rd ed. Norton, New York.
  • Freedman, D. and Zeisel, H. (1988). From mouse to man: the quantitative assessment of cancer risks (with discussion). Statist. Sci. 3 3-56.
  • Friedman, M. (1953). Essays in Positive Economics. Univ. Chicago Press.
  • Gagnon, F. (1950). Contribution to the study of the etiology and prevention of cancer of the cervix. American Journal of Obstetrics and Gynecology 60 516-522.
  • Gail, M. H. (1996). Statistics in action. J. Amer. Statist. Assoc. 433 1-13.
  • Gamble, J. F. (1998). PM25 and mortality in long-term prospective cohort studies: cause-effect or statistical associations? Environmental Health Perspectives 106 535-549.
  • Gardner, M. J. (1992). Leukemia in children and paternal radiation exposure at the Sellafield nuclear site. Monographs of the National Cancer Institute 12 133-135. Gardner, M. J., Snee, M. P., Hall, A. J., Powell, C. A., Downes,
  • S. and Terrell, J. D. (1990). Results of case-control study of leukaemia and lymphoma among young people near Sellafield nuclear plant in West Cumbria. British Medical Journal 300 423-433. [Erratum (1992) 305 715; and see letter (1991) 302 907.]
  • Gauss, C. F. (1809). Theoria Motus Corporum Coelestium. Perthes et Besser, Hamburg. [Reprinted (1963) by Dover, New York.]
  • Gavarret, J. (1840). Principes G´en´eraux de Statistique M´edicale, ou, D´eveloppement des R egles Qui Doivent Pr´esider a Son Emploi. Bechet jeune et Labe, Paris.
  • Goldthorpe, J. H. (1998). Causation, statistics and sociology. Twenty-ninth Geary Lecture, Nuffield College, Oxford. (Published by Economic and Social Research Institute, Dublin, Ireland.)
  • Greenland, S., Pearl, J. and Robins, J. M. (1999). Causal diagrams for epidemiologic research. Epidemiology, 10 37-48. Hakama, M., Lehtinen, M., Knekt, P., Aromaa, A., Leinikki, P., Miettinen, A., Paavonen, J., Peto, R. and Teppo,
  • L. (1993). Serum antibodies and subsequent cervical neoplasms: A prospective study with 12 years of followup. American Journal of Epidemiology 137 166-170.
  • Hodges, J. L. and Lehmann, E. L. (1964). Basic Concepts of Probability and Statistics. Holden-Day, San Francisco.
  • Holland, P. (1988). Causal inference, path analysis, and recursive structural equations models. In Sociological Methodology (C. Clogg, ed.) Blackwell, Oxford.
  • Howard-Jones, N. (1975). The Scientific Background of the International Sanitary Conferences 1851-1938. World Health Organization, Geneva.
  • Humphreys, P. and Freedman, D. (1996). The grand leap. British J. Philos. Sci. 47 113-123.
  • Humphreys, P. and Freedman, D. (1999). Are there algorithms that discover causal structure? Synth ese. To appear.
  • IARC (1986). Tobacco Smoking. Monograph 38, International Agency for Research on Cancer, Lyon. (Distributed by Oxford Univ. Press.) Kanarek, M. S., Conforti, P. M., Jackson, L. A., Cooper, R. C.
  • and Murchio, J. C. (1980). Asbestos in drinking water and cancer incidence in the San Francisco Bay Area. American Journal of Epidemiology 112 54-72.
  • Kaprio, J. and Koskenvuo, M. (1989). Twins, smoking and mortality: a 12-year prospective study of smoking-discordant twin pairs. Social Science and Medicine 29 1083-1089.
  • Kinlen, L. J. and John, S. M. (1994). Wartime evacuation and mortality from childhood leukaemia in England and Wales in 1945-9. British Medical Journal 309 1197-1201.
  • Lang, J. M., Rothman, K. J. and Cann, C. I. (1998). That confounded P-value. Epidemiology 9 7-8.
  • Legendre, A. M. (1805). Nouvelles M´ethodes pour la D´etermination des Orbites des Com etes. Courcier, Paris. [Reprinted (1959) Dover, New York.]
  • Lieberson, S. (1985). Making it Count. Univ. California Press, Berkeley.
  • Liu, T. C. (1960). Under-identification, structural estimation, and forecasting. Econometrica 28 855-865.
  • Lombard, H. L. and Doering, C. R. (1928). Cancer studies in Massachusetts: habits, characteristics and environment of individuals with and without lung cancer. New England Journal of Medicine 198 481-487.
  • Louis, P. (1835). Recherches sur les Effets de la Saign´ee dans Quelques Maladies Inflammatoires: Et sur l'Action de l' ´Em´etique et des V´esicatoires dans la Pneumonie. Bailli ere, Paris. [Reprinted (1986) The Classics of Medicine Library, Birmingham, AL.]
  • Lucas, R. E. Jr. (1976). Econometric policy evaluation: a critique (with discussion). In The Phillips Curve and Labor Markets (K. Brunner and A. Melzer, eds.) Carnegie-Rochester Conferences on Public Policy (Supplementary series to the Journal of Monetary Economics) 19-64. North-Holland, Amsterdam.
  • Manski, C. F. (1995). Identification Problems in the Social Sciences. Harvard Univ. Press.
  • McKim, V. and Turner, S., eds. (1997). Causality in Crisis? Proceedings of the Notre Dame Conference on Causality. Notre Dame Press.
  • Mill, J. S. (1843). A System of Logic, Ratiocinative and Inductive, 8th ed. Parker, London. [Reprinted (1965) Longman, Green, London. See especially Book III, Chapter VIII. Reprinted (1974) Univ. Toronto Press.]
  • Miller, J. F., Mekalanos, J. J. and Fialkow, S. (1989). Coordinate regulation and sensory transduction in the control of bacterial virulence. Science 243 916-922.
  • M ¨uller, F. H. (1939). Tabakmissbrauch und Lungcarcinom. Zeitschrift f ¨ur Krebsforsuch 49 57-84.
  • National Research Council (1997). Possible Health Effects of Exposure to Residential Electric and Magnetic Fields. National Academy of Science, Washington, DC.
  • Neyman, J. (1923). Sur les applications de la th´eorie des probabilit´es aux experiences agricoles: essai des principes. Roczniki Nauk Rolniczki 10 1-51. [In Polish. English translation by D. Dabrowska and T. Speed, Statist. Sci. 5 (1990) 463-480.]
  • Ottenbacher, K. J. (1998). Quantitative evaluation of multiplicity in epidemiology and public health research. American Journal of Epidemiology 147 615-619. Paneth, N., Vinten-Johansen, P., Brody, H. and Rip, M.
  • (1998). A rivalry of foulness: official and unofficial investigations of the London cholera epidemic of 1854. American Journal of Public Health 88 1545-1553.
  • Pasteur, L. (1878). La Th´eorie des Germes et Ses Applications a la M´edecine et a la Chirurgie, Lecture Faite a l'Academie de M´edecine le 30 Avril 1878, par M. Pasteur en Son Nom et au Nom de MM. Joubert et Chamberland. G. Masson, Paris.
  • Pearl, J. (1995). Causal diagrams for empirical research. Biometrika 82 689-709.
  • Perneger, T. V. (1998). What's wrong with Bonferroni adjustments. British Medical Journal 316 1236-1238.
  • Pope, C. A., Schwartz, J. and Ransom, M. R. (1992). Daily mortality and PM10 pollution in Utah Valley. Archives of Environmental Health 47 211-217.
  • Quetelet, A. (1835). Sur l'Homme et le D´eveloppement de Ses Facult´es, ou Essai de Physique Sociale. Bachelier, Paris
  • Raufman, J. P. (1998). Cholera. American Journal of Medicine 104 386-394.
  • Robinson, W. S. (1950). Ecological correlations and the behavior of individuals. American Sociological Review 15 351-357.
  • Røjel, J. (1953). The Interrelation between Uterine Cancer and Syphilis. Copenhagen.
  • Rosenberg, C. E. (1962). The Cholera Years. Chicago Univ. Press.
  • Rothman, K. J. (1990). No adjustments are needed for multiple comparisons. Epidemiology 1 43-46.
  • Rothman, K. J. (1996). Lessons from John Graunt. The Lancet 347 37-39.
  • Rothman, K. J. and Greenland, S., eds. (1998). Modern Epidemiology, 2nd ed. Lippincott-Raven.
  • Rubin, D. (1974). Estimating causal effects of treatments in randomized and nonrandomized studies. Journal of Educational Psychology 66 688-701.
  • Scharfstein, D. O., Rotnitzky, A. and Robins, J. M. (1999). Adjusting for non-ignorable drop-out using semiparametric non-response models. J. Amer. Statist. Assoc. To appear.
  • Semmelweiss, I. (1867). The Etiology, Concept, and Prophylaxis of Childbed Fever. [Translated (1983) by K. C. Carter, Univ. Wisconsin Press.]
  • Snow, J. (1855). On the Mode of Communication of Cholera. Churchill, London. [Reprinted (1965) by Hafner, New York.]
  • Stigler, S. M. (1986). The History of Statistics. Harvard Univ. Press.
  • Stolley, P. (1991). When genius errs. American Journal of Epidemiology 133 416-425. Storey, A., Thomas, M., Kalita, A., Harwood, C., Gardiol, D., Mantovani, F., Breuer, J., Leigh, I. M., Matlashewski, G.
  • and Banks, L. (1998). Role of a p53 polymorphism in the development of human papillomavirus-associated cancer. Nature 393 229-234. Styer, P., McMillan, N., Gao, F., Davis, J. and Sacks, J.
  • (1995). Effect of outdoor airborne particulate matter on daily death counts. Environmental Health Perspectives 103 490- 497.
  • Taubes, G. (1995). Epidemiology faces its limits. Science 269 164-169. [Letters, (8 Sep 1995), 1325-1328.]
  • Taubes, G. (1998). The (political) science of salt. Science 281 898-907.
  • Terris, M., ed. (1964). Goldberger on Pellagra. Louisiana State Univ. Press.
  • Vandenbroucke, J. P. and Pardoel, V. P. (1989). An autopsy of epidemiologic methods: the case of "poppers" in the early epidemic of the acquired immunodeficiency syndrome (AIDS). American Journal of Epidemiology 129 455-457. (Also see comments.)
  • Wald, N. and Nicolaides-Bouman, A., eds. (1991). UK Smoking Statistics, 2nd ed. Oxford Univ. Press.
  • Winkelstein, W. (1995). A new perspective on John Snow's communicable disease theory. American Journal of Epidemiology (Suppl.) 142 3-9.
  • Wynder, E. L. and Graham, E. A. (1950). Tobacco smoking as a possible etiological factor in bronchogenic carcinoma: a study of six hundred and eighty-four proved cases. Journal of the American Medical Association 143 329-336. Wynder, E. L., Cornfield, J., Schroff, P. D. and Doraiswami,
  • K. R. (1954). A study of environmental factors in carcinoma of the cervix. American Journal of Obstetrics and Gynecology 68 1016-1052.
  • Yule, G. U. (1899). An investigation into the causes of changes in pauperism in England, chiefly during the last two intercensal decades. J. Roy. Statist. Soc. 62 249-295.