I present an overview of two methods controversies that are central to analysis and inference: That surrounding causal modeling as reflected in the “causal inference” movement, and that surrounding null bias in statistical methods as applied to causal questions. Human factors have expanded what might otherwise have been narrow technical discussions into broad philosophical debates. There seem to be misconceptions about the requirements and capabilities of formal methods, especially in notions that certain assumptions or models (such as potential-outcome models) are necessary or sufficient for valid inference. I argue that, once these misconceptions are removed, most elements of the opposing views can be reconciled. The chief problem of causal inference then becomes one of how to teach sound use of formal methods (such as causal modeling, statistical inference, and sensitivity analysis), and how to apply them without generating the overconfidence and misinterpretations that have ruined so many statistical practices.
This is a preview of subscription content, access via your institution.
Buy single article
Instant access to the full article PDF.
Tax calculation will be finalised during checkout.
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
Tax calculation will be finalised during checkout.
The same comment may well apply to physical sciences, but those are far outside my scope.
In these papers, “identification” has its strict statistical meaning of estimability rather than its more recent epidemiologic meaning of qualitative identification, as in Schwartz et al. (2016) and VanderWeele (2016).
Apart from invertible equation systems, which do not exist in realistic models for health and social phenomena.
In a common notation, knowing the treatment indicator X is positively associated with the outcome indicator Y0 under X=0 yet unassociated with the observed outcome Yobs leads us to infer that Y1 > Y0 for some observed unit.
In terms of potential outcomes Yx indexed by drug dose x, we would infer that the unobserved variable Y40 is sometimes greater than Y0 even though Pr(X=40) = 0.
In notation: With Yx the potential outcome and Yobs its measurement, we can have Yobs ≠ Yx yet still infer that Y1 ≠ Y0 for some unit.
Adding confusion, the term ‘consistency' is already well established for unrelated concepts such as estimator convergence and freedom from contradiction.
Even more startling is that temporality (cause preceding effect) is not necessary in some counterfactual accounts of causation (Price 1996).
In logic this syntactical structure is called a theory, and the interpretations that follow that structure are called models of the theory. I instead call this structure a model, which I think more in line with common usage in statistics and applied sciences.
This fact is one way of seeing why quantum physics has defied classical causal explanations: Robins et al. (2015) show that potential-outcome models obey Bell’s inequality, whose observed violations conflict with local definiteness (local realism, local hidden variables) and local causal diagrams (Gill 2014).
Notably, similar concerns about untestable mathematical theory arise in hard sciences like physics (Ellis and Silk 2014).
When in addition to the causal graph we can assume faithfulness (open paths imply association), the number of logically possible structures is reduced drastically – to the point that a certain limited type of conditional causal identification can be enabled (Spirtes et al. 2001; Robins et al. 2003).
One measure of the evidence against a model (whether causal or not) supplied by the P-value p from a test of its fit is the binary information or surprisal −log2(p).
The retrolental-fibroplasia controversy provides one such case study (Greenland 1991).
Aalen OO, Røysland K, Gran JM, Kouyos R, Lange T. Can we believe the DAGs? A comment on the relationship between causal DAGs and mechanisms. Stat Meth Med Res. 2016;25(5):2294–314.
Altman DG, Machin D, Bryant TN, Gardner MJ, editors. Statistics with Confidence. 2nd ed. London: BMJ Books; 2000.
Baggerly K, Gunsalus CK. Penalty too light. Cancer Letter. 2015;41(42):1–9.
Bancroft TW, Han CP. Inference based on conditional specification. Int Stat Rev. 1977;45:117–28.
Belluz J, Plumer B, Resnick B. The 7 biggest problems facing science, according to 270 scientists. Vox, September 7, 2016, accessed Oct. 16, 2016 from http://www.vox.com/2016/7/14/12016710/science-challeges-research-funding-peer-review-process
Box GEP. Sampling and Bayes inference in scientific modeling and robustness. J R Stat Soc Ser A. 1980;143:383–430.
Box GEP. Comment. Statist Sci. 1990;5:448–9.
Breslow NE. Are statistical contributions to medicine undervalued? Biometrics. 2003;59(1):1–8.
Broadbent A, Vandenbroucke JP, Pearce N. Authors’ Reply to: VanderWeele et al., Chiolero, and Schooling et al. (letter). Int J Epidemiol 2016; in press.
Bross IDJ. Pertinency of an extraneous variable. J Chronic Dis. 1967;20:487–95.
Chiolero A. Counterfactual and interventionist approach to cure risk factor epidemiology (letter). Int J Epidemiol 2016; in press.
Cornfield J, Haenszel WH, Hammond EC, Lilienfeld AM, Shimkin MB, Wynder EL. Smoking and lung cancer: recent evidence and a discussion of some questions. J Natl Cancer Inst. 1959;22:173–203.
Cox DR. Some problems connected with statistical inference. Ann Math Stat. 1958;29:357–72.
Daniel RM, De Stavola BL, Vansteelandt S. The formal approach to quantitative causal inference in epidemiology: misguided or misrepresented? Int J Epidemiol 2016; in press.
Dawid AP. The well-calibrated Bayesian (with discussion). JASA. 1982;77:604–13.
Dawid AP. Causal inference without counterfactuals (with discussion). JASA. 2000;95:407–48.
Dawid AP. Beware of the DAG! In: D Janzing IG, Schoelkopf B (eds). Proceedings of the NIPS 2008 Workshop on Causality. Journal of Machine Learning Research Workshop and Conference Proceedings, Whistler, Canada, 2008, 59–86.
Discacciati A, Orsini N, Greenland S. Approximate Bayesian logistic regression via penalized likelihood by data augmentation. Stata Journal. 2015;15(3):712–36.
Dunning T. Improving causal inference: Strengths and limitations of natural experiments. Political Research Quarterly. 2008;61(2):282–93.
Ellis G, Silk J. Defend the integrity of physics. Nature. 2014;516:321–3.
Farsides T, Sparks P. Opinion: Buried in bullshit. The Psychologist. 2016;29:368–71.
Feyerabend P. Against Method. New York: New Left Books, 1975; 3rd ed. New York: Verso, 1993.
Feyerabend P. Killing Time. Chicago: U Chicago Press; 1995.
Flanders WD, Johnson CY, Howards PP, Greenland S. Dependence of confounding on the target population: A modification of causal graphs to account for coaction. Ann Epidemiol. 2011;21:698–705.
Fleiss JL. Significance tests have a role in epidemiologic research: reactions to A. M. Walker. Am J Public Health. 1986a;76:559–60.
Fleiss JL. Dr. Fleiss responds. Am J Public Health. 1986b;76:1033–4.
Freedman DA. As others see us: a case study in path analysis (with discussion). J Educ Stat. 1987;12:101–223.
Freedman DA, Navidi W, Peters SC. On the impact of variable selection in fitting regression equations. In: Dijlestra TK, editor. On model uncertainty and its statistical implications. Berlin: Springer-Verlag; 1988. p. 1–16.
Galea S. An argument for a consequentialist epidemiology. Am J Epidemiol. 2013;178:1185–91.
Gelman A. Causality and statistical learning. Am J Sociol. 2011;117:955–66.
Gelman A. P-values and statistical practice. Epidemiology. 2013;24:69–72.
Gelman A, Loken E. The statistical crisis in science: Data-dependent analysis—a “garden of forking paths”—explains why many statistically significant comparisons don’t hold up. Am Sci 2014a;102:460–465. Erratum at http://andrewgelman.com/2014/10/14/didnt-say-part-2/, accessed 25 Oct 2016.
Gelman A, Loken E. The AAA tranche of subprime science. Chance. 2014;27(1):51–7.
Gelman A, Shalizi CS. Philosophy and the practice of Bayesian statistics (with discussion). Br J Math Stat Psych. 2013;66:8–80.
Gelman A, Stern HS. The difference between “significant” and “not significant” is not itself statistically significant. Am Stat. 2006;60:328–31.
George SL, Buyse M. Data fraud in clinical trials. Clin. Invest (London). 2015;5(2):161–73.
Gigerenzer G. We need statistical thinking, not statistical rituals. Behavioral & Brain Sciences. 1998;21:199–200.
Gigerenzer G. Mindless statistics. J Socioecon. 2004;33:567–606.
Gigerenzer G, Marewski JN. Surrogate science: the idol of a universal method for scientific inference. J Manag. 2015;41:421–40.
Gill RD. Statistics, causality and Bell’s theorem. Statistical Science. 2014;29(4):512–28.
Gilovich T, Griffin D, Kahneman D. Heuristics and biases: the psychology of intuitive judgment. New York: Cambridge University Press; 2002.
Glass TA, Goodman SN, Hernán MA, Samet JM. Causal inference in public health. Annu Rev Public Health. 2013;34:61–75.
Glymour C. Comment: Statistics and metaphysics. JASA. 1986;81:964–6.
Glymour C, Glymour MR. Commentary: race and sex are causes. Epidemiology. 2014;25:488–90.
Glymour MM, Greenland S. Causal diagrams. Ch. 12 in: Rothman KJ, Greenland S, Lash TL. Modern Epidemiology, 3rd ed. Philadelphia: Lippincott 2008; 183-209.
Goodman SN. P Values, hypothesis tests, and likelihood: implications for epidemiology of a neglected historical debate. Am J Epidemiol. 1993;137:485–96.
Goodman SN. Introduction to Bayesian methods I: measuring the strength of evidence. Clin Trials. 2005;2:282–90.
Goodman SN, Royall R. Evidence and scientific research. Am J Public Health. 1988;78:1568–74.
Greenhouse SW. Some epidemiologic issues for the 1980s. Am J Epidemiol. 1980;112(2):269–73.
Greenland S. The author replies to Newman and Browner. Am J Epidemiol. 1988;128:1182–4.
Greenland S. Randomization, statistics, and causal inference. Epidemiol. 1990;1:421–9.
Greenland S. Science versus advocacy: The challenge of Dr. Feinstein. Epidemiol. 1991;2:72–79.
Greenland S. The sensitivity of a sensitivity analysis (invited paper). In: 1997 Proceedings of the Biometrics Section. Alexandria, VA: American Statistical Association 1998; 19-21.
Greenland S. Epidemiologic measures and policy formulation: Lessons from potential outcomes (with discussion). Emerging Themes in Epidemiology (online). 2005;2:1–4.
Greenland S. Introduction to Bayesian statistics. Ch. 18 in: Rothman KJ, Greenland S, Lash TL. Modern Epidemiology, 3rd ed. Philadelphia: Lippincott 2008; 328-44.
Greenland S. Weaknesses of certain Bayesian methods for meta-analysis: The case of vitamin E and mortality (invited commentary). Clinical Trials. 2009a;6:42–6.
Greenland S. Relaxation penalties and priors for plausible modeling of nonidentified bias sources. Statistical Science. 2009b;24:195–210.
Greenland S. Overthrowing the tyranny of null hypotheses hidden in causal diagrams. Ch. 22 in: Dechter R, Geffner H, Halpern JY, eds. Heuristics, Probabilities, and Causality: A Tribute to Judea Pearl. London: College Press, 2010a, 365–382. Available at http://intersci.ss.uci.edu/wiki/pdf/Pearl/22_Greenland.pdf
Greenland S. Comment: The need for syncretism in applied statistics. Statist Sci. 2010b;25:158–61.
Greenland S. Null misinterpretation in statistical testing and its impact on health risk assessment. Preventive Medicine. 2011;53:225–8.
Greenland S. Causal inference as a prediction problem: Assumptions, identification, and evidence synthesis. Ch. 5 in: Berzuini C, Dawid AP, Bernardinelli L (eds.). Causal Inference: Statistical Perspectives and Applications. Chichester: Wiley 2012a, 43-58.
Greenland S. Nonsignificance plus high power does not imply support for the null over the alternative. Annals of Epidemiology. 2012a;22:364–8.
Greenland S. Transparency and disclosure, neutrality and balance: shared values or just shared words? Journal of Epidemiology and Community Health. 2012b;66:967–70.
Greenland S. The ASA guidelines and null bias in current teaching and practice. Am Statist 2016; 70: suppl. 10 at http://www.tandfonline.com/doi/suppl/10.1080/00031305.2016.1154108
Greenland S. A serious misinterpretation of a consistent inverse association of statin use with glioma across 3 case-control studies. Eur J Epidemiol 2017a;32: in press.
Greenland S. The biases of bias analyses will not help validity or reproducibility. Am J Epidemiol 2017b; to appear.
Greenland S, Brumback BA. An overview of relations among causal modeling methods. Int J Epidemiol. 2002;31:1030–7.
Greenland S, Lash TL. Bias analysis. Ch. 19 in: Rothman KJ, Greenland S, Lash TL. Modern Epidemiology, 3rd ed. Philadelphia: Lippincott 2008; 345-80.
Greenland S, Maclure M, Schlesselman JJ, Poole C, Morgenstern H. Standardized regression coefficients: a further critique and review of some alternatives. Epidemiology. 1991;2:387–92.
Greenland S, Mansournia MA. Limitations of individual causal models, causal graphs, and ignorability assumptions, as illustrated by random confounding and design unfaithfulness. Eur J Epidemiol. 2015a;30:1101–10.
Greenland S, Mansournia MA. Penalization, bias reduction, and default priors in logistic and related categorical and survival regressions. Stat Med 2015b;34:3133–43.
Greenland S, Neutra RR. Control of confounding in the assessment of medical technology. Int J Epidemiol. 1980;9:361–7.
Greenland S, Pearl J, Robins JM. Causal diagrams for epidemiologic research. Epidemiology. 1999;10:37–48.
Greenland S, Poole C. Living with statistics in observational research. Epidemiology. 2013;24:73–8.
Greenland S, Robins JM. Identifiability, exchangeability and epidemiological confounding. Int J Epidemiol. 1986;15:413–9.
Greenland S, Senn SJ, Rothman KJ, Carlin JC, Poole C, Goodman SN, Altman DG. Statistical tests, confidence intervals, and power: A guide to misinterpretations. Eur J Epidemiol 2016; 31:337-50. https://dx.doi.org/10.1007%2Fs10654-016-0149-3
Greenwood M. Is the statistical method of any value in medical research? Lancet. 1924;204:153–8.
Gustafson P. Bayesian inference for partially identified models. Int J Biostatist. 2010;6(2):17.
Gustafson P, Greenland S. The performance of random coefficient regression in accounting for residual confounding. Biometrics. 2006;62:760–8.
Gustafson P, Greenland S. Interval estimation for messy observational data. Stat Sci. 2009;24:328–42.
Gustafson P, McCandless L. Priors, parameters, and probability: A Bayesian perspective on sensitivity analysis. Epidemiol. 2014;26:910–2.
Hall JB. An address on yesterday, to-day, and to-morrow. Lancet. 1924;204:151–3.
Hernán MA. Invited commentary: hypothetical interventions to define causal effects afterthought or prerequisite? Am J Epidemiol. 2005;162:618–20.
Hernán MA. Does water kill? A call for less casual causal inferences. Ann Epidemiol. 2016;26:683–4.
Hernán MA, Clayton D, Keiding N. The Simpson’s paradox unraveled. Int J Epidemiol. 2011;40:780–5.
Hernán MA, Robins JM. Causal inference. New York, Chapman & Hall, 2017, to appear.
Hernán MA, Taubman SL. Does obesity shorten life? The importance of well-defined interventions to answer causal questions. Int J Obes. 2008;32(suppl 3):S8–14.
Hill AB. The environment and disease: association or causation? Proc R Soc Med. 1965;58:295–300.
Höfler M. The Bradford Hill considerations on causality: a counterfactual perspective. Emerg Themes Epidemiol. 2005;2(1):11.
Holland PW. Statistics and causal inference (with discussion). J Am Stat Assoc. 1986;81:945–70.
Hume, D. An Enquiry Concerning Human Understanding. Reprint of 1748 original by Oxford University Press, New York, 1999.
Ioannidis JPA. Why most discovered true associations are inflated. Epidemiol. 2008;19:640–8.
Kaufman JS. Race: ritual, regression, and reality. Epidemiol. 2014;25:485–7.
Kaufman JS. There is no virtue in vagueness. Ann Epidemiol. 2016;26:683–4.
Keyes K, Galea S. What matters most: quantifying an epidemiology of consequence. Ann Epidemiol. 2015;25(5):305–11.
King G, Zeng L. When can history be our guide? The pitfalls of counterfactual inference. Int Stud Q. 2007;51:183–210.
Krieger N, Davey Smith G. The tale wagged by the DAG: broadening the scope of causal inference and explanation for Epidemiology. Int J Epidemiol 2016; in press.
Lachenbruch PA, Clark VA, Cumberland WG, Chang PC, Afifi AA, Flack VF, Elashoff RM. Letter to the Editor. AJPH. 1987;77(2):237.
Lash TL. Heuristic thinking and inference from observational epidemiology. Epidemiology. 2007;18:67–72.
Lash TL, Fox MP, Fink AK. Applying Quantitative Bias Analysis to Epidemiologic Data. Boston: Springer; 2009.
Leamer EE. Specification Searches. New York: Wiley; 1978.
Leamer EE. Sensitivity analyses would help. Am Econ Rev. 1985;75:308–13.
Lewis D. Causation J. Philos 1973;70:556–567. Reprinted with postscript in: Lewis D. Philosophical papers. New York: Oxford University Press, 1986.
Little RJA. Calibrated Bayes: A Bayes/frequentist roadmap. Am Statist. 2006;60:1–11.
Maclure M, Schneeweiss S. Causation of bias: The Episcope. Epidemiol. 2001;12:114–22.
MacMahon B, Pugh TF. Causes and entities of disease. In: Clark DW, MacMahon B, eds. Preventive medicine. Boston: Little, Brown, 1967.
Maldonado G. Toward a clearer understanding of causal concepts in epidemiology. Ann Epidemiol. 2013;23:743–9.
Maldonado G. The role of counterfactual theory in causal reasoning. Ann Epidemiol. 2016;26:681–2.
Maldonado G, Greenland S. Response: Defining and estimating causal effects. Int J Epidemiol. 2002;31:434–8.
Mansournia MA, Higgins JPT, Sterne JAC, Hernán MA. Biases in randomized trials-A conversation between trialists and epidemiologists. Epidemiol. 2017;28:54–9.
Mill JS. A System of Logic. Reprint by Longmans, Green, London: Ratiocinative and Inductive; 1843. p. 1956.
Morabia A. Has epidemiology become infatuated with methods? Annu Rev Public Health. 2015;36:69–88.
Naimi AI, Kaufman JS, MacLehose RF. Mediation misgivings: ambiguous clinical and public health interpretations of natural direct and indirect effects. In J Epidemiol. 2014;43:1656–61.
Naimi AI. The counterfactual implications of fundamental cause theory. Curr Epidemiol Rep. 2016;3:92–7.
Neyman J. On the application of probability theory to agricultural experiments. Essay on principles. Section 9, 1923 (in Polish; translation in Statistical Science 1990, 465–472).
Neyman J. Frequentist probability and frequentist statistics. Synthese. 1977;36:97–131.
Newman TB, Browner WS. Re: “Interpretation and choice of effect measures in epidemiologic analyses” (letter). Am J Epidemiol. 1988;12:1181–2.
Pearce N, Vandenbroucke JP. Commentary: Causation, mediation and explanation. Int J Epidemiol 2017;46: in press.
Pearl J. Causal diagrams for empirical research. Biometrika. 1995;82:669–710.
Pearl J. Causality: models, reasoning and inference. 2nd ed. Cambridge, UK: Cambridge University Press; 2009.
Pearl J. On the consistency rule in causal inference: Axiom, definition, assumption, or theorem? Am J Epidemiol. 2010;21(6):872–5.
Pearl J. Causes of effects and effects of causes. Soc Meth Res. 2015;44(1):149–64.
Phillips CV. Quantifying and reporting uncertainty from systematic errors. Epidemiology. 2003;14:459–66.
Phillips CV, Goodman KJ. The missed lessons of Sir Austin Bradford Hill. Epidemiol Perspect Innov. 2004;1:3. doi:10.1186/1742-5573-1-3.
Phillips CV, Goodman KJ. Causal criteria and counterfactuals: nothing more (or less) than scientific common sense. Emerg Themes Epidemiol. 2006;3:5. doi:10.1186/1742-7622-3-5.
Price H. Time’s Arrow and Archimedes’ Point. New York: Oxford, 1996.
Poole C. Beyond the confidence interval. Am J Public Health. 1987;77:195–9.
Poole C. Low P-values or narrow confidence intervals: Which are more durable? Epidemiol. 2001;12:291–4.
Poole C, Greenland S. How a court accepted a possible explanation: A comment on Gastwirth, Krieger, and Rosenbaum. Am Statist. 1997;51:112–4.
Porta M, Bolúmar F. Caution: work in progress. Eur J Epidemiol. 2016;31:535–9.
Porta M, Vineis P, Bolúmar F. The current deconstruction of paradoxes: one sign of the ongoing methodological “revolution”. Eur J Epidemiol. 2015;30:1079–87.
Rhodes E. Replication: Is the glass half full, half empty, or irrelevant? The Psychologist, 7th March 2016.
Richardson T, Robins JM. Single world intervention graphs (SWIGs): a unification of the counterfactual and graphical approaches to causality. Working Paper 128. Center for the Statistics and the Social Sciences, University of Washington, Seattle, 2013.
Robins JM. A graphical approach to the identification and estimation of causal parameters in mortality studies with sustained exposure periods. J Chron Dis. 1987;40(supplement 2):139S–61S.
Robins JM, Greenland S. Identifiability and exchangeability for direct and indirect effects. Epidemiology. 1992;3:143–55.
Robins JM, Greenland S. Comment. J Am Stat Assoc. 2000;95:431–5.
Robins JM, Richardson TS. Alternative graphical causal models and the identification of direct effects. Ch. 6 in Shrout P, Keyes K, Ornstein K, eds. Causality and Psychopathology: Finding the Determinants of Disorders and their Cures. New York: Oxford, 2011, 1-52.
Robins JM, Vander Weele TJ, Gill RD. A proof of Bell’s inequality in quantum mechanics using causal interactions. Scand J Statistics. 2015;42:329–35.
Robins JM, Weissman M. Counterfactual causation and streetlamps: What is to be done? Int J Epidemiol 2016; in press.
Robins JM, Wasserman L. On the impossibility of inferring causation from association without background knowledge (with discussion). In: Glymour C, Cooper G, editors. Computation, Causation, and Discovery. Cambridge, MA: MIT Press; 1999. p. 305–42.
Robins JM, Scheines R, Spirtes P, Wasserman L. Uniform consistency in causal inference. Biometrika. 2003;90:491–515.
Romer P. The trouble with macroeconomics. Am Economist 2016;to appear.
Rosenbaum PR, Rubin DB. The central role of the propensity score in observational studies for causal effects. Biometrika. 1983;70:41–55.
Rothman KJ. Causes. Am J Epidemiol. 1976;104:587–92.
Rothman KJ. A show of confidence. NEJM. 1978;299:1362–3.
Rothman KJ. Significance questing. Ann Intern Med. 1986;105:445–7.
Rouen TA. Letter to the Editor. AJPH. 1987;77(2):237.
Rubin DB. Estimating causal effects of treatments in randomized and nonrandomized studies. J Educ Psychol. 1974;66:688–701.
Rubin DB. Comment: Neyman (1923) and causal inference in experiments and observational studies. Stat Sci. 1990;5:472–80.
Rubin DB. Practical implications of modes of statistical inference for causal effects, and the critical role of the assignment mechanism. Biometrics. 1991;47:1213–34.
Schooling C, Chow C, Au Yeung S. Causality and causal inference in epidemiology: we need also to address causes of effects (letter). Int J Epidemiol 2016; in press.
Schwartz S, Gatto NM, Campbell UB. Causal identification: A charge of epidemiology in danger of marginalization. Ann Epidemiol. 2016;26:669–73.
Schwartz S, Gatto NM, Campbell UB. Heeding the call for less casual causal inferences: The utility of realized (quantitative) causal effects. Ann Epidemiol 2017;27: in press.
Seliger C, Meier CR, Becker C, Jick SS, Bogdahn U. Hau1 P, Leitzmann MF. Statin use and risk of glioma: population-based case-control analysis. Eur J Epidemiol. 2016;31:947–51.
Sellke TM, Bayarri MJ, Berger JO. Calibration of p values for testing precise null hypotheses. Am Stat. 2001;55:62–71.
Senn SJ. Two cheers for P-values. J Epidemiol Biostat. 2001;6(2):193–204.
Senn SJ. Letter to the Editor re: Goodman 1992. Stat Med. 2002;21:2437–44.
Shafer G. Comment: Estimating causal effects. Int J Epidemiol. 2002;31:434–5.
Simon HA, Rescher N. Cause and counterfactual. Philosophy of Science. 1966;33(4):323–40.
Spirtes P, Glymour C, Scheines R. Causation, prediction, and search. Cambridge MA: MIT Press; 2001.
Stallones RA. To advance epidemiology. Ann Rev Public Health. 1980;1:69–82.
Stalnaker RC. A theory of conditionals. In: Studies in Logical Theory, ed. Rescher N, 98-112. Oxford: Blackwell, 1968. Repr. in Causation and Conditionals, ed. E. Sosa, 165-79. Oxford: Oxford University Press, 1975.
Stolley PD. When genius errs: R.A. Fisher and the lung cancer controversy. Am J Epidemiol. 1991;133(5):416–25.
Student (Gossett, WS). The probable error of a mean. Biometrika 1908;VI:1–25.
Sullivan S, Greenland S. Bayesian regression in SAS software. Int J Epidemiol 2013;42:308-317. Erratum. Int J Epidemiol. 2014;43:1667–8.
Susser M. Judgment and causal inference. Am J Epidemiol. 1977;105:1–15.
Susser M. What is a cause and how do we know one? A grammar for pragmatic epidemiology. Am J Epidemiol. 1991;133:635–48.
Taleb NN. The Black Swan: The Impact of the Highly Improbable, 2nd ed. Random House 2010.
Tukey JW. Causation, regression, and path analysis. In: Kempthorne O, ed. Statistics and Mathematics in Biology. Ames: Iowa State Press, 1954; Ch. 3.
Tukey JW. The future of data analysis. Ann Math Stat. 1962;33:1–67.
Vandenbroucke JP. Commentary: ‘Smoking and lung cancer’ the embryogenesis of modern epidemiology. Int J Epidemiol. 2009;38:1193–6.
Vandenbroucke JP, Broadbent A, Pearce N. Causality and causal inference in epidemiology: the need for a pluralistic approach. Int J Epidemiol 2016; in press.
VanderWeele TJ. Explanation in causal inference: methods for mediation and interaction. New York, NY: Oxford University Press; 2015.
VanderWeele TJ. On causes, causal inference, and potential outcomes. Int J Epidemiol 2016a; in press.
VanderWeele TJ. The role of potential outcomes thinking in assessing mediation and interaction. Int J Epidemiol 2016b; in press.
VanderWeele TJ. Discussion of “Causal inference using invariant prediction: identification and confidence intervals” by Peters, Bühlmann and Meinshausen. J Roy Stat Soc B. 2016;78:995.
VanderWeele TJ, Hernán MA. Causal effects and natural laws: Towards a conceptualization of causal counterfactuals for nonmanipulable exposures, with application to the effects of race and sex. Ch. 9 in: Berzuini C, Dawid AP, Bernardinelli L (eds.). Causal Inference: Statistical Perspectives and Applications. Chichester: Wiley 2012, 101-13.
VanderWeele TJ, Hernán MA, Tchetgen Tchetgen EJ, Robins JM. Re: Causality and causal inference in epidemiology: the need for a pluralistic approach (letter). Int J Epidemiol 2016; in press.
VanderWeele TJ, Robins JM. Stochastic counterfactuals and stochastic sufficient causes. Statistica Sinica. 2012;22:279–92.
VanderWeele TJ, Robinson WR. On causal interpretation of race in regressions adjusting for confounding and mediating variables. Epidemiol. 2014;25:473–84.
Wagenmakers E-J. A practical solution to the pervasive problem of p values. Psychon Bull Rev. 2007;14:779–804.
Walker AM. Reporting the results of epidemiologic studies. Am J Public Health. 1986a;76:556–8.
Walker AM. Significance tests represent consensus and standard practice. Am J Public Health. 1986b;76:1033.
Wasserstein RL, Lazar NA. The ASA’s statement on p-values: context, process, and purpose. Am Statist. 2016;70(2):129–33.
Anonymous. A new low in drug research: 21 fabricated studies. Wall Street Journal Mar. 11, 2009.
Welch BL. On the z-test in randomized blocks and Latin squares. Biometrika. 1937;29:21–52.
Wilk MB. The randomization analysis of a generalized randomized block design. Biometrika. 1955;42:70–9.
Wright S. Correlation and causation. Journal of Agricultural Research. 1921;20:557–85.
Yates F. The influence of statistical methods for research workers on the development of the science of statistics. J Am Stat Assoc. 1951;46:19–34.
I am deeply indebted to many colleagues for extensive comments and correspondence on the initial draft of this paper, including Alex Broadbent, Jan Vandenbroucke, Neil Pearce, Ashley Naimi, Jay Kaufman, Sharon Schwartz, Nicolle Gatto, Ulka Campbell, George Maldonado, Alfredo Morabia, James Robins, and Tyler VanderWeele. Any errors that remain are solely my responsibility.
About this article
Cite this article
Greenland, S. For and Against Methodologies: Some Perspectives on Recent Causal and Statistical Inference Debates. Eur J Epidemiol 32, 3–20 (2017). https://doi.org/10.1007/s10654-017-0230-6
- Causal inference
- Potential outcomes
- Effect estimation
- Hypothesis testing
- Intervention analysis
- Significance testing
- Research synthesis
- Statistical inference