The Bradford Hill Predicate: Ruling Out Random and Systematic Error
In two recent posts, I spent some time discussing a recent law review, which had some important things to say about specific causation.[1] One of several points from which I dissented was the article’s argument that Sir Austin Bradford Hill had not made explicit that ruling out random and systematic error was required before assessing his nine “viewpoints” on whether an association was causal. I take some comfort in the correctness of my interpretation of Sir Austin’s famous article by reading the analysis of no less than Sir Richard Doll’s own analysis of his friend and colleague’s views:
“In summary, we have to show, first, that the association cannot reasonably be explained by chance (bearing in mind that extreme chances do turn up from time to time or no one would buy a ticket in a national lottery), by methodological bias (which can have many sources), or by confounding (which needs to be explored but should not be postulated without some idea of what it might be). Second, we have to see whether the available evidence gives positive support to the concept of causality: that is to say, how it matches up to Hill’s (1965) guidelines (Table 1).”[2]
On the issue of whether small relative risks can establish general causation, the Differential Etiology paper urged caution in interpreting results when “strength of a relationship is modest.” The strength of an association is, of course, one of the nine Bradford Hill viewpoints, which come into play after we have a “clear-cut” association beyond what we would care to attribute to chance. Additionally, strength of association is primarily a quantitive assessment, and the advice given about caution in the face of “modest” associations is not terribly helpful. The scientific literature does better.
Sir Richard’s 2002 paper is in a sense a scientific autobiography about some successes in discerning causal associations from observational studies. Unlike expert witnesses for the lawsuit industry, Sir Richard’s essay is notably for its intellectual humility. In addition to its clear and explicit articulation of the need to rule out random and systematic error before proceeding to a consideration of Sir Austin’s nine guidelines, Sir Richard Doll’s 2002 essay is instructive for judges and lawyers, for other reasons. For example, he raises and explains the problem encountered for causal inference by small relative risks:
“Small relative risks of the order of 2:1 or even less are what are likely to be observed, like the risk now recorded for childhood leukemia and exposure to magnetic fields of 0.4 µT or more (Ahlbom et al. 2000) that are seldom encountered in the United Kingdom. And here the problems of eliminating bias and confounding are immense.”[3]
Sir Richard opines that relative risks under two can be shown to be causal associations, but often with massive data, randomization, and a good deal of support from experimental work.
Another Sir Richard, Sir Richard Peto, along with Sir Richard Doll, raised this concern in their classic essay on the causes of cancer, where they noted that relative risks between one and two create extremely difficult problems of interpretation because the role of the association cannot be confidently disentangled from the contribution of biases.[4] Small relative risks are thus seen as raising a concern about bias and confounding.[5]
In the legal world, courts have recognized that the larger the relative risk, or the strength of association, the more likely a general causation inference can be drawn, even when they blithely ignored the role of actual or residual confounding.[6]
The chapters on statistics and on epidemiology in the current (third) edition of the Reference Manual on Scientific Evidence directly tie the magnitude of the association to the elimination of confounding as an alternative explanation for causality of an association. A larger “effect size,” such as for smoking and lung cancer (greater than ten-fold, and often higher than 30-fold), eliminates the need to worry about confounding:
“Many confounders have been proposed to explain the association between smoking and lung cancer, but careful epidemiological studies have ruled them out, one after the other.”[7]
* * * * * *
“A relative risk of 10, as seen with smoking and lung cancer, is so high that it is extremely difficult to imagine any bias or confounding factor that might account for it. The higher the relative risk, the stronger the association and the lower the chance that the effect is spurious. Although lower relative risks can reflect causality, the epidemiologist will scrutinize such associations more closely because there is a greater chance that they are the result of uncontrolled confounding or biases.”[8]
The Reference Manual omits the converse: the lower relative risk, the weaker the association and the greater the chance that the apparent effect is spurious. The authors’ intent, however, is clear enough. In the Appendix, below, I have collected some pronouncements from the scientific literature that urge caution in drawing causal inferences in the face of weak associations, but with more quantitative guidance.
Small RRs and Specific Causation
Sir Richard Doll was among the first generation of epidemiologists in the academic world. He eschewed the use of epidemiology for discerning the cause of an individual’s disease:
“That asbestos is a cause of lung cancer in this practical sense is incontrovertible, but we can never say that asbestos was responsible for the production of the disease in a particular patient, as there are many other etiologically significant agents to which the individual may have been exposed, and we can speak only of the extent to which the risk of the disease was increased by the extent of his or her exposure.”[9]
On the individual attribution issue, Sir Richard’s views do not hold up as well as his analysis of general causation. Epidemiologic study results are used to predict future disease in individuals, to guide screening and prophylaxis decisions, to determine pharmacologic and surgical interventions in individuals, and to provide prognoses to individuals. Just as confounding falls by the wayside in the analysis of general causation with relative risks greater than 20, so too do the concerns about equating increased risk with specific causation.
The urn model of probability, however, gives us some insight into attributability. If we expected 100 cases of a disease in a sample of a certain size, but we observed 200 cases, then we would have 100 expected and 100 excess cases. Attribution would be no better than a flip of a coin. If, however, in a situation where the relative risk was 20, we might have 100 expected cases and 2,000 excess cases. The odds of a given case’s being an excess case are rather strong, and even the agnostics and dissenters from probabilistic reasoning in individual cases become weak kneed about denying recovery when the claimant is similar to the cases seen in the study sample.
******************Appendix*************************
Norman E. Breslow & N. E. Day, “Statistical Methods in Cancer Research,” in The Analysis of Case-Control Studies 36 (IARC Pub. No. 32, 1980) (“[r]elative risks of less than 2.0 may readily reflect some unperceived bias or confounding factor”)
Richard Doll & Richard Peto, The Causes of Cancer 1219 (1981) (“when relative risk lies between 1 and 2 … problems of interpretation may become acute, and it may be extremely difficult to disentangle the various contributions of biased information, confounding of two or more factors, and cause and effect.”)
Iain K. Crombie, “The limitations of case-control studies in the detection of environmental carcinogens,” 35 35 J. Epidem. & Community Health 281, 281 (1981) (“The case-control study is unable to detect very small relative risks (< 1.5) even where exposure is widespread and large numbers of cases of cancer are occurring in the population.”)
Ernst L. Wynder & Geoffrey C. Kabat, “Environmental Tobacco Smoke and Lung Cancer: A Critical Assessment,” in H. Kasuga, ed., Indoor Air Quality 5, 6 (1990) (“An association is generally considered weak if the odds ratio is under 3.0 and particularly when it is under 2.0, as is the case in the relationship of ETS and lung cancer. If the observed relative risk is small, it is important to determine whether the effect could be due to biased selection of subjects, confounding, biased reporting, or anomalies of particular subgroups.”).
Ernst L. Wynder, “Epidemiological issues in weak associations,” 19 Internat’l J. Epidemiol. S5 (1990)
David Sackett, R. Haynes, Gordon Guyatt, and Peter Tugwell, Clinical Epidemiology: A Basic Science for Clinical Medicine (2d ed. 1991)
Muin J. Khoury, Levy M. James, W. Dana Flanders, and David J. Erickson, “Interpretation of recurring weak associations obtained from epidemiologic studies of suspected human teratogens,” 46 Teratology 69 (1992);
Lynn Rosenberg, “Induced Abortion and Breast Cancer: More Scientific Data Are Needed,” 86 J. Nat’l Cancer Instit. 1569, 1569 (1994) (“A typical difference in risk (50%) is small in epidemiologic terms and severely challenges our ability to distinguish if it reflects cause and effect or if it simply reflects bias.”) (commenting upon Janet R. Daling, K. E. Malone, L. F. Voigt, E. White, and Noel S. Weiss, “Risk of breast cancer among young women: relationship to induced abortion,” 86 J. Nat’l Cancer Inst. 1584 (1994);
Linda Anderson, “Abortion and possible risk for breast cancer: analysis and inconsistencies,” (Wash. D.C., Nat’l Cancer Institute, Oct. 26,1994) (“In epidemiologic research, relative risks of less than 2 are considered small and are usually difficult to interpret. Such increases may be due to chance, statistical bias, or effects of confounding factors that are sometimes not evident.”);
Washington Post (Oct. 27, 1994) (quoting Dr. Eugenia Calle, Director of Analytic Epidemiology for the American Cancer Society: “Epidemiological studies, in general are probably not able, realistically, to identify with any confidence any relative risks lower than 1.3 (that is a 30% increase in risk) in that context, the 1.5 [reported relative risk of developing breast cancer after abortion] is a modest elevation compared to some other risk factors that we know cause disease.”)
Gary Taubes, “Epidemiology Faces Its Limits,” 269 Science 164, 168 (July 14, 1995) (quoting Marcia Angell, former editor of the New England Journal of Medicine, as stating that “[a]s a general rule of thumb, we are looking for a relative risk of 3 or more [before accepting a paper for publication], particularly if it is biologically implausible or if it’s a brand new finding.”) (quoting John C. Bailar: “If you see a 10-fold relative risk and it’s replicated and it’s a good study with biological backup, like we have with cigarettes and lung cancer, you can draw a strong inference. * * * If it’s a 1.5 relative risk, and it’s only one study and even a very good one, you scratch your chin and say maybe.”)
Samuel Shapiro, “Bias in the evaluation of low-magnitude associations: an empirical perspective,” 151 Am. J. Epidemiol. 939 (2000)
David A. Freedman & Philip B. Stark, “The Swine Flu Vaccine and Guillain-Barré Syndrome: A Case Study in Relative Risk and Specific Causation,” 64 Law & Contemp. Probs. 49, 61 (2001) (“If the relative risk is near 2.0, problems of bias and confounding in the underlying epidemiologic studies may be serious, perhaps intractable.”).
S. Straus, W. Richardson, P. Glasziou, and R. Haynes, Evidence-Based Medicine. How to Teach and Practice EBM (3d ed. 2005)
David F. Goldsmith & Susan G. Rose, “Establishing Causation with Epidemiology,” in Tee L. Guidotti & Susan G. Rose, eds., Science on the Witness Stand: Evaluating Scientific Evidence in Law, Adjudication, and Policy 57, 60 (2001) (“There is no clear consensus in the epidemiology community regarding what constitutes a ‘strong’ relative risk, although, at a minimum, it is likely to be one where the RR is greater than two; i.e., one in which the risk among the exposed is at least twice as great as among the unexposed.”)
Samuel Shapiro, “Looking to the 21st century: have we learned from our mistakes, or are we doomed to compound them?” 13 Pharmacoepidemiol. & Drug Safety 257 (2004)
Mark Parascandola, Douglas L Weed & Abhijit Dasgupta, “Two Surgeon General’s reports on smoking and cancer: a historical investigation of the practice of causal inference,” 3 Emerging Themes in Epidemiol. 1 (2006)
Heinemann, “Epidemiology of Selected Diseases in Women,” chap. 4, in M.A. Lewis, M. Dietel, P.C. Scriba, W.K. Raff, eds., Biology and Epidemiology of Hormone Replacement Therapy 47, 48 (2006) (discussing the “small relative risks in relation to bias/confounding and causal relation.”)
Roger D. Peng, Francesca Dominici, and Scott L. Zeger, “Reproducible Epidemiologic Research,” 163 Am. J. Epidem. 783, 784 (2006) (“The targets of current investigations tend to have smaller relative risks that are more easily confounded.”)
R. Bonita, R. Beaglehole & T. Kjellström, Basic Epidemiology 93 (W.H.O. 2d ed. 2006) (“A strong association between possible cause and effect, as measured by the size of the risk ratio (relative risk), is more likely to be causal than is a weak association, which could be influenced by confounding or bias. Relative risks greater than 2 can be considered strong.”)
David A. Grimes & Kenneth F. Schulz, “False alarms and pseudo-epidemics: the limitations of observational epidemiology,” 120 Obstet. & Gynecol. 920 (2012) (“Most reported associations in observational clinical research are false, and the minority of associations that are true are often exaggerated. This credibility problem has many causes, including the failure of authors, reviewers, and editors to recognize the inherent limitations of these studies. This issue is especially problematic for weak associations, variably defined as relative risks (RRs) or odds ratios (ORs) less than 4.”)
Kenneth F. Schulz & David A. Grimes, Essential Concepts in Clinical Research:
Randomised Controlled Trials and Observational Epidemiology at 75 (2d ed. 2019) (“Even after attempts to minimise selection and information biases and after control for known potential confounding factors, bias often remains. These biases can easily account for small associations. As a result, weak associations (which dominate in published studies) must be viewed with circumspection and humility.43 Weak associations, defined as relative risks between 0.5 and 2.0, in a cohort study can readily be accounted for by residual bias (Fig. 7.2). Because case-control studies are more susceptible to bias than are cohort studies, the bar must be set higher. ln case-control studies, weak associations can be viewed as odds ratios between 0.33 and 3.0 (Fig. 7.3). Results that full within these zones may be due to bias. Results that full outside these bounds in either direction may deserve attention.”)
Brian L. Strom, “Basic Principles of Clinical Epidemiology Relevant to Pharmacoepidemiologic Studies,” chap. 3, in Brian L. Strom, Stephen E. Kimmel & Sean Hennessy, eds., Pharmacoepidemiology 48 (6th ed. 2020) (“Conventionally, epidemiologists consider an association with a relative risk of less than 2.0 a weak association.”)
[1] Joseph Sanders, David L. Faigman, Peter B. Imrey, and Philip Dawid, “Differential Etiology: Inferring Specific Causation in the Law from Group Data in Science,” 63 Ariz. L. Rev. 851 (2021) [Differential Etiology].
[2] Richard Doll, “Proof of Causality: deduction from epidemiological observation,” 45 Persp. Biology & Med. 499, 501 (2002) (emphasis added).
[3] Id. at 512.
[4] Richard Doll & Richard Peto, The Causes of Cancer 1219 (1981) (“when relative risk lies between 1 and 2 … problems of interpretation may become acute, and it may be extremely difficult to disentangle the various contributions of biased information, confounding of two or more factors, and cause and effect.”).
[5] “Confounding in the Courts” (Nov. 2, 2018); “General Causation and Epidemiologic Measures of Risk Size” (Nov. 24, 2012).
[6] See King v. Burlington Northern Santa Fe Railway Co., 762 N.W.2d 24, 40 (Neb. 2009) (“the higher the relative risk, the greater the likelihood that the relationship is causal”); Landrigan v. Celotex Corp., 127 N.J. 404, 605 A.2d 1079, 1086 (1992) (“The relative risk of lung cancer in cigarette smokers as compared to nonsmokers is on the order of 10:1, whereas the relative risk of pancreatic cancer is about 2:1. The difference suggests that cigarette smoking is more likely to be a causal factor for lung cancer than for pancreatic cancer.”).
[7] RMSE3d at 219.
[8] RMSE3d at 602.
[9] Richard Doll, “Proof of Causality: deduction from epidemiological observation,” 45 Persp. Biology & Med. 499, 500 (2002).
