For your delectation and delight, desultory dicta on the law of delicts.

Broadbent on the Relative Risk > 2 Argument

October 31st, 2012

Alex Broadbent, of the University of Johannesburg, Department of Philosophy, has published a paper that contributes to the debate over whether a relative risk (RR) greater than (>) two is irrelevant, helpful, necessary, or sufficient in inferring that an exposure more likely than not caused an individual claimant’s disease. Alex Broadbent, “Epidemiological Evidence in Proof of Specific Causation,” 17 Legal Theory 237 (2011) [cited as Broadbent].  I am indebted to his having called his paper to my attention. Professor Broadbent’s essay is clearly written, which is helpful in assessing the current use of the RR > 2 argument in judicial decisions.

General vs. Specific Causation

Broadbent carefully distinguishes between general and specific causation.  By focusing exclusively upon specific causation (and assuming that general causation is accepted), he avoids the frequent confusion over when RR > 2 might play a role in legal decisions. Broadbent also “sanitizes” his portrayal of RR by asking us to assume that “the RR is not due to anything other than the exposure.” Id. at 241. This is a BIG assumption and a tall order for observational epidemiologic evidence.  The study or studies that establishes the RR we are reasoning from must be free of bias and confounding. Id.  Broadbent does not mention, however, the statistical stability of the RR, which virtually always will be based upon a sample, and thus subject to the play of random error.  He sidesteps the need for statistical significance in comparing two proportions, but the most charitable interpretation of his paper requires us to assume further that the hypothetical RR from which we are reasoning is sufficiently statistically stable that random error, along with bias and confounding, can be also ruled out as likely explanations for the RR > 1.

Broadbent sets out to show that RR > 2 may, in certain circumstances, suffices to show specific causation, but he argues that RR > 2 is never logically necessary, and must never be required to support a claim of specific causation.  Broadbent at 237.  On the same page in which he states that epidemiologic evidence of increased risk is a “last resort,” Broadbent contradicts himself by stating RR > 2 evidence “must never be required,” and then, in an apparent about face, he argues:

“that far from being epistemically irrelevant, to achieve correct and just outcomes it is in fact mandatory to take (high-quality) epidemiological evidence into account in deciding specific causation. Failing to consider such evidence when it is available leads to error and injustice. The conclusion is that in certain circumstances epidemiological evidence of RR > 2 is not necessary to prove specific causation but that it is sufficient.”

Id. at 237 (emphasis added). I am not sure how epidemiologic evidence can be mandatory but never logically necessary, and something that we should never require.

Presumably, Broadbent is using “to prove” in its legal and colloquial sense, and not as a mathematician.  Let us also give Broadbent his assumptions of “high quality” epidemiologic studies, with established general causation, and ask why, and explore when and whether, RR > 2 is not necessary to show specific causation.

The Probability of Causation vs. The Fact of Causation

Broadbent notes that he is arguing against what he perceives to be Professor Haack’s rejection of probabilistic inference, which would suggest that epidemiologic evidence is “never sufficient to establish specific causation.” Id. at 239 & n.3 (citing Susan Haack, “Risky Business: Statistical Proof of Individual Causation,” in Causación y Atribucion de Responsabilidad (J. Beltran ed., forthcoming)). He correctly points out that sometimes the probabilistic inference is the only probative inference available to support specific causation.  His point, however, does not resolve the dispute; it suffices only to show that whether we allow the probabilistic inference may be outcome determinative in many lawsuits.  Broadbent characterizes Haack’s position as one of two “serious mistakes in judicial and academic literature on this topic.”  Broadbent at 239.  The other alleged mistake is the claim that RR > 2 is needed to show specific causation:

“What follows, I conclude, is that epidemiological evidence is relevant to the proof of specific causation. Epidemiological evidence says that a particular exposure causes a particular harm within a certain population. Importantly, it quantifies: it says how often the exposure causes the harm. However, its methods are limited: they measure only the net effect of the exposure, leaving open the possibility that the exposure is causing more harm than the epidemiological evidence suggests—but ruling out the possibility that it causes less. Accordingly I suggest that epidemiological evidence can be used to estimate a lower bound on the probability of causation but that no epidemiological measure can be required. Thus a relative risk (RR, defined in Section II) of greater than 2 can be used to prove causation when there is no other evidence; but RR < 2 does not disprove causation. Given high-quality epidemiological evidence, RR > 2 is sufficient for proof of specific causation when no other evidence is available but not necessary when other evidence is available.”

Some of this seems reasonable enough.  Contrary to the claims of authors such as Haack and Wright, Broadbent maintains that some RR evidence is relevant and indeed probative of specific causation.  In a tobacco lung cancer, with a plaintiff who has smoked three packs a day, for 50 years (and RR > 50), we can confidently attribute the lung cancer to smoking, and rest assured that background cosmic radiation did not likely play a substantial role. The RR quantifies the strength of the association, and it does lead us to a measure of “attributable risk” (AR), also known as the attributable fraction (AF):

AR = 1 – 1/RR.

So far, so good.

Among the perplexing statements above, however, Broadbent suggests that:

1. The methods of epidemiologic evidence measure only the net effect of the exposure.  Epidemiologic evidence (presumably the RR or other risk ratio) provides a lower bound on the probability of causation.  I take up this suggestion in discussing Broadbent’s distinction between the “excess fraction,” and the “etiologic fraction,” below.

2. A RR > 2 “can be used to prove causation when there is no other evidence; but RR < 2 does not disprove causation.” (My emphasis.) When an author is usually clear about his qualifications, and his language generally, it is distressing for him to start comparing apples to oranges.  Note that RR > 2 suffices “when there is no other evidence,” but the parallel statement about RR < 2 is not similarly qualified, and the statement about RR < 2 is framed in terms of disproof of causation. Even if the RR < 2 did not “disprove” specific causation, when there was no other evidence, it would not prove causation.  And if there is no other evidence, judgment for the defense must result. Broadbent fails to provide us a persuasive scenario in which a RR ≤ 2, with no other evidence, would support an inference of specific causation.

Etiological Fraction vs. Excess Fraction — Occam’s Disposable Razor

Broadbent warns that the expression “attributable risk” (AR or “attributable fraction,” AF) is potentially misleading.  The numerical calculation identifies the excess number of cases, above “expected” per base rate, and proceeds from there.  The AR thus identifies the “excess fraction,” and not the “etiological fraction,” which is the fraction of all cases in which exposure makes a contribution. Broadbent tells us that:

“Granted a sound causal inference, we can infer that all the excess cases are caused by the exposure. But we cannot infer that the remaining cases are not caused by the exposure. The etiologic fraction—the cases in which the exposure makes a causal contribution—could be larger. Roughly speaking, this is because, in the absence of substantive biological assumptions, it is possible that the exposure could contribute to cases that would have occurred12 even without the exposure.13 For example, it might be that smoking is a cause of lung cancer even among some of those who would have developed it anyway. The fact that a person would have developed lung cancer anyway does not offer automatic protection against the carcinogenic effects of cigarette smoke (a point we return to in Section IV).”

Id. at 241. In large measure here, Broadbent has adopted (and acknowledged) his borrowings from Professor Sander Greenland.  Id. at 242 n.11. The argument  still fails.  What Broadbent has interposed is a “theoretical possibility” that the exposure in question may contribute to those cases that would have occurred anyway.  Note that raising theoretical possibilities here now alters the hypothetical; Broadbent is no longer working from a hypothetical that we have a RR and no other evidence.  Even more important, we are left guessing what it means to say that an exposure causes some cases that would have occurred anyway.  If we accept the postulated new evidence at face value, we can say confidently that the exposure is not the “but for” cause of the case at issue.  Without sufficient evidence of “but for” causation, plaintiff will lose. Furthermore, we are being told to add a new fact to the hypothetical, namely that the non-excess cases are causally over-determined.  If this is the only additional new fact being added, a court might invoke the rule in Summers v. Tice, but even so, the defense will be entitled to a directed verdict if the RR < 2. (If the RR = 2, I suppose, the new fact, and the change in the controlling rule, might alter the result.)

Exposures that Cause Some and Prevent Some Cases of Disease

Broadbent raises yet another hypothetical possibility, which adds to, and materially alters,  his original hypothetical.  If the exposure in question, causes some cases, and prevents others, then the RR ≤ 2 will not permit us to infer that a given case is less likely than not the result of the exposure.  (Broadbent might have given an example of what he had in mind, from well-established biological causal relationships; I am skeptical that he would have found one that would have satisfactorily made his argument.) The bimodal distribution of causal effects is certainly not typical of biological processes, but even if we indulge the “possibility,” we are now firmly in the realm of speculation.  This is a perfectly acceptable realm for philosophers, but in court, we want evidence.  Assuming that the claimant could present such evidence, finders of fact would still founder because the new evidence would leave them guessing whether the claimant was a person who would have gotten the disease anyway, or got it because of the exposure, or even got it in spite of the exposure.

Many commentators who urge a “probability of [specific] causation” approach equate the probability of causation (PC) with the AR.  Broadbent argues that because of the possibility that some biological model results in the etiologic fraction exceeded the excess fraction, the usual equation of PC = AR, must be represented as an equality:


While the point is logically unexceptional, Broadbent must concede that some other evidence, which supports and justifies the postulated biological model, is required to change the equality to an inequality.  If no other evidence besides the RR is available, we are left with the equality.  Broadbent tells us that the biological model “often” requires that the etiological fraction exceeds the excess fraction, but he never tells us how often, or how we would ascertain the margin of error.  Id. at 256.

Broadbent does not review any of the decided judicial cases to point out which ones involved biological models that invalidated the equality.  Doing so would be an important exercise because it might well show that even where PC ≥ AR, with a non-quantified upper bound, the plaintiff might still fail in presenting a prima facie case of specific causation.  Suppose the population RR for the exposure in question were 1.1, and we “know” (and are not merely speculating) that the etiological fraction > excess fraction.   Unless we know how much greater is the etiological fraction, such that we can recalculate the PC, then we are left agnostic about specific causation.

Broadbent treats us to several biological scenarios in which PC possibly is greater than AR.  All of these scenarios violate his starting premiss that we have a RR with no other evidence. For instance, Broadbent hypothesizes that exposure might accelerate onset of a disease.  Id. at 256. This biological model of acceleration can be established with the same epidemiologic evidence that established the RR for the population.  Epidemiologists will frequently look at time windows from onset of exposure to explore whether there is an acceleration of onset of cases in a younger age range that offsets a deficit later in the lives of the exposed population.  If there were firm evidence of such a phenomenon, then we would look to the RR within the relevant time window.  If the relevant RR ≤ 2, the biological model will have added nothing to the plaintiff’s case.

Broadbent cites Greenland for the proposition that PC > AR:

“We know of no cancer or other important chronic disease for which current biomedical knowledge allows one to exclude mechanisms that violate the assumptions needed to claim that PC = [AF].”

Id. at 259, quoting form Sander Greenland & James Robins, “Epidemiology, Justice, and the Probability of Causation,” 40 Jurimetrics J. 321, 325 (2000).  Here, not only has Broadbent postulated a mechanism that makes PC > AR, but he has shifted the burden of proof to the defense to exclude it!

The notion that the etiological fraction may exceed the excess fraction is an important caveat.  Courts and lawyers should take note.  It will not do, however, wave hands and exclaim that the RR > 2 is not a “litmus test,” and proceed to let any RR > 1, or even RR ≤ 1 support a verdict.  The biological models that may push the etiological fraction higher than the excess fraction can be tested, and quantified, with the same epidemiologic approaches that provided a risk ratio, in the first place.  Broadbent gives us an example of this sort of hand waving:

“Thus, for example, evidence that an exposure would be likely to aggravate an existing predisposition to the disease in question might suffice, along with RR between 1 and 2, to make it more likely than not that the claimant’s disease was caused by the exposure.”

Id. at 275. This is a remarkable, and unsupported claim.  The magnitude of the aggravation might still leave the RR ≤ 2.  What is needed is evidence that would allow quantification of the risk ratio in the scenario presented. Speculation will not do the trick; nor will speculation get the case to a jury, or support a verdict.


Call for Evidence-Based Medicine in Medical Expert Opinions

October 30th, 2012

Evidence-based medicine (EBM) seeks to put health care decision making on a firm epistemic foundation, rather than on the personal opinion of health care providers.  David Sackett, et al., “Evidence based medicine: what it is and what it isn’t,” 312 Brit. Med. J. 71 (1996).  EBM thus offers a therapeutic intervention, sometimes in the form of strong medicine, to the sloppy thinking, intuition, mothers’ hunches, and leveling of studies that remain prevalent in the Rule 702 gatekeeping of medical causation opinion testimony in courts.  There are some who have suggested that EBM addresses therapeutic interventions only, and not disease causation by exogenous substances or processes.  A very recent publication in the Tort Trial & Insurance Practice Law Journal provides a strong rebuttal to the naysayers and a clear articulation of the need now, more than ever, for greater acknowledgment of EBM in the evaluation of expert witness opinion testimony.  Terence M. Davidson & Christopher P. Guzelian, “Evidence-based Medicine (EBM): The (Only) Means for Distinguishing Knowledge of Medical Causation from Expert Opinion in the Courtroom,” 47 Tort Trial & Ins. Practice L. J. 741 (2012) [cited as Davidson].

Terence M. Davidson is a physician, a Professor of Surgery, and the Associate Dean for Continuing Medical Education at the University of California, San Diego School of Medicine.  Christopher P. Guzelian   is an Assistant Professor of Law at Thomas Jefferson School of Law, in San Diego, California. Davidson and Guzelian bring the Rule 702 discussion and debate back to the need for epistemic warrant, not glitz, glamour, hunches, prestige, and the like.  Their article is a valuable contribution, and the authors’ presentation and defense of EBM in the gatekeeping process is commendable.

There are some minor dissents I would offer.  For instance, in applying EBM principles to causation of harm assessments, we should recognize that there are asymmetries between determining therapeutic benefit and environmental or occupational harm.  Physicians, even those practicing EBM, may well recommend removal from a potentially toxic exposure because the very nature of their clinical judgment is often precautionary.  Tamraz v. BOC Group Inc., No. 1:04-CV-18948, 2008 WL 2796726 (N.D. Ohio July 18, 2008) (denying Rule 702 challenge to treating physician’s causation opinion), rev’d sub nom., Tamraz v. Lincoln Elec. Co., 620 F.3d 665, 673 (6th Cir. 2010) (carefully reviewing record of trial testimony of plaintiffs’ treating physician; reversing judgment for plaintiff based in substantial part upon treating physician’s speculative causal assessment created by plaintiffs’ counsel; “Getting the diagnosis right matters greatly to a treating physician, as a bungled diagnosis can lead to unnecessary procedures at best and death at worst. But with etiology, the same physician may often follow a precautionary principle: If a particular factor might cause a disease, and the factor is readily avoidable, why not advise the patient to avoid it? Such advice—telling a welder, say, to use a respirator—can do little harm, and might do a lot of good. This low threshold for making a decision serves well in the clinic but not in the courtroom, where decision requires not just an educated hunch but at least a preponderance of the evidence.”) (internal citations omitted), cert. denied, ___ U.S. ___ , 131 S. Ct. 2454, 2011 WL 863879 (2011).

The wisdom of the Tamraz decision (in the 6th Circuit) lies in its recognition of the asymmetries involved in medical decision making.  For most diseases, physicians rarely have to identify an etiology to select efficacious treatment.  This asymmetry affects the general – specific causation distinction.  A physician will want some epistemic warrant for the judgment that a therapy or medication is efficacious.  In other words, the physician needs to know that there is efficacy, even though the intervention may not be efficacious in every case.  If the risk ratio for an intervention (where the risk is cure of the disease or disorder), is greater than 1.0, and chance, bias, and confounding are eliminated as explanations for the observed efficacy, then that intervention likely goes into the physician’s therapeutic armamentarium.  The risk ratio, of course, need not be greater than two for the intervention to remain clinically attractive.  Furthermore, if the therapy is provided, and the patient improves, the determination whether therapy itself was efficacious is often not a pressing clinical matter.  After all, if the risk ratio was greater than one, but two or less, then the improvement may have been spontaneous and unrelated to therapy.

Davidson and Guzelian do not fully recognize this asymmetry, which leads the authors into error.  They give an example in which a defense expert witness proferred a personal opinion about general causation of breast cancer by post-menopausal hormone replacement therapy, which opinion is undermined and contradicted by a judgment reached with EBM principles.  See Cross v. Wyeth Pharm., Inc., 2011 U.S. Dist. LEXIS 89078, at *10 (M.D. Fla. Aug. 10, 2011).  Fair enough, but Davidson and Guzelian then claim that the errant defense expert had no basis for claiming that there was no generally accepted basis for “diagnosing specific medical causation.” Davidson at 757.  The authors go even further and claim that the defense expert’s statement is “simply false.” Id.

I would suggest that the authors have gotten this dead wrong.  In this sort of case, the plaintiff’s expert witness is usually the one casting about for a basis to support specific attribution.  The authors offer no basis for their judgment that the defense expert witness is wrong, or lacks a basis for his specific causation judgment. The poor, pilloried defense expert was, in the cited case, opining that there was no way to attribute a particular patient’s breast cancer to her prior use of post-menopausal hormone replacement therapy.  Putting aside the possibility of long-term use (with risk ratio greater than 2.0), the expert’s opinion is reasonable. General causation does not logically or practically imply specific causation; they are separate and distinct determinations.  Perhaps a high risk ratio might justify a probabilistic inference that the medication caused the specific patient’s breast cancer, but for many HRT-use factual scenarios, the appropriate risk ratio is two or less.  If there is some other method Davidson and Guzelian have in mind, they should say so. The authors miss an important point, which is that EBM sets out to provide a proper foundation for judgments of causality (whether of therapeutic benefit or harm), but it often does not have the epistemic foundation to provide a resolution of the individual causation issue. In medicine, there often is simply no need to do so.

One other nit.  The authors briefly discuss statistical significance, citing the Supreme Court’s recent foray into statistical theory.  Davidson at 747 & n. 14 (citing Matrixx Initiatives, Inc. v. Siracusano, 131 S. Ct. 1309, 1321 (2011)).  In their explanatory parenthetical, however, the authors describe the case as “holding that a lack of statistical significance in a pharmaceutical company’s results does not exempt the company from material disclosure requirements for reporting adverse events during product testing.”  Id. 

Matrixx Initiatives held no such thing; the Supreme Court was faced with an adequacy of pleadings case. No evidence was ever offered; nor was there any ruling on the reliability or insufficiency of evidence of causation. Matrixx Initiative’s attempt to import Rule 702 principles of reliability into a motion to dismiss on the pleadings was seriously misguided. Even assuming that statistical significance was necessary to causation, regulatory action did not require a showing of causality. Therefore, statistical significance was never necessary for the plaintiffs’ case. Second, the company’s argument that the adverse event reports at issue were “not statistically significant” was fallacious because adverse event reports, standing alone, could not be “statistically significant” or “insignificant.” The company would need to know the expected base rate for anosmia among Zicam users, and it would need to frame the adverse event reports in terms of an observed rate, so that the expected and observed rates could be compared against an assumption of no difference. Third, the class plaintiffs had alleged considerably more than just the adverse events, and the allegations taken together deserved the attention of a reasonable investor.  Bottom line:  the comments that the Court made about the lack of necessity for statistical significance were pure obiter dictum.

Highlighting these two issues in the Davidson & Guzelian article should not detract from the importance of the authors’ general enterprise. There is an aversion to examining the “epistemic warrant” behind opinion evidence in federal court gatekeeping.  Anything that treats that aversion, such as Davidson & Guzelian’s article, is good medicine.

Old-Fashioned Probablism – Origins of Legal Probabilism

October 26th, 2012

In several posts, I have addressed Professor Haack’s attack on legal probabilism.  See

Haack Attack on Legal Probabilism (May 6, 2012).  The probabilistic mode of reasoning is not a modern innovation; nor is the notion that the universe is entirely determined, although revealed to humans as a stochastic phenomenon:

“I returned, and saw under the sun, that the race is not to the swift, nor the battle to the strong, neither yet bread to the wise, nor yet riches to men of understanding, nor yet favour to men of skill; but time and chance happeneth to them all.”

Ecclesiastes 9:11 King James Bible (Cambridge ed.)

The Old Testament describes the “casting of lots,” some sort of dice rolling or coin flipping, in a wide variety of human decision making.  The practice is described repeatedly in the Old Testament, and half a dozen times in the New Testament.

Casting of lots figures more prominently in the Old Testament, in the making of important decisions, and in attempting to ascertain “God’s will.”  The Bible describes matters of inheritance, Numbers 34:13; Joshua 14:2, and division of property, Joshua 14-21, Numbers 26:55, as decided by lots.  Elections to important office, including offices and functions in the Temple, were determined by lot. 1 Chronicles 24:5, 31; 25:8-9; 26:13-14; Luke 1:9.

Casting lots was an early form of alternative dispute resolution – alternative to slaying and smiting.  Proverbs describes the lot as used as a method to resolve quarrels.  Proverbs 18:18.  Lot casting determined fault in a variety of situations.  Lots were cast to identify the culprit who had brought God’s wrath upon Jonah’s ship. Jonah 1:7 (“Come, let us cast lots, that we may know on whose account this evil has come upon us.”).

What we might take as a form of gambling appeared to have been understood by the Israelites as a method for receiving instruction from God. Proverbs 16:33 (“The lot is cast into the lap, but its every decision is from the Lord.”).  This Old Testament fortune cookie suggests that the Lord knows the outcome of the lot casting, but mere mortals must wager.  I like to think the passage means that events that appear to be stochastic to humans may have a divinely determined mechanism.  In any event, the Bible describes various occasions on which lots were cast to access the inscrutable intentions and desires of the Lord.  Numbers 26:55; 33:54; 34:13; 36:2; Joshua 18:6-10; 1 Chronicles 24:5,31; 1 Samuel 14:42; Leviticus 16:8-10 (distinguishing between sacrificial and scape goat).

In the New Testament, the Apostles cast lots to decide upon a replacement for Judas (Acts 1:26). Matthias was the winner.  Matthew, Mark, and John describe Roman soldiers casting lots for Jesus’ garments (Matthew 27:35; Mark 15:24; John 19:24.  See also Psalm 22:18.  This use of lots by the Roman soldiers seems to have taken some of the magic out of lot casting, which fell into disrepute and gave way to consultations with the Holy Spirit for guidance on important decisions.

The Talmud deals with probabilistic inference in more mundane settings.  The famous “Nine Shops” hypothetical poses 10 butcher shops in a town, nine of which sell kosher meat.  The hypothetical addresses whether the dietary laws permit eating a piece of meat found in town, when its butchering cannot be attributed to either the nine kosher shops or the one non-kosher shop:

“A typical question involves objects whose identity is not known and reference is made to the likelihood that they derive from a specific type of source in order to determine their legal status, i.e. whether they be permitted or forbidden, ritually clean or unclean, etc. Thus, only meat which has been slaughtered in the prescribed manner is kasher, permitted for food. If it is known that most of the meat available in a town is kasher, there being, say, nine shops selling kasher meat and only one that sells non-kasher meat, then it can be assumed when an unidentified piece of meat is found in the street that it came from the majority and is therefore permitted.”

Nachum L. Rabinovitch, “Studies in the History of Probability and Statistics.  XXII Probability in the Talmud,” 56 Biometrika 437, 437 (1969).  Rabinovitch goes on to describe the Talmud’s resolution of this earthly dilemma:  “follow the majority” or the most likely inference.

A small digression on this Talmudic hypothetical.  First, why not try to find out whether someone has lost this package of meat? Or turn the package in to the local “lost and found.” Second, how can it be kosher to eat a piece of meat found lying around in the town?  This is really not very appetizing, and it cannot be good hygiene.  Third, why not open the package and determine whether it’s a nice pork tenderloin or a piece of cow?  This alone could resolve the issue. Fourth, the hypothetical posed asks us to assume a 9:1 ratio of kosher to non-kosher shops, but what if the one non-kosher shop had a market share equal to the other nine? The majority rule could lead to an untoward result for those who wish to keep kosher.

The Talmud’s proposed resolution is, nevertheless, interesting in anticipating the controversy over the use of “naked statistical inferences” in deciding specific causation or discrimination cases.  Of course, the 9:1 ratio is sufficiently high that it might allow an inference about the “likely” source of the meat.  The more interesting case would have been a town with 11 butcher shops, six of which were kosher.  Would the rabbis of old have had the intestinal fortitude to eat lost & found meat, on the basis of a ratio of 6:5?

In the 12th century, Maimonides rejected probabilistic conclusions for assigning criminal liability, at least where the death penalty was at issue:

“The 290th Commandment is a prohibition to carry out punishment on a high probability, even close to certainty . . .No punishment [should] be carried out except where . . . the matter is established in certainty beyond any doubt, and , moreover, it cannot be explained otherwise in any manner.  If we do not punish on very strong probabilities, nothing can happen other than a sinner be freed; but if punishment be done on probability and opinion it is possible that one day we might kill an innocent man — and it is better and more desirable to free a thousand sinners, than ever kill one innocent.”

Stephen E. Fienberg, ed., The Evolving Role of Statistical Assessments as Evidence in the Courts 213 (N.Y. 1989), quoting from Nachum Rabinovitch, Probability and Statistical Inference in Ancient and Medieval Jewish Literature 111 (Toronto 1973).

Indiana Senate candidate and theocrat, Republican Richard E. Mourdock, recently opined that conception that results from rape was God’s will:

“I’ve struggled with it myself for a long time, but I came to realize that life is that gift from God.  And even when life begins in that horrible situation of rape, that it is something that God intended to happen.”

Jonathan Weisman, “Rape Remark Jolts a Senate Race, and the Presidential One, Too,” N.Y. Times (Oct. 25, 2012 ).

Mourdock’s comments about pregnancies resulting from rape representing God’s will show that stochastic events continue to be interpreted as determined mechanistic events at some “higher plane.” Magical thinking is still with us.

Origins of the Relative Risk of Two Argument for Specific Causation

October 20th, 2012

In an unpublished paper, which Professor Susan Haack has presented several times over the last few years, she has criticized the relative risk [RR] >2 argument.  In these presentations, Haack has argued that the use of RR to infer specific causation is an example of flawed “probabilism” in the law.  Susan Haack, “Risky Business:  Statistical Proof of Individual Causation,” in Jordi Ferrer Beltrán, ed., Casuación y atribución de responsibilidad (Madrid: Marcial Pons, forthcoming)[hereafter Risky Business]; Presentation at the Hastings Law School (Jan. 20, 2012);  Presentation at University of Girona (May 24, 2011).  Elsewhere, Haack has criticized the use of relative risks for inferring specific causation on logical grounds.  See, e.g., Susan Haack, “Warrant, Causation, and the Atomism of Evidence Law,” 5 Episteme 253, 261 (2008)[hereafter “Warrant“];  “Proving Causation: The Holism of Warrant and the Atomism of Daubert,” 4 J. Health & Biomedical Law 273, 304 (2008)[hereafter “Proving Causation“].  (See Schachtman, “On the Importance of Showing Relative Risks Greater Than Two – Haack’s Arguments” (May 23, 2012) (addressing errors in Haack’s analysis).

In “Risky Business,” Haack describes the RR > 2 argument as the creation of government lawyers from the litigation over claims of Guillain-Barré syndrome (GBS), by patients who had received swine flu vaccine.  Like her logical analyses, Haack’s historical description is erroneous.  The swine flu outbreak of 1976, indeed, had led to a federal governmental immunization program, which in turn generated claims that the flu vaccine caused GBS.  Litigation, of course, ensued.  The origins of the RR > 2 argument, however, predate this litigation.

GBS is an auto-immune disease of the nervous system.  The cause or causes of GBS are largely unknown. In the GBS vaccine cases, the government took the reasonable position that treating physicians or clinicians have little or nothing to contribute to understanding whether the swine-flu vaccine can cause GBS or whether the vaccine caused a particular patient’s case.  Cook v. United States, 545 F. Supp. 306 (N.D. Cal. 1982); Iglarsh v. United States, No. 79 C 2148, 1983 U.S. Dist. Lexis 10950 (N.D. Ill. Dec. 9, 1983).  The government did, however, concede that cases that arose within 10 weeks of vaccination were more likely than not related on the basis of surveillance data from the Centers for Disease Control.  After 10 weeks, the relative risk dropped to two or less, and thus the plaintiffs who developed GBS 10 weeks, or more, after immunization were more likely than not idiopathic cases (or at least non-vaccine cases).  See Michael D. Green, “The Impact of Daubert on Statistically Based Evidence in the United States,” Am. Stat. Ass’n, Proc. Comm. Stat. Epidem. 35, 37-38 (1998) (describing use of probabilistic evidence in the GBS cases).

Haack’s narrative of the evolution of the RR > 2 argument creates the impression that the government lawyers developed their defense out of thin air.  This impression is false.  By the time, the Cook and Iglarsh cases were litigated, the doubling of risk notion had been around for decades in the medical literature on radiation risks and effects.  Ionizing radiation had been shown to have genetic effects, including cancer risk, in the 1920’s.  By the time of the Manhattan project, radiation was a known cause of certain types of cancer. Although there was an obvious dose-response relationship between radiation and cancer, the nature of the relationship and the existence of thresholds were not well understood.  Medical scientists, aware that there were background mutations and genetic mistakes, thus resorted to a concept of a “doubling dose” to help isolate exposures that would likely be of concern.  See, e.g., Laurence L. Robbins, “Radiation Hazards:  III. Radiation Protection in Diagnostic Procedures,” 257 New Engl. J. Med. 922, 923 (1957) (discussing doubling dose in context of the medical use of radiation).

By 1960, the connection between “doubling dose” and a legal “more likely than not” evidentiary standard was discussed in the law review literature.  See, e.g., Samuel D. Estep, “Radiation Injuries and Statistics: The Need for a New Approach to Injury Litigation, 59 Mich. L. Rev. 259 (1960).  If the doubling dose concept was not obviously important for specific causation previously, Professor Estep made it so in his lengthy law review article.  By 1960, the prospect of litigation over radiation-induced cancers, which had a baseline prevalence in the population, was a real threat.  Estep described the implications of the doubling dose:

“This number is known technically as the doubling dose and has great legal significance under existing proof rules.”

Id. at 271.

* * *

“The more-probable-than-not test surely means simply that the trier of fact must find that the chances that defendant’s force caused the plaintiff’s injuries are at least slightly better than 50 percent; or, to put it the other way, that the chances that all other forces or causes together could have caused the injury are at least no greater than just short of 50 percent. Even if such an analysis is inapplicable to other types of cases, in those cases in which the only proof of causal connection is a statistical correlation between radiation dose and injury, the only just approach is to use a percentage formula. This is the case with all nonspecific injuries, including leukemia. Under existing rules the only fair place to draw the line is at 50 percent. These rules apply when the injury is already manifested as of the time of trial.”

Id. at 274.

The RR >2 argument was also percolating through the biostatistical and epidemiologic communities before the Cook and Iglarsh cases.  For instance, Philip Enterline,  a biostatistician at the University of Pittsburgh, specifically addressed the RR > 2 argument in a 1980 paper:

“The purpose of this paper is to illustrate how epidemiologic data can be used to make statements about causality in a particular case.” 

* * *

“In summary, while in a given instance we cannot attribute an individual case of disease to a particular occupational exposure, we can, based on epidemiologic observation, make a statement as to the probability that a particular occupational exposure was the cause.  Moreover, we can modify this probability by taking into consideration various aspects of a particular case.” 

Philip Enterline, “Attributability in the Face of Uncertainty,” 78 (Supp.) Chest 377, 377, 378 (1980).

About the time of the Cook case, the scientific media discussed Enterline’s suggestion for using epidemiologic data to infer specific causation.  See, e.g., Janet Raloff, “Compensating radiation victims,” 124 Science News 330 (1983).  Dr. David Lilienfeld, son of the well-known epidemiologist Abraham Lilienfeld, along with a lawyer, further popularized the use of attributable risk, derived from a relevant RR to quantify the probability that an individual case is causally related to an exposure of interest.  See David Lilienfeld & Bert Black, “The Epidemiologist in Court,” 123 Am. J. Epidem. 961, 963 (1986) (describing how a relative risk of 1.5 allows an inference of attributable risk of 33%, which means any individual case is less likely than not to causally related to the exposure).

In the meanwhile, the RR argument picked up support from other professional epidemiologists.  In 1986, Dr. Otto Wong explained that for many common cancers, tied to multiple non-specific risk factors, probabilistic reasoning was the only way to make a specific attribution:

“In fact, all cancers have multiple causes. Furthermore, clinical features of cancer cases, caused by different risk factors, are seldom distinguishable from one another. Therefore, the only valid scientific way to address causation in a specific individual is through use of probability.”

Otto Wong, “Using Epidemiology to Determine Causation in Disease,” 3 Natural Resources & Env’t 20, 23 (1988).  The attributable risk [AR], derived from the RR, was the only rational link that could support attribution in many cases:

“For AR [attributable risk] to be greater than 50% (more likely than not), RR has to be greater than 2.  Thus, for any exposure with a RR of less than 2, the cancer cannot be attributed to that exposure according to the ‘more likely than not’ criterion.  That is, that cancer is ‘more likely than not’ a background case.”


“The epidemiologic measure for probability of causation is attributable risk, which can be used to determine whether a particular cause in an individual case meets the ‘more likely than not’ criterion.”

Id. at 24.

In 1988, three Canadian professional epidemiologists described the acceptance of the use of epidemiologic data to attribute bladder cancer cases in the aluminum industry. Ben Armstrong, Claude Tremblay, and Gilles Theriault, “Compensating Bladder Cancer Victims Employed in Aluminum Reduction Plants,” 30 J. Occup. Med. 771 (1988).

The use of the RR > 2 argument was not a phenomenon limited to defense counsel or defense-friendly expert witnesses.  In 1994, a significant textbook, edited by two occupational physicians who were then and now associated with plaintiffs’ causes, explicitly embraced the RR argument. Mark R. Cullen & Linda Rosenstock, “Principles and Practice of Occupational and Environmental Medicine,” chap. 1, in Linda Rosenstock & Marc Cullen, eds., Textbook of Clinical Occupational and Environmental Medicine 1 (Phila. 1994) [Cullen & Rosenstock].

The editors of this textbook were also the authors of the introductory chapter, which discussed the RR > 2 argument.  The first editor-author, Mark R. Cullen,  is now a Professor of Medicine in Stanford University’s School of Medicine.  He is a member of the Institute of Medicine (IOM). Professor Cullen has been involved in several litigations, almost always on the plaintiffs’ side.  In the welding fume litigation, Cullen worked on a plaintiff-sponsored study of Mississippi welders.  Linda Rosenstock was the director for the National Institute for Occupational Safety and Health (NIOSH) from 1994 through 2000. Dr. Rosenstock left NIOSH to become the dean of the University of California, Los Angeles School of Public Health.  She too is a member of the IOM.  Here is how Cullen and Rosenstock treat the RR > 2 argument in their textbook:

“In most workers’ compensation and legal settings, one of the physician’s roles in OEM [occupational and environmental medicine] practice is to establish whether or not it is probable (greater, than 50% likelihood) that the patient’s injury or disease is occupationally or environmentally related. Physicians, whose standards of scientific certainty are usually considerably higher than those of the legal field (for example, often at the 95% level that an observed association did not occur by chance), need to appreciate that a disease may be deemed work related (i.e., in legal jargon, with medical certainty or more probable than not) even when there remains significant uncertainty (up to 50%) about this judgment.

Epidemiologic or population-based data may be used to provide evidence of both the causal relationship between an exposure and an outcome and the likelihood that the exposure is related to the outcome in an individual case. *** Although they are not fully conclusive, well-performed and interpreted epidemiologic studies can play an important role in determining the work-relatedness of disease in a person, using some of the additional guidelines below.”


“The concept of attributable fraction, known by many names, including attributable risk and etiologic fraction, has particular utility in determining the likelihood of importance of a hazardous exposure. Although these numbers refer to risks in groups, as shown in the following section, reasonable extrapolations from these numbers can often be made about risks in individuals.”

Cullen & Rosenstock at 13. Cullen & Rosenstock work through an easy example and discuss its implications:

“For example, if all the members of a population are exposed to a factor, and there is a RR of 5 of disease in relation to the factor, then the PAR = 80% (= (5 – 1)/5 X 100). If exposures and other population characteristics are similar in a second population, then it also can be assumed that this factor will account for 80% of cases of the disease. A short conceptual leap can be made to individual attribution:  if an affected individual is similar (e.g., in age and gender) to those in the population and is similarly exposed (e.g., similar duration, intensity, and latency), then there is an 80% likelihood that the factor caused the disease in that individual.”


“By this reasoning of assuming that all in a population are exposed and the relative risk is greater that [sic] 2, then the PAR [population attributable risk] is greater than 50% (where PAR = (2 – 1)/2 X 100%).  Accordingly, if an affected individual is similar to the population in a study that has demonstrated a RR ≥  2, then the legal test (that there is a greater than 50% likelihood that the factor caused disease) can be met.”


“In cases in which the relative risks are stable (i.e., very narrow confidence intervals) and the patient is typical of the population studied, one can state these individual attributable risks with some assurance that they are valid estimates. When the studies are of limited power or give varying results, or if the patient’s exposure cannot be easily related to the study population., caution in using this method is appropriate.”

Cullen & Rosenstock at 13-14. Cullen and Rosenstock embraced probabilistic evidence because they understood that antipathy to probabilistic inference meant that there could be no rational basis for supporting recoveries in the face of known hazards that carried low relative risks (greater than 2).  The “conceptual leap” these authors described is small compared to the unbridgeable analytical gaps that result from trying to infer specific causation from clinicians’ hunches.