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

Let’s Require Health Claims to Be Evidence Based

June 28th, 2012

Litigation arising from the FDA’s refusal to approval “health claims” for foods and dietary supplements is a fertile area for disputes over the interpretation of statistical evidence. A ‘‘health claim’’ is ‘‘any claim made on the label or in labeling of a food, including a dietary supplement, that expressly or by implication … characterizes the relationship of any substance to a disease or health-related condition.’’ 21 C.F.R. § 101.14(a)(1); see also 21 U.S.C. § 343(r)(1)(A)-(B).

Unlike the federal courts exercising their gatekeeping responsibility, the FDA has committed to pre-specified principles of interpretation and evaluation. By regulation, the FDA gives notice of standards for evaluating complex evidentiary displays for the ‘‘significant scientific agreement’’ required for approving a food or dietary supplement health claim. 21 C.F.R. § 101.14. See FDA – Guidance for Industry: Evidence-Based Review System for the Scientific Evaluation of Health Claims – Final (2009).

If the FDA’s refusal to approve a health claim requires pre-specified criteria of evaluation, then we should be asking ourselves why have the federal courts failed to develop a set of criteria for evaluating health effects claims as part of its Rule 702 (“Daubert“) gatekeeping responsibilities. Why, after close to 20 years after the Supreme Court decided Daubert, can lawyers make “health claims” without having to satisfy evidence-based criteria?

Although the FDA’s guidance is not always as precise as might be hoped, it is far better than the suggestion of the new Reference Manual for Scientific Evidence (3d ed. 2011) that there is no hierarchy of evidence. See RMSE 3d at 564 & n.48 (citing and quoting idiosyncratic symposium paper that “[t]here should be no hierarchy [among different types of scientific methods to determine cancer causation]; “Late Professor Berger’s Introduction to the Reference Manual on Scientific Evidence” (Oct. 23, 2011).

The FDA’s attempt to articulate an evidence-based hierarchy is noteworthy because the agency must evaluate a wide range of evidence, from in vitro, to animal studies, to observational studies of varying kinds, to clinical trials, to meta-analyses and reviews. The FDA’s criteria are a good start, and I imagine that they will develop and improve over time. Although imperfect, the criteria are light years ahead of the situation in federal and state court gatekeeping. Unlike gatekeeping in civil actions, the FDA criteria are pre-stated and not devised post hoc. The FDA’s attempt to implement evidence-based principles in the evaluation of health claims made is a model that would much improve the Reference Manual for Scientific Evidence. See Christopher Guzelian & Philip Guzelian, “Prevention of false scientific speech: a new role for an evidence-based approach,” 27 Human & Experimental Toxicol. 733 (2008).

The FDA’s evidence-based criteria need work in some areas. For instance, the FDA’s Guidance on meta-analysis is not particularly specific or helpful:

“Research Synthesis Studies

Reports that discuss a number of different studies, such as review articles, do not provide sufficient information on the individual studies reviewed for FDA to determine critical elements such as the study population characteristics and the composition of the products used. Similarly, the lack of detailed information on studies summarized in review articles prevents FDA from determining whether the studies are flawed in critical elements such as design, conduct of studies, and data analysis. FDA must be able to review the critical elements of a study to determine whether any scientific conclusions can be drawn from it. Therefore, FDA intends to use review articles and similar publications to identify reports of additional studies that may be useful to the health claim review and as background about the substance/disease relationship. If additional studies are identified, the agency intends to evaluate them individually. Most meta-analyses, because they lack detailed information on the studies summarized, will only be used to identify reports of additional studies that may be useful to the health claim review and as background about the substance-disease relationship. FDA, however, intends to consider as part of its health claim review process a meta-analysis that reviews all the publicly available studies on the substance/disease relationship. The reviewed studies should be consistent with the critical elements, quality and other factors set out in this guidance and the statistical analyses adequately conducted.”

FDA – Guidance for Industry: Evidence-Based Review System for the Scientific Evaluation of Health Claims – Final at 10 (2009).

The dismissal of review articles as a secondary source is welcome, but meta-analyses are quantitative reviews that can add additional insights and evidence, if methodologically appropriate, by providing a summary estimate of association, sensitivity analyses, meta-regression, etc. The FDA’s guidance was applied in connection with the agency’s refusal to approve a health claim for vitamin C and lung cancer. Proponents claimed that a particular meta-analysis supported their health claim, but the FDA disagreed. The proponents sought injunctive relief in federal district court, which upheld the FDA’s decision on vitamin C and lung cancer. Alliance for Natural Health US v. Sebelius, 786 F.Supp. 2d 1, 21 (D.D.C. 2011). The district court found that the FDA’s refusal to approve the health claim was neither arbitrary nor capricious with respect to its evaluation of the cited meta-analysis:

‘‘The FDA discounted the Cho study because it was a ‘meta-analysis’ of studies reflected in a review article. FDA Decision at 2523. As explained in the 2009 Guidance Document, ‘research synthesis studies’, and ‘review articles’, including ‘most meta-analyses’, ‘do not provide sufficient information on the individual studies reviewed’ to determine critical elements of the studies and whether those elements were flawed. 2009 Guidance Document at A.R. 2432. The Guidance Document makes an exception for meta-analyses ‘that review[ ] all the publicly available studies on the substance/disease relationship’. Id. Based on the Court’s review of the Cho article, the FDA’s decision to exclude this article as a meta-analysis was not arbitrary and capricious.’’

Id. at 19.

The FDA’s Guidance was adequate for its task in the vitamin C/lung cancer health claim, but notably absent from the Guidance are any criteria to evaluate competing meta-analyses that do include “all the publicly available studies on the substance/disease relationship.” The model assumptions of meta-analyses, fixed effect versus random effects, lack of heterogeneity, as well as other considerations will need to be spelled out in advance. Still not a bad start. Implementing evidence-based criteria in Rule 702 gatekeeping has the potential to tame the gatekeeper’s discretion.

Posted in Causation, Reference Manual on Scientific Evidence, Rule 702, Scientific Evidence | Comments Off on Let’s Require Health Claims to Be Evidence Based

Meta-Meta-Analysis — The Gadolinium MDL — More Than Ix’se Dixit

June 8th, 2012

There is an tendency, for better or worse, for legal bloggers to be partisan cheerleaders over litigation outcomes. I admit that most often I am dismayed by judicial failures or refusals to exclude dubious plaintiffs’ expert witnesses’ opinion testimony, and I have been known to criticize such decisions. Indeed, I wouldn’t mind seeing courts exclude dubious defendants’ expert witnesses. I have written approvingly about cases in which judges have courageously engaged with difficult scientific issues, seen through the smoke screen, and properly assessed the validity of the opinions expressed. The Gadolinium MDL (No. 1909) Daubert motions and decision offer a fascinating case study of a challenge to an expert witness’s meta-analysis, an effective defense of the meta-analysis, and a judicial decision to admit the testimony, based upon the meta-analysis. In re Gadolinium-Based Contrast Agents Prods. Liab. Litig., 2010 WL 1796334 (N.D. Ohio May 4, 2010) [hereafter Gadolinium], reconsideration denied, 2010 WL 5173568 (June 18, 2010).

Plaintiffs proffered general causation opinions (between gadolinium contrast media and Nephrogenic Systemic Fibrosis (“NSF”), by a nephrologist, Joachim H. Ix, M.D., with training in epidemiology. Dr. Ix’s opinions were based in large part upon a meta-analysis he conducted on data in published observational studies. Judge Dan Aaron Polster, the MDL judge, itemized the defendant’s challenges to Dr. Ix’s proposed testimony:

“The previously-used procedures GEHC takes issue with are:

(1) the failure to consult with experts about which studies to include;

(2) the failure to independently verify which studies to select for the meta-analysis;

(3) using retrospective and non-randomized studies;

(4) relying on studies with wide confidence intervals; and

(5) using a “more likely than not” standard for causation that would not pass scientific scrutiny.”

Gadolinium at *23. Judge Polster confidently dispatched these challenges. Dr. Ix, as a nephrologist, had subject-matter expertise with which to develop inclusionary and exclusionary criteria on his own. The defendant never articulated what, if any, studies were inappropriately included or excluded. The complaint that Dr. Ix had used retrospective and non-randomized studies also rang hollow in the absence of any showing that there were randomized clinical trials with pertinent data at hand. Once a serious concern of nephrotoxicity arose, clinical trials were unethical, and the defendant never explained why observational studies were somehow inappropriate for inclusion in a meta-analysis.

Relying upon studies with wide confidence intervals can be problematic, but that is one of the reasons to conduct a meta-analysis, assuming the model assumptions for the meta-analysis can be verified. The plaintiffs effectively relied upon a published meta-analysis, which pre-dated their expert witness’s litigation effort, in which the authors used less conservative inclusionary criteria, and reported a statistically significant summary estimate of risk, with an even wider confidence interval. R. Agarwal, et al., ” Gadolinium-based contrast agents and nephrogenic systemic fibrosis: a systematic review and meta-analysis,” 24 Nephrol. Dialysis & Transplantation 856 (2009). As the plaintiffs noted in their opposition to the challenge to Dr. Ix:

“Furthermore, while GEHC criticizes Dr. Ix’s CI from his meta-analysis as being “wide” at (5.18864 and 25.326) it fails to share with the court that the peer-reviewed Agarwal meta-analysis, reported a wider CI of (10.27–69.44)… .”

Plaintiff’s Opposition to GE Healthcare’s Motion to Exclude the Opinion Testimony of Joachim Ix at 28 (Mar. 12, 2010)[hereafter Opposition].

Wider confidence intervals certainly suggest greater levels of random error, but Dr. Ix’s intervals suggested statistical significance, and he had carefully considered statistical heterogeneity. Opposition at 19. (Heterogeneity was never advanced by the defense as an attack on Dr. Ix’s meta-analysis). Remarkably, the defendant never advanced a sensitivity analysis to suggest or to show that reasonable changes to the evidentiary dataset could result in loss of statistical significance, as might be expected from the large intervals. Rather, the defendant relied upon the fact that Dr. Ix had published other meta-analyses in which the confidence interval was much narrower, and then claimed that he had “required” these narrower confidence intervals for his professional, published research. Memorandum of Law of GE Healthcare’s Motion to Exclude Certain Testimony of Plaintiffs’ Generic Expert, Joachim H. Ix, MD, MAS, In re Gadolinium MDL No. 1909, Case: 1:08-gd-50000-DAP Doc #: 668 (Filed Feb. 12, 2010)[hereafter Challenge]. There never was, however, a showing that narrower intervals were required for publication, and the existence of the published Agarwal meta-analysis contradicted the suggestion.

Interestingly, the defense did not call attention to Dr. Ix’s providing an incorrect definition of the confidence interval! Here is how Dr. Ix described the confidence interval, in language quoted by plaintiffs in their Opposition:

“The horizontal lines display the “95% confidence interval” around this estimate. This 95% confidence interval reflects the range of odds ratios that would be observed 95 times if the study was repeated 100 times, thus the narrower these confidence intervals, the more precise the estimate.”

Opposition at 20. The confidence interval does not provide a probability distribution of the parameter of interest; rather the distribution of confidence intervals has a probability of covering the hypothesized “true value” of the parameter.

Finally, the defendant never showed any basis for suggesting that a scientific opinion on causation requires something more than a “more likely than not” basis.

Judge Polster also addressed some more serious challenges:

“Defendants contend that Dr. Ix’s testimony should also be excluded because the methodology he utilized for his generic expert report, along with varying from his normal practice, was unreliable. Specifically, Defendants assert that:

(1) Dr. Ix could not identify a source he relied upon to conduct his meta-analysis;

(2) Dr. Ix imputed data into the study;

(3) Dr. Ix failed to consider studies not reporting an association between GBCAs and NSF; and

(4) Dr. Ix ignored confounding factors.”

Gadolinium at *24

IMPUTATION

The first point, above – the alleged failure to identify a source for conducting the meta-analysis – rings fairly hollow, and Judge Polster easily deflected it. The second point raised a more interesting challenge. In the words of defense counsel:

“However, in arriving at this estimate, Dr. Ix imputed, i.e., added, data into four of the five studies. (See Sept. 22 Ix Dep. Tr. (Ex. 20), at 149:10-151:4.) Specifically, Dr. Ix added a single case of NSF without antecedent GBCA exposure to the patient data in the underlying studies.

* * *

During his deposition, Dr. Ix could not provide any authority for his decision to impute the additional data into his litigation meta-analysis. (See Sept. 22 Ix Dep. Tr. (Ex. 20), at 149:10-151:4.) When pressed for any authority supporting his decision, Dr. Ix quipped that ‘this may be a good question to ask a Ph.D level biostatistician about whether there are methods to [calculate an odds ratio] without imputing a case [of NSF without antecedent GBCA exposure]’.”

Challenge at 12-13.

The deposition reference suggests that the examiner had scored a debating point by catching Dr. Ix unprepared, but by the time the parties briefed the challenge, the plaintiffs had the issue well in hand, citing A. W. F. Edwards, “The Measure of Association in a 2 × 2 Table,” 126 J. Royal Stat. Soc. Series A 109 (1963); R.L. Plackett, “The Continuity Correction in 2 x 2 Tables,” 51 Biometrika 327 (1964). Opposition at 36 (describing the process of imputation in the event of zero counts in the cells of a 2 x 2 table for odds ratios). There are qualms to be stated about imputation, but the defense failed to make them. As a result, the challenge overall lost momentum and credibility. As the trial court stated the matter:

“Next, there is no dispute that Dr. Ix imputed data into his meta-analysis. However, as Defendants acknowledge, there are valid scientific reasons to impute data into a study. Here, Dr. Ix had a valid basis for imputing data. As explained by Plaintiffs, Dr. Ix’s imputed data is an acceptable technique for avoiding the calculation of an infinite odds ratio that does not accurately measure association.7 Moreover, Dr. Ix chose the most conservative of the widely accepted approaches for imputing data.8 Therefore, Dr. Ix’s decision to impute data does not call into question the reliability of his meta-analysis.”

Gadolinium at *24.

FAILURE TO CONSIDER NULL STUDIES

The defense’s challenged including a claim that Dr. Ix had arbitrarily excluded studies in which there was no reported incidence of NSF. The defense brief unfortunately does not describe the studies excluded, and what, if any, effect their inclusion in the meta-analysis would have had. This was, after all, the crucial issue. The abstract nature of the defense claim left the matter ripe for misrepresentation by the plaintiffs:

“GEHC continues to misunderstand the role of a meta-analysis and the need for studies that included patients both that did or did not receive GBCAs and reported on the incidence of NSF, despite Dr. Ix’s clear elucidation during his deposition. (Ix Depo. TR [Exh.1] at 97-98). Meta-analyses such as performed by Dr. Ix and Dr. Agarwal search for whether or not there is a statistically valid association between exposure and disease event. In order to ascertain the relationship between the exposure and event one must have an event to evaluate. In other words, if you have a study in which the exposed group consists of 10,000 people that are exposed to GBCAs and none develop NSF, compared to a non-exposed group of 10,000 who were not exposed to GBCAs and did not develop NSF, the study provides no information about the association between GBCAs and NSF or the relative risk of developing NSF.”

Challenge at 37 – 38 (emphasis in original). What is fascinating about this particular challenge, and the plaintiffs’ response, is the methodological hypocrisy exhibited. In essence, the plaintiffs argued that imputation was appropriate in a case-control study, in which one cell contained a zero, but they would ignore a great deal of data in a cohort study with data. To be sure, case-control studies are more efficient than cohort studies for identifying and assessing risk ratios for rare outcomes. Nevertheless, the plaintiffs could easily have been hoisted with their own hypothetical petard. No one in 10,000 gadolinium-exposed patients developed NSF; and no one in a control group did either. The hypothetical study suggests that the rate of NSF is low and not different in the exposed and in the unexposed patients. The risk ratio could be obtained by imputing an integer for the cells containing zero, and a confidence interval calculated. The risk ratio, of course, would be 1.0.

Unfortunately, the defense did not make this argument; nor did it explore where the meta-analysis might have come out had a more even-handed methodology been taken by Dr. Ix. The gap allowed the trial court to brush the challenge aside:

“The failure to consider studies not reporting an association between GBCAs and NSF also does not render Dr. Ix’s meta-analysis unreliable. The purpose of Dr. Ix’s meta-analysis was to study the strength of the association between an exposure (receiving GBCA) and an outcome (development of NSF). In order to properly do this, Dr. Ix necessarily needed to examine studies where the exposed group developed NSF.”

Gadolinium at *24. Judge Polster, with no help from the defense brief, missed the irony of Dr. Ix’s willingness to impute data in the case-control 2 x 2 contingency tables, but not in the relative risk tables.

CONFOUNDING

Defendants complained that Dr. Ix had ignored the possibility that confounding factors had contributed to the development of NSF. Challenge at 13. Defendants went so far as to charge Dr. Ix with misleading the court by failing to consider other possible causative exposures or conditions. Id.

Defendants never identified the existence, source, and likely magnitude of confounding factors. As a result, the plaintiffs’ argument, based in the Reference Manual, that confounding was an unlikely explanation for a very large risk ratio was enthusiastically embraced by the trial court, virtually verbatim from the plaintiffs’ Opposition (at 14):

“Finally, the Court rejects Defendants’ argument that Dr. Ix failed to consider confounding factors. Plaintiffs argued and Defendants did not dispute that, applying the Bradford Hill criteria, Dr. Ix calculated a pooled odds ratio of 11.46 for the five studies examined, which is higher than the 10 to 1 odds ratio of smoking and lung cancer that the Reference Manual on Scientific Evidence deemed to be “so high that it is extremely difficult to imagine any bias or confounding factor that may account for it.” Id. at 376. Thus, from Dr. Ix’s perspective, the odds ratio was so high that a confounding factor was improbable. Additionally, in his deposition, Dr. Ix acknowledged that the cofactors that have been suggested are difficult to confirm and therefore he did not try to specifically quantify them. (Doc # : 772-20, at 27.) This acknowledgement of cofactors is essentially equivalent to the Agarwal article’s representation that “[t]here may have been unmeasured variables in the studies confounding the relationship between GBCAs and NSF,” cited by Defendants as a representative model for properly considering confounding factors. (See Doc # : 772, at 4-5.)”

Gadolinium at *24.

The real problem is that the defendant’s challenge pointed only to possible, unidentified causal agents. The smoking/lung cancer analogy, provided by the Reference Manual, was inapposite. Smoking is indeed a large risk factor for lung cancer, with relative risks over 20. Although there are other human lung carcinogens, none is consistently in the same order of magnitude (not even asbestos), and as a result, confounding can generally be excluded as an explanation for the large risk ratios seen in smoking studies. It would be easy to imagine that there are confounders for NSF, especially given that it is relatively recently been identified, and that they might be of the same or greater magnitude as that suggested for the gadolinium contrast media. The defense, however, failed to identify confounders that actually threatened the validity of any of the individual studies, or of the meta-analysis.

CONCLUSION

The defense hinted at the general unreliability of meta-analysis, with references to References Manual on Scientific Evidence at 381 (2d ed. 2000)(noting problems with meta-analysis), and other, relatively dated papers. See, e.g., John Bailar, “Assessing Assessments,” 277 Science 529 (1997)(arguing that “problems have been so frequent and so deep, and overstatements of the strength of conclusions so extreme, that one might well conclude there is something seriously and fundamentally wrong with [meta-analysis].”). The Reference Manual language carried over into the third edition, is out of date, and represents a failing of the new edition. See “The Treatment of Meta-Analysis in the Third Edition of the Reference Manual on Scientific Evidence” (Nov. 14, 2011).

The plaintiffs came forward with some descriptive statistics of the prevalence of meta-analysis in contemporary biomedical literature. The defendants gave mostly argument; there is a dearth of citation to defense expert witnesses, affidavits, consensus papers on meta-analysis, textbooks, papers by leading authors, and the like. The defense challenge suffered from being diffuse and unfocused; it lost persuasiveness by including weak, collateral issues such as claiming that Dr. Ix was opining “only” on a “more likely than not” basis, and that he had not consulted with other experts, and that he had failed to use randomized trial data. The defense was quick to attack perceived deficiencies, but it did not illustrate how or why the alleged deficiencies threatened the validity of Dr. Ix’s meta-analysis. Indeed, even when the defense made strong points, such as the exclusion of zero-event cohort studies, it failed to document that such studies existed, and that their inclusion might have made a difference.

Posted in Causation, Meta-analysis, Reference Manual on Scientific Evidence, Rule 702, statistical evidence | Comments Off on Meta-Meta-Analysis — The Gadolinium MDL — More Than Ix’se Dixit

WOE-fully Inadequate Methodology – An Ipse Dixit By Another Name

May 1st, 2012

Take all the evidence, throw it into the hopper, close your eyes, open your heart, and guess the weight. You could be a lucky winner! The weight of the evidence suggests that the weight-of-the-evidence (WOE) method is little more than subjective opinion, but why care if it helps you to get to a verdict?

The scientific community has never been seriously impressed by the so-called weight of the evidence (WOE) approach to determining causality. The phrase is vague and ambiguous; its use, inconsistent. See, e.g., V. H. Dale, G.R. Biddinger, M.C. Newman, J.T. Oris, G.W. Suter II, T. Thompson, et al., “Enhancing the ecological risk assessment process,” 4 Integrated Envt’l Assess. Management 306 (2008)(“An approach to interpreting lines of evidence and weight of evidence is critically needed for complex assessments, and it would be useful to develop case studies and/or standards of practice for interpreting lines of evidence.”); Igor Linkov, Drew Loney, Susan M. Cormier, F.Kyle Satterstrom, Todd Bridges, “Weight-of-evidence evaluation in environmental assessment: review of qualitative and quantitative approaches,” 407 Science of Total Env’t 5199–205 (2009); Douglas L. Weed, “Weight of Evidence: A Review of Concept and Methods,” 25 Risk Analysis 1545 (2005) (noting the vague, ambiguous, indefinite nature of the concept of “weight of evidence” review); R.G. Stahl Jr., “Issues addressed and unaddressed in EPA’s ecological risk guidelines,” 17 Risk Policy Report 35 (1998); (noting that U.S. Environmental Protection Agency’s guidelines for ecological weight-of-evidence approaches to risk assessment fail to provide guidance); Glenn W. Suter II, Susan M. Cormier, “Why and how to combine evidence in environmental assessments: Weighing evidence and building cases,” 409 Science of the Total Environment 1406, 1406 (2011)(noting arbitrariness and subjectivity of WOE “methodology”).

General Electric v. Joiner

Most savvy judges quickly figured out that weight of the evidence (WOE) was suspect methodology, woefully lacking, and indeed, not really a methodology at all.

The WOE method was part of the hand waving in Joiner by plaintiffs’ expert witnesses, including the frequent testifier Rabbi Teitelbaum. The majority recognized that Rabbi Teitelbaum’s WOE weighed in at less than a peppercorn, and affirmed the district court’s exclusion of his opinions. The Joiner Court’s assessment provoked a dissent from Justice Stevens, who was troubled by the Court’s undressing of the WOE methodology:

“Dr. Daniel Teitelbaum elaborated on that approach in his deposition testimony: ‘[A]s a toxicologist when I look at a study, I am going to require that that study meet the general criteria for methodology and statistical analysis, but that when all of that data is collected and you ask me as a patient, Doctor, have I got a risk of getting cancer from this? That those studies don’t answer the question, that I have to put them all together in my mind and look at them in relation to everything I know about the substance and everything I know about the exposure and come to a conclusion. I think when I say, “To a reasonable medical probability as a medical toxicologist, this substance was a contributing cause,” … to his cancer, that that is a valid conclusion based on the totality of the evidence presented to me. And I think that that is an appropriate thing for a toxicologist to do, and it has been the basis of diagnosis for several hundred years, anyway’.

* * * *

Unlike the District Court, the Court of Appeals expressly decided that a ‘weight of the evidence’ methodology was scientifically acceptable. To this extent, the Court of Appeals’ opinion is persuasive. It is not intrinsically “unscientific” for experienced professionals to arrive at a conclusion by weighing all available scientific evidence—this is not the sort of ‘junk science’ with which Daubert was concerned. After all, as Joiner points out, the Environmental Protection Agency (EPA) uses the same methodology to assess risks, albeit using a somewhat different threshold than that required in a trial. Petitioners’ own experts used the same scientific approach as well. And using this methodology, it would seem that an expert could reasonably have concluded that the study of workers at an Italian capacitor plant, coupled with data from Monsanto’s study and other studies, raises an inference that PCB’s promote lung cancer.”

General Electric v. Joiner, 522 U.S. 136, 152-54 (1997)(Stevens, J., dissenting)(internal citations omitted)(confusing critical assessment of studies with WOE; and quoting Rabbit Teitelbaum’s attempt to conflate diagnosis with etiological attribution). Justice Stevens could reach his assessment only by ignoring the serious lack of internal and external validity in the studies relied upon by Rabbi Teitelbaum. Those studies did not support his opinion individually or collectively.

Justice Stevens was wrong as well about the claimed scientific adequacy of WOE. Courts have long understood that precautionary, preventive judgments of regulatory agencies are different from scientific conclusions that are admissible in civil and criminal litigation. See Allen v. Pennsylvania Engineering Corp., 102 F.3d 194 (5th Cir. 1996)(WOE, although suitable for regulatory risk assessment, is not appropriate in civil litigation). Justice Stevens’ characterization of WOE was little more than judicial ipse dixit, and it was, in any event, not the law; it was the argument of a dissenter.

Milward v. Acuity Specialty Products

Admittedly, dissents can sometimes help lower court judges chart a path of evasion and avoidance of a higher court’s holding. In Milward, Justice Stevens’ mischaracterization of WOE and scientific method was adopted as the legal standard for expert witness testimony by a panel of the United States Court of Appeals, for the First Circuit. Milward v. Acuity Specialty Products Group, Inc., 664 F.Supp. 2d 137 (D. Mass. 2009), rev’d, 639 F.3d 11 (1st Cir. 2011), cert. denied, U.S. Steel Corp. v. Milward, ___ U.S. ___, 2012 WL 33303 (2012).

Mr. Milward claimed that he was exposed to benzene as a refrigerator technician, and developed acute promyelocytic leukeumia (APL) as result. 664 F. Supp. 2d at 140. In support of his claim, Mr. Milward offered the testimony of Dr. Martyn T. Smith, a toxicologist, who testified that the “weight of the evidence” supported his opinion that benzene exposure causes APL. Id. Smith, in his litigation report, described his methodology as an application of WOE:

“The term WOE has come to mean not only a determination of the statistical and explanatory power of any individual study (or the combined power of all the studies) but the extent to which different types of studies converge on the hypothesis.) In assessing whether exposure to benzene may cause APL, I have applied the Hill considerations . Nonetheless, application of those factors to a particular causal hypothesis, and the relative weight to assign each of them, is both context dependent and subject to the independent judgment of the scientist reviewing the available body of data. For example, some WOE approaches give higher weight to mechanistic information over epidemiological data.”

Smith Report at ¶¶19, 21 (citing Sheldon Krimsky, “The Weight of Scientific Evidence in Policy and Law,” 95(S1) Am. J. Public Health 5130, 5130-31 (2005))(March 9, 2009). Smith marshaled several bodies of evidence, which he claimed collectively supported his opinion that benzene causes APL. Milward, 664 F. Supp. 2d at 143.

Milward also offered the testimony of a philosophy professor, Carl F. Cranor, for the opinion that WOE was an acceptable methodology, and that all scientific inference is subject to judgment. This is the same Cranor who, advocating for open admissions of all putative scientific opinions, showcased his confusion between statistical significance probability and the posterior probability involved in a conclusion of causality. Carl F. Cranor, Regulating Toxic Substances: A Philosophy of Science and the Law at 33-34(Oxford 1993)(“One can think of α, β (the chances of type I and type II errors, respectively) and 1- β as measures of the “risk of error” or “standards of proof.”) See also id. at 44, 47, 55, 72-76.

After a four-day evidentiary hearing, the district court found that Martyn Smith’s opinion was merely a plausible hypothesis, and not admissible. Milward, 664 F. Supp. 2d at 149. The Court of Appeals, in an opinion by Chief Judge Lynch, however, reversed and ruled that an inference of general causation based on a WOE methodology satisfied the reliability requirement for admission under Federal Rule of Evidence 702. 639 F.3d at 26. According to the Circuit, WOE methodology was scientifically sound, Id. at 22-23.

WOE Cometh

Because the WOE methodology is not well described, either in the published literature or in Martyn Smith’s litigation report, it is difficult to understand exactly what the First Circuit approved by reversing Smith’s exclusion. Usually the burden is on the proponent of the opinion testimony, and one would have thought that the vagueness of the described methodology would count against admissibility. It is hard to escape the conclusion that the Circuit elevated a poorly described method, best characterized as hand waving, into a description of scientific method

The Panel appeared to have been misled by Carl F. Cranor, who described “inference to the best explanation” as requiring a scientist to “consider all of the relevant evidence” and “integrate the evidence using professional judgment to come to a conclusion about the best explanation. Id at 18. The available explanations are then weighed, and a would-be expert witness is free to embrace the one he feels offers the “best” explanation. The appellate court’s opinion takes WOE, combined with Cranor’s “inference to the best explanation,” to hold that an expert witness need only opine that he has considered the range of plausible explanations for the association, and that he believes that the causal explanation is the best or “most plausible.” Id. at 20 (upholding this approach as “methodologically reliable”).

What is missing of course is the realization that plausible does not mean established, reasonably certain, or even more likely than not. The Circuit’s invocation of plausibility also obscures the indeterminacy of the available data for supporting a reliable conclusion of causation in many cases.

Curiously, the Panel likened WOE to the use of differential diagnosis, which is a method for inferring the specific cause of a particular patient’s disease or disorder. Id. at 18. This is a serious confusion between a method concerned with general causation and one concerned with specific causation. Even if, by the principle of charity, we allow that the First Circuit was thinking of some process of differential etiology rather than diagnosis, given that diagnoses (other than for infectious diseases and a few pathognomonic disorders) do not usually carry with them information about unique etiologic agents. But even such a process of differential etiology is a well-structured dysjunctive syllogism of the form:

A v B v C

~A ∩ ~B

∴ C

There is nothing subjective about assigning weights or drawing inferences in applying such a syllogism. In the Milward case, one of the propositional facts that might have well explained the available evidence was chance, but plaintiff’s expert witness Smith could not and did not rule out chance in that the studies upon which he relied were not statistically significant. Smith could thus never get past “therefore” in any syllogism or in any other recognizable process of reasoning.

The Circuit Court provides no insight into the process Smith used to weigh the available evidence, and it failed to address the analytical gaps and evidentiary insufficiencies addressed by the trial court, other than to invoke the mantra that all these issues go to “the weight, not the admissibility” of Smith’s opinions. This, of course, is a conclusion, not an explanation or a legal theory.

There is also a cute semantic trick lurking in plaintiffs’ position in Milward, which results from their witnesses describing their methodology as “WOE.” Since the jury is charged with determining the “weight of the evidence,” any evaluation of the WOE would be an invasion of the province of the jury. Milward, 639 F.3d at 20. QED by the semantic device of deliberating conflating the name of the putative scientific methodology with the term traditionally used to describe jury fact finding.

In any event, the Circuit’s chastisement of the district court for evaluating Smith’s implementation of the WOE methodology, his logical, mathematical, and epidemiological errors, his result-driven reinterpretation of study data, threatens to read an Act of Congress — the Federal Rules of Evidence, and especially Rules 702 and 703 — out of existence by judicial fiat. The Circuit’s approach is also at odds with Supreme Court precedent (now codified in Rule 702) on the importance and the requirement of evaluating opinion testimony for analytical gaps and the ipse dixit of expert witnesses. General Electic Co. v. Joiner, 522 U.S. 136, 146 (1997).

Smith’s Errors in Recalculating Odds Ratios of Published Studies

In the district court, the defendants presented testimony of an epidemiologist, Dr. David H. Garabrant, who took Smith to task for calculating risk ratios incorrectly. Smith did not have any particular expertise in epidemiologist, and his faulty calculations were problematic from the perspective of both Rule 702 and Rule 703. The district court found the criticisms of Smith’s calculations convincing, 664 F. Supp. 2d at 149, but the appellate court held that the technical dispute was for the jury; “both experts’ opinions are supported by evidence and sound scientific reasoning,” Milward, 639 F.3d at 24. This ruling is incomprehensible. Plaintiffs had the burden of showing admissibility of Smith opinion generally, but also the reasonability of his reliance upon the calculated odds ratio. The defendants had no burden of persuasion on the issue of Smith’s calculations, but they presented testimony, which apparently carried the day. The appellate court had no basis for reversing the specific ruling with respect to the erroneously calculated risk ratio.

Smith’s Reliance upon Statistically Insignificant Studies

Smith relied upon studies that were not statistically significant at any accepted level. An opinion of causality requires a showing that chance, bias, and confounding have been excluded in assessing an existing association. Smith failed to exclude chance as an explanation for the association, and the burden to make this exclusion was on the plaintiffs. This failure was not something that could readily be patched by adverting to other evidence of studies in animals or in test tubes. The Court of Appeals excused the important analytical gap in plaintiffs’ witness’s opinion because APL is rare, and data collection is difficult in the United States. Id. at 24. Evidence “consistent with” and “suggestive of” the challenged witness’s opinion thus suffices. This is a remarkable homeopathic dilution of both legal and scientific causation. Now we have a rule of law that allows plaintiffs to be excused from having to prove their case with reliable evidence if they allege a rare disease for which they lack evidence.

Leveling the Hierarchy of Evidence

Imagine trying to bring a medication to market with a small case-control study, with a non-statistically significant odds ratio! Oh, but these clinical trials are so difficult and expensive; and they take such a long time. Like a moment’s thought, when thinking is so hard and a moment such a long time. We would be quite concerned if the FDA abridged the standard for causal efficacy in the licensing of new medications; we should be just as concerned about judicial abridgments of standards for causation of harm in tort actions.

Leveling the hierarchy of evidence has been an explicit or implicit goal of several law professors. Some of the leveling efforts even show up in the new Reference Manual for Scientific Evidence (RMSE 3d ed. 2011). See “New-Age Levellers – Flattening Hierarchy of Evidence.”

The Circuit, in Milward, quoted an article published in the Journal of the National Cancer Institute by Michele Carbone and others who suggest that there should be no hierarchy, but the Court ignored a huge body of literature that explains and defends the need for recognizing that not all study designs or types are equal. Interestingly, the RMSE chapter on epidemiology by Professor Green (see more below) cites the same article. RMSE 3d at 564 & n.48 (citing and quoting symposium paper that “[t]here should be no hierarchy [among different types of scientific methods to determine cancer causation]. Epidemiology, animal, tissue culture and molecular pathology should be seen as integrating evidences in the determination of human carcinogenicity.” Michele Carbone et al., “Modern Criteria to Establish Human Cancer Etiology,” 64 Cancer Res. 5518, 5522 (2004).) Carbone, of course, is best known for his advocacy of a viral cause (SV40), of human mesothelioma, a claim unsupported, and indeed contradicted, by epidemiologic studies. Carbone’s statement does not support the RMSE chapter’s leveling of epidemiology and toxicology, and Carbone is, in any event, an unlikely source to cite.

The First Circuit, in Milward, studiously ignored a mountain of literature on evidence-based medicine, including the RSME 3d chapter on “Reference Guide on Medical Testimony,” which teaches that leveling of study designs and types is inappropriate. The RMSE chapter devotes several pages to explaining the role of study design in assessing an etiological issue:

“3. Hierarchy of medical evidence

With the explosion of available medical evidence, increased emphasis has been placed on assembling, evaluating, and interpreting medical research evidence. A fundamental principle of evidence-based medicine (see also Section IV.C.5, infra) is that the strength of medical evidence supporting a therapy or strategy is hierarchical.

When ordered from strongest to weakest, systematic review of randomized trials (meta-analysis) is at the top, followed by single randomized trials, systematic reviews of observational studies, single observational studies, physiological studies, and unsystematic clinical observations.¹⁵⁰ An analysis of the frequency with which various study designs are cited by others provides empirical evidence supporting the influence of meta-analysis followed by randomized controlled trials in the medical evidence hierarchy.¹⁵¹ Although they are at the bottom of the evidence hierarchy, unsystematic clinical observations or case reports may be the first signals of adverse events or associations that are later confirmed with larger or controlled epidemiological studies (e.g., aplastic anemia caused by chloramphenicol,¹⁵² or lung cancer caused by asbestos153). Nonetheless, subsequent studies may not confirm initial reports (e.g., the putative association between coffee consumption and pancreatic cancer).¹⁵⁴“

John B. Wong, Lawrence O. Gostin, and Oscar A. Cabrera, “Reference Guide on Medical Testimony,” RMSE 3d 687, 723 -24 (2011). The implication that there is no hierarchy of evidence in causal inference, and that tissue culture studies are as relevant as epidemiology, is patently absurd. The Circuit not only went out on a limb, it managed to saw the limb off, while “out there.”

Milward – Responses Critical and Otherwise

The First Circuit’s decision in Milward made an immediate impression upon those writers who have worked hard to dismantle or marginalize Rule 702. The Circuit’s decision was mysteriously cited with obvious approval by Professor Margaret Berger, even though she had died before the decision was published! Margaret A. Berger, “The Admissibility of Expert Testimony,” RMSE 3d at 20 & n. 51(2011). Professor Michael Green, one of the reporters for the ALI’s Restatement (Third) of Torts hyperbolically called Milward “[o]ne of the most significant toxic tort causation cases in recent memory.” Michael D. Green, “Introduction: Restatement of Torts as a Crystal Ball,” 37 Wm. Mitchell L. Rev. 993, 1009 n.53 (2011).

The WOE approach, and its embrace in Milward, obscures the reality that sometimes the evidence does not logically or analytically support the offered conclusion, and at other times, the best explanation is uncertainty. By adopting the WOE approach, vague and ambiguous as it is, the Milward Court was beguiled into holding that WOE determinations are for the jury. The lack of meaningful content of WOE means that decisions such as Milward effectively remove the gatekeeping function, or permit that function to be minimally satisfied by accepting an expert witness’s claim to have employed WOE. The epistemic warrant required by Rule 702 is diluted if not destroyed. Scientific hunch and speculation, proper in their place, can be passed off for scientific knowledge to gullible or result-oriented judges and juries.

Posted in Causation, Reference Manual on Scientific Evidence, Rule 702, Rule 703, Scientific Evidence | Comments Off on WOE-fully Inadequate Methodology – An Ipse Dixit By Another Name

Confidence in Intervals and Diffidence in the Courts

March 4th, 2012

Next year, the Supreme Court’s Daubert decision will turn 20. The decision, in interpreting Federal Rule of Evidence 702, dramatically changed the landscape of expert witness testimony. Still, there are many who would turn the clock back to disabling the gatekeeping function. In past posts, I have identified scholars, such as Erica Beecher-Monas and the late Margaret Berger, who tried to eviscerate judicial gatekeeping. Recently a student note argued for the complete abandonment of all judicial control of expert witness testimony. See Note, “Admitting Doubt: A New Standard for Scientific Evidence,” 123 Harv. L. Rev. 2021 (2010)(arguing that courts should admit all relevant evidence).

One advantage that comes from requiring trial courts to serve as gatekeepers is that the expert witnesses’ reasoning is approved or disapproved in an open, transparent, and rational way. Trial courts subject themselves to public scrutiny in a way that jury decision making does not permit. The critics of Daubert often engage in a cynical attempt to remove all controls over expert witnesses in order to empower juries to act on their populist passions and prejudices. When courts misinterpret statistical and scientific evidence, there is some hope of changing subsequent decisions by pointing out their errors. Jury errors on the other hand, unless they involve determinations of issues for which there were “no evidence,” are immune to institutional criticism or correction.

Despite my whining, not all courts butcher statistical concepts. There are many astute judges out there who see error and call it error. Take for instance, the trial judge who was confronted with this typical argument:

“While Giles admits that a p-value of .15 is three times higher than what scientists generally consider statistically significant—that is, a p-value of .05 or lower—she maintains that this ‘‘represents 85% certainty, which meets any conceivable concept of preponderance of the evidence.’’ (Doc. 103 at 16).”

Giles v. Wyeth, Inc., 500 F.Supp. 2d 1048, 1056-57 (S.D.Ill. 2007), aff’d, 556 F.3d 596 (7th Cir. 2009). Despite having case law cited to it (such as In re Ephedra), the trial court looked to the Reference Manual on Scientific Evidence, a resource that seems to be ignored by many federal judges, and rejected the bogus argument. Unfortunately, the lawyers who made the bogus argument still are licensed, and at large, to incite the same error in other cases.

This business perhaps would be amenable to an empirical analysis. An enterprising sociologist of the law could conduct some survey research on the science and math training of the federal judiciary, on whether the federal judges have read chapters of the Reference Manual before deciding cases involving statistics or science, and whether federal judges expressed the need for further education. This survey evidence could be capped by an analysis of the prevalence of certain kinds of basic errors, such as the transpositional fallacy committed by so many judges (but decisively rejected in the Giles case). Perhaps such an empirical analysis would advance our understanding whether we need specialty science courts.

One of the reasons that the Reference Manual on Scientific Evidence is worthy of so much critical attention is that the volume has the imprimatur of the Federal Judicial Center, and now the National Academies of Science. Putting aside the idiosyncratic chapter by the late Professor Berger, the Manual clearly present guidance on many important issues. To be sure, there are gaps, inconsistencies, and mistakes, but the statistics chapter should be a must-read for federal (and state) judges.

Unfortunately, the Manual has competition from lesser authors whose work obscures, misleads, and confuses important issues. Consider an article by two would-be expert witnesses, who testify for plaintiffs, and confidently misstate the meaning of a confidence interval:

“Thus, a RR [relative risk] of 1.8 with a confidence interval of 1.3 to 2.9 could very likely represent a true RR of greater than 2.0, and as high as 2.9 in 95 out of 100 repeated trials.”

Richard W. Clapp & David Ozonoff, “Environment and Health: Vital Intersection or Contested Territory?” 30 Am. J. L. & Med. 189, 210 (2004). This misstatement was then cited and quoted with obvious approval by Professor Beecher-Monas, in her text on scientific evidence. Erica Beecher-Monas, Evaluating Scientific Evidence: An Interdisciplinary Framework for Intellectual Due Process 60-61 n. 17 (2007). Beecher-Monas goes on, however, to argue that confidence interval coefficients are not the same as burdens of proof, but then implies that scientific standards of proof are different from the legal preponderance of the evidence. She provides no citation or support for the higher burden of scientific proof:

“Some commentators have attributed the causation conundrum in the courts to the differing burdens of proof in science and law.²⁸ In law, the civil standard of ‘more probable than not’ is often characterized as a probability greater than 50 percent.²⁹ In science, on the other hand, the most widely used standard is a 95 percent confidence interval (corresponding to a 5 percent level of significance, or p-level).³⁰ Both sound like probabilistic assessment. As a result, the argument goes, civil judges should not exclude scientific testimony that fails scientific validity standards because the civil legal standards are much lower. The transliteration of the ‘more probable than not’ standard of civil factfinding into a quantitative threshold of statistical evidence is misconceived. The legal and scientific standards are fundamentally different. They have different goals and different measures. Therefore, one cannot justifiably argue that evidence failing to meet the scientific standards nonetheless should be admissible because the scientific standards are too high for preponderance determinations.”

Id. at 65. This seems to be on the right track, although Beecher-Monas does not state clearly whether she subscribes to the notion that the burdens of proof in science and law differ. The argument then takes a wrong turn:

“Equating confidence intervals with burdens of persuasion is simply incoherent. The goal of the scientific standard – the 95 percent confidence interval – is to avoid claiming an effect when there is none (i.e., a false positive).³¹“

Id. at 66. But this is crazy error; confidence intervals are not burdens of persuasion, legal or scientific. Beecher-Monas is not, however, content to leave this alone:

“Scientists using a 95 percent confidence interval are making a prediction about the results being due to something other than chance.”

Id. at 66 (emphasis added). Other than chance? Well this implies causality, as well as bias and confounding, but the confidence interval, like the p-value, addresses only random or sampling error. Beecher-Monas’s error is neither random nor scientific. Indeed, she perpetuates the same error committed by the Fifth Circuit in a frequently cited Bendectin case, which interpreted the confidence interval as resolving questions of the role of matters “other than chance,” such as bias and confounding. Brock v. Merrill Dow Pharmaceuticals, Inc., 874 F.2d 307, 311-12 (5th Cir. 1989)(“Fortunately, we do not have to resolve any of the above questions [as to bias and confounding], since the studies presented to us incorporate the possibility of these factors by the use of a confidence interval.”)(emphasis in original). See, e.g., David H. Kaye, David E. Bernstein, and Jennifer L. Mnookin, The New Wigmore – A Treatise on Evidence: Expert Evidence § 12.6.4, at 546 (2d ed. 2011) Michael O. Finkelstein, Basic Concepts of Probability and Statistics in the Law 86-87 (2009)(criticizing the overinterpretation of confidence intervals by the Brock court).

Clapp, Ozonoff, and Beecher-Monas are not alone in offering bad advice to judges who must help resolve statistical issues. Déirdre Dwyer, a prominent scholar of expert evidence in the United Kingdom, manages to bundle up the transpositional fallacy and a misstatement of the meaning of the confidence interval into one succinct exposition:

“By convention, scientists require a 95 per cent probability that a finding is not due to chance alone. The risk ratio (e.g. ‘2.2’) represents a mean figure. The actual risk has a 95 per cent probability of lying somewhere between upper and lower limits (e.g. 2.2 ±0.3, which equals a risk somewhere between 1.9 and 2.5) (the ‘confidence interval’).”

Déirdre Dwyer, The Judicial Assessment of Expert Evidence 154-55 (Cambridge Univ. Press 2008).

Of course, Clapp, Ozonoff, Beecher-Monas, and Dwyer build upon a long tradition of academics’ giving errant advice to judges on this very issue. See, e.g., Christopher B. Mueller, “Daubert Asks the Right Questions: Now Appellate Courts Should Help Find the Right Answers,” 33 Seton Hall L. Rev. 987, 997 (2003)(describing the 95% confidence interval as “the range of outcomes that would be expected to occur by chance no more than five percent of the time”); Arthur H. Bryant & Alexander A. Reinert, “The Legal System’s Use of Epidemiology,” 87 Judicature 12, 19 (2003)(“The confidence interval is intended to provide a range of values within which, at a specified level of certainty, the magnitude of association lies.”) (incorrectly citing the first edition of Rothman & Greenland, Modern Epidemiology 190 (Philadelphia 1998); John M. Conley & David W. Peterson, “The Science of Gatekeeping: The Federal Judicial Center’s New Reference Manual on Scientific Evidence,” 74 N.C.L.Rev. 1183, 1212 n.172 (1996)(“a 95% confidence interval … means that we can be 95% certain that the true population average lies within that range”).

Who has prevailed? The statistically correct authors of the statistics chapter of the Reference Manual on Scientific Evidence, or the errant commentators? It would be good to have some empirical evidence to help evaluate the judiciary’s competence. Here are some cases, many drawn from the Manual‘s discussions, arranged chronologically, before and after the first appearance of the Manual:

Before First Edition of the Reference Manual on Scientific Evidence:

DeLuca v. Merrell Dow Pharms., Inc., 911 F.2d 941, 948 (3d Cir. 1990)(“A 95% confidence interval is constructed with enough width so that one can be confident that it is only 5% likely that the relative risk attained would have occurred if the true parameter, i.e., the actual unknown relationship between the two studied variables, were outside the confidence interval. If a 95% confidence interval thus contains ‘1’, or the null hypothesis, then a researcher cannot say that the results are ‘statistically significant’, that is, that the null hypothesis has been disproved at a .05 level of significance.”)(internal citations omitted)(citing in part, D. Barnes & J. Conley, Statistical Evidence in Litigation § 3.15, at 107 (1986), as defining a CI as “a limit above or below or a range around the sample mean, beyond which the true population is unlikely to fall”).

United States ex rel. Free v. Peters, 806 F. Supp. 705, 713 n.6 (N.D. Ill. 1992) (“A 99% confidence interval, for instance, is an indication that if we repeated our measurement 100 times under identical conditions, 99 times out of 100 the point estimate derived from the repeated experimentation will fall within the initial interval estimate … .”), rev’d in part, 12 F.3d 700 (7th Cir. 1993)

DeLuca v. Merrell Dow Pharms., Inc., 791 F. Supp. 1042, 1046 (D.N.J. 1992)(”A 95% confidence interval means that there is a 95% probability that the ‘true’ relative risk falls within the interval”) , aff’d, 6 F.3d 778 (3d Cir. 1993)

Turpin v. Merrell Dow Pharms., Inc., 959 F.2d 1349, 1353-54 & n.1 (6th Cir. 1992)(describing a 95% CI of 0.8 to 3.10, to mean that “random repetition of the study should produce, 95 percent of the time, a relative risk somewhere between 0.8 and 3.10”)

Hilao v. Estate of Marcos, 103 F.3d 767, 787 (9th Cir. 1996)(Rymer, J., dissenting and concurring in part).

After the first publication of the Reference Manual on Scientific Evidence:

American Library Ass’n v. United States, 201 F.Supp. 2d 401, 439 & n.11 (E.D.Pa. 2002), rev’d on other grounds, 539 U.S. 194 (2003)

SmithKline Beecham Corp. v. Apotex Corp., 247 F.Supp.2d 1011, 1037-38 (N.D. Ill. 2003)(“the probability that the true value was between 3 percent and 7 percent, that is, within two standard deviations of the mean estimate, would be 95 percent”)(also confusing attained significance probability with posterior probability: “This need not be a fatal concession, since 95 percent (i.e., a 5 percent probability that the sign of the coefficient being tested would be observed in the test even if the true value of the sign was zero) is an arbitrary measure of statistical significance. This is especially so when the burden of persuasion on an issue is the undemanding ‘preponderance’ standard, which requires a confidence of only a mite over 50 percent. So recomputing Niemczyk’s estimates as significant only at the 80 or 85 percent level need not be thought to invalidate his findings.”), aff’d on other grounds, 403 F.3d 1331 (Fed. Cir. 2005)

In re Silicone Gel Breast Implants Prods. Liab. Litig, 318 F.Supp.2d 879, 897 (C.D. Cal. 2004) (interpreting a relative risk of 1.99, in a subgroup of women who had had polyurethane foam covered breast implants, with a 95% CI that ran from 0.5 to 8.0, to mean that “95 out of 100 a study of that type would yield a relative risk somewhere between on 0.5 and 8.0. This huge margin of error associated with the PUF-specific data (ranging from a potential finding that implants make a woman 50% less likely to develop breast cancer to a potential finding that they make her 800% more likely to develop breast cancer) render those findings meaningless for purposes of proving or disproving general causation in a court of law.”)(emphasis in original)

Ortho–McNeil Pharm., Inc. v. Kali Labs., Inc., 482 F.Supp. 2d 478, 495 (D.N.J.2007)(“Therefore, a 95 percent confidence interval means that if the inventors’ mice experiment was repeated 100 times, roughly 95 percent of results would fall within the 95 percent confidence interval ranges.”)(apparently relying party’s expert witness’s report), aff’d in part, vacated in part, sub nom. Ortho McNeil Pharm., Inc. v. Teva Pharms Indus., Ltd., 344 Fed.Appx. 595 (Fed. Cir. 2009)

Eli Lilly & Co. v. Teva Pharms, USA, 2008 WL 2410420, *24 (S.D.Ind. 2008)(stating incorrectly that “95% percent of the time, the true mean value will be contained within the lower and upper limits of the confidence interval range”)

Benavidez v. City of Irving, 638 F.Supp. 2d 709, 720 (N.D. Tex. 2009)(interpreting a 90% CI to mean that “there is a 90% chance that the range surrounding the point estimate contains the truly accurate value.”)

Estate of George v. Vermont League of Cities and Towns, 993 A.2d 367, 378 n.12 (Vt. 2010)(erroneously describing a confidence interval to be a “range of values within which the results of a study sample would be likely to fall if the study were repeated numerous times”)

Correct Statements

There is no reason for any of these courts to have struggled so with the concept of statistical significance or of the confidence interval. These concepts are well elucidated in the Reference Manual on Scientific Evidence (RMSE):

“To begin with, ‘confidence’ is a term of art. The confidence level indicates the percentage of the time that intervals from repeated samples would cover the true value. The confidence level does not express the chance that repeated estimates would fall into the confidence interval.91

* * *

According to the frequentist theory of statistics, probability statements cannot be made about population characteristics: Probability statements apply to the behavior of samples. That is why the different term ‘confidence’ is used.”

RMSE 3d at 247 (2011).

Even before the Manual, many capable authors have tried to reach the judiciary to help them learn and apply statistical concepts more confidently. Professors Michael Finkelstein and Bruce Levin, of the Columbia University’s Law School and Mailman School of Public Health, respectively, have worked hard to educate lawyers and judges in the important concepts of statistical analyses:

“It is the confidence limits PL and PU that are random variables based on the sample data. Thus, a confidence interval (PL, PU ) is a random interval, which may or may not contain the population parameter P. The term ‘confidence’ derives from the fundamental property that, whatever the true value of P, the 95% confidence interval will contain P within its limits 95% of the time, or with 95% probability. This statement is made only with reference to the general property of confidence intervals and not to a probabilistic evaluation of its truth in any particular instance with realized values of PL and PU. “

Michael O. Finkelstein & Bruce Levin, Statistics for Lawyers at 169-70 (2d ed. 2001)

Courts have no doubt been confused to some extent between the operational definition of a confidence interval and the role of the sample point estimate as an estimator of the population parameter. In some instances, the sample statistic may be the best estimate of the population parameter, but that estimate may be rather crummy because of the sampling error involved. See, e.g., Kenneth J. Rothman, Sander Greenland, Timothy L. Lash, Modern Epidemiology 158 (3d ed. 2008) (“Although a single confidence interval can be much more informative than a single P-value, it is subject to the misinterpretation that values inside the interval are equally compatible with the data, and all values outside it are equally incompatible. * * * A given confidence interval is only one of an infinite number of ranges nested within one another. Points nearer the center of these ranges are more compatible with the data than points farther away from the center.”); Nicholas P. Jewell, Statistics for Epidemiology 23 (2004)(“A popular interpretation of a confidence interval is that it provides values for the unknown population proportion that are ‘compatible’ with the observed data. But we must be careful not to fall into the trap of assuming that each value in the interval is equally compatible.”); Charles Poole, “Confidence Intervals Exclude Nothing,” 77 Am. J. Pub. Health 492, 493 (1987)(“It would be more useful to the thoughtful reader to acknowledge the great differences that exist among the p-values corresponding to the parameter values that lie within a confidence interval … .”).

Admittedly, I have given an impressionistic account, and I have used anecdotal methods, to explore the question whether the courts have improved in their statistical assessments in the 20 years since the Supreme Court decided Daubert. Many decisions go unreported, and perhaps many errors are cut off from the bench in the course of testimony or argument. I personally doubt that judges exercise greater care in their comments from the bench than they do in published opinions. Still, the quality of care exercised by the courts would be a worthy area of investigation by the Federal Judicial Center, or perhaps by other sociologists of the law.

Posted in Reference Manual on Scientific Evidence, Rule 702, Scientific Evidence, statistical evidence | 16 Comments »

Scientific illiteracy among the judiciary

February 29th, 2012

Ken Feinberg, speaking at a symposium on mass torts, asks what legal challenges do mass torts confront in the federal courts. The answer seems obvious.

Pharmaceutical cases that warrant federal court multi-district litigation (MDL) treatment typically involve complex scientific and statistical issues. The public deserves having MDL cases assigned to judges who have special experience and competence to preside in cases in which these complex issues predominate. There appears to be no procedural device to ensure that the judges selected in the MDL process have the necessary experience and competence, and a good deal of evidence to suggest that the MDL judges are not up to the task at hand.

In the aftermath of the Supreme Court’s decision in Daubert, the Federal Judicial Center assumed responsibility for producing science and statistics tutorials to help judges grapple with technical issues in their cases. The Center has produced videotaped lectures as well as the Reference Manual on Scientific Evidence, now in its third edition. Despite the Center’s best efforts, many federal judges have shown themselves to be incorrigible. It is time to revive the discussions and debates about implementing a “science court.”

The following three federal MDLs all involved pharmaceutical products, well-respected federal judges, and a fundamental error in statistical inference.

Avandia

Avandia is a prescription oral anti-diabetic medication licensed by GlaxoSmithKline (GSK). Concerns over Avandia’s association with excess heart attack risk resulted in regulatory revisions of its availability, as well as thousands of lawsuits. In a decision that affected virtually all of those several thousand claims, aggregated for pretrial handing in a federal MDL, a federal judge, in ruling on a Rule 702 motion, described a clinical trial with a risk ratio greater than 1.0, with a p-value of 0.08, as follows:

“The DREAM and ADOPT studies were designed to study the impact of Avandia on prediabetics and newly diagnosed diabetics. Even in these relatively low-risk groups, there was a trend towards an adverse outcome for Avandia users (e.g., in DREAM, the p-value was .08, which means that there is a 92% likelihood that the difference between the two groups was not the result of mere chance).^FN72“

In re Avandia Marketing, Sales Practices and Product Liability Litigation, 2011 WL 13576, *12 (E.D. Pa. 2011)(Rufe, J.). This is a remarkable error by a trial judge given the responsibility for pre-trial handling of so many cases. There are many things you can argue about a p-value of 0.08, but Judge Rufe’s interpretation is not an argument; it is error. That such an error, explicitly warned against in the Reference Manual on Scientific Evidence, could be made by an MDL judge, over 15 years since the first publication of the Manual, highlights the seriousness and the extent of the illiteracy problem.

What possible basis could the Avandia MDL court have to support this clearly erroneous interpretation of crucial studies in the litigation? Footnote 72 in Judge Rufe’s opinion references a report by plaintiffs’ expert witness, Allan D. Sniderman, M.D, “a cardiologist, medical researcher, and professor at McGill University.” Id. at *10. The trial court goes on to note that:

“GSK does not challenge Dr. Sniderman’s qualifications as a cardiologist, but does challenge his ability to analyze and draw conclusions from epidemiological research, since he is not an epidemiologist. GSK’s briefs do not elaborate on this challenge, and in any event the Court finds it unconvincing given Dr. Sniderman’s credentials as a researcher and published author, as well as clinician, and his ability to analyze the epidemiological research, as demonstrated in his report.”

Id.

What more evidence could the Avandia MDL trial court possibly have needed to show that Sniderman was incompetent to give statistical and epidemiologic testimony? Fundamentally at odds with the Manual on an uncontroversial point, Sniderman had given the court a baseless, incorrect interpretation of a p-value. Everything else he might have to say on the subject was likely suspect. If, as the court suggested, GSK did not elaborate upon its challenge with specific examples, then shame on GSK. The trial court, however, could have readily determined that Sniderman was speaking nonsense by reading the chapter on statistics in the Reference Manual on Scientific Evidence. For all my complaints about gaps in coverage in the Manual, the text, on this issue is clear and concise. It really is not too much to expect an MDL trial judge to be conversant with the basic concepts of scientific and statistical evidence set out in the Manual, which is prepared to help federal judges.

Phenylpropanolamine (PPA) Litigation

Litigation over phenylpropanolamine was aggregated, within the federal system, before Judge Barbara Rothstein. Judge Rothstein is not only a respected federal trial judge, she was the director of the Federal Judicial Center, which produces the Reference Manual on Scientific Evidence. Her involvement in overseeing the preparation of the third edition of the Manual, however, did not keep Judge Rothstein from badly misunderstanding and misstating the meaning of a p-value in the PPA litigation. See In re Phenylpropanolamine (PPA) Prods. Liab. Litig., 289 F.Supp. 2d 1230, 1236 n.1 (W.D. Wash. 2003)(“P-values measure the probability that the reported association was due to chance… .”). Tellingly, Judge Rothstein denied, in large part, the defendants’ Rule 702 challenges. Juries, however, overwhelmingly rejected the claims that PPA caused their strokes.

Ephedra Litigation

Judge Rakoff, of the Southern District of New York, notoriously committed the transposition fallacy in the Ephedra litigation:

“Generally accepted scientific convention treats a result as statistically significant if the P-value is not greater than .05. The expression ‘P=.05’ means that there is one chance in twenty that a result showing increased risk was caused by a sampling error—i.e., that the randomly selected sample accidentally turned out to be so unrepresentative that it falsely indicates an elevated risk.”

In re Ephedra Prods. Liab. Litig., 393 F.Supp. 2d 181, 191 (S.D.N.Y. 2005).

Judge Rakoff then fallaciously argued that the use of a critical value of less than 5% of significance probability increased the “more likely than not” burden of proof upon a civil litigant. Id. at 188, 193. See Michael O. Finkelstein, Basic Concepts of Probability and Statistics in the Law 65 (2009).

Judge Rakoff may well have had help in confusing the probability used to characterize the plaintiff’s burden of proof with the probability of attained significance. At least one of the defense expert witnesses in the Ephedra cases gave an erroneous definition of “statistically significant association,” which may have invited the judicial error:

“A statistically significant association is an association between exposure and disease that meets rigorous mathematical criteria demonstrating that the finding is unlikely to be the result of chance.”

Report of John Concato, MD, MS, MPH, at 7, ¶29 (Sept. 13, 2004). Dr. Concato’s error was picked up and repeated in the defense briefing of its motion to preclude:

“The likelihood that an observed association could occur by chance alone is evaluated using tests for statistical significance.”

Memorandum of Law in Support of Motion by Ephedra Defendants to Exclude Expert Opinions of Charles Buncher, [et alia] …That Ephedra Causes Hemorrhagic Stroke, Ischemic Stroke, Seizure, Myocardial Infarction, Sudden Cardiac Death, and Heat-Related Illnesses at 9 (Dec. 3, 2004).

Judge Rakoff’s insistence that requiring “statistical significance” at the customary 5% level would change the plaintiffs’ burden of proof, and require greater certitude for epidemiologists than for other expert witnesses who opine in less “rigorous” fields of learning, is wrong as a matter of fact. His Honor’s comparison, however, ignores the Supreme Court’s observation that the point of Rule 702 is:

‘‘to make certain that an expert, whether basing testimony upon professional studies or personal experience, employs in the courtroom the same level of intellectual rigor that characterizes the practice of an expert in the relevant field.’’

Kumho Tire Co. v. Carmichael, 526 U.S. 137, 152 (1999).

Judge Rakoff not only ignored the conditional nature of significance probability, but he overinterpreted the role of significance testing in arriving at a conclusion of causality. Statistical significance may answer the question of the strength of the evidence for ruling out chance in producing the data observed based upon an assumption of the no risk, but it doesn’t alone answer the question whether the study result shows an increased risk. Bias and confounding must be considered, along with other Bradford Hill factors.

Even if the p-value could be turned into a posterior probability of the null hypothesis, there would be many other probabilities that would necessarily diminish that probability. Some of the other factors (which could be expressed as objective or subjective probabilities) include:

accuracy of the data reporting
data collection
data categorization
data cleaning
data handling
data analysis
internal validity of the study
external validity of the study
credibility of study participants
credibility of study researchers
credibility of the study authors
accuracy of the study authors’ expression of their research
accuracy of the editing process
accuracy of the testifying expert witness’s interpretation
credibility of the testifying expert witness
other available studies, and their respective data and analysis factors
all the other Bradford Hill factors

If these largely independent factors each had a probability or accuracy of 95%, the conjunction of their probabilities would likely be below the needed feather weight on top of 50%. In sum, Judge Rakoff’s confusing significance probability and the posterior probability of the null hypothesis does not subvert the usual standards of proof in civil cases. See also Sander Greenland, “Null Misinterpretation in Statistical Testing and Its Impact on Health Risk Assessment,” 53 Preventive Medicine 225 (2011).

WHENCE COMES THIS ERROR

As a matter of intellectual history, I wonder where this error entered into the judicial system. As a general matter, there was not much judicial discussion of statistical evidence before the 1970s. The earliest manifestation of the transpositional fallacy in connection with scientific and statistical evidence appears in an opinion of the United States Court of Appeals, for the District of Columbia Circuit. Ethyl Corp. v. EPA, 541 F.2d 1, 28 n.58 (D.C. Cir.), cert. denied, 426 U.S. 941 (1976). The Circuit’s language is worth looking at carefully:

“Petitioners demand sole reliance on scientific facts, on evidence that reputable scientific techniques certify as certain.

Typically, a scientist will not so certify evidence unless the probability of error, by standard statistical measurement, is less than 5%. That is, scientific fact is at least 95% certain. Such certainty has never characterized the judicial or the administrative process. It may be that the ‘beyond a reasonable doubt’ standard of criminal law demands 95% certainty. Cf. McGill v. United States, 121 U.S.App.D.C. 179, 185 n.6, 348 F.2d 791, 797 n.6 (1965). But the standard of ordinary civil litigation, a preponderance of the evidence, demands only 51% certainty. A jury may weigh conflicting evidence and certify as adjudicative (although not scientific) fact that which it believes is more likely than not. ***”

Id. The 95% certainty appears to derive from 95% confidence intervals, although “confidence” is a technical term in statistics, and it most certainly does not mean the probability of the alternative hypothesis under consideration. Similarly, the error that is less than 5% is not the probability of error of the belief in hypothesis of no difference between observations and expectations, but rather the probability of observing the data or the data even more extreme, on the assumption that observed would equal the expected. The District of Columbia Circuit thus created a strawman: scientific certainty is 95%, whereas civil and administrative law certainty is 51%. This is rubbish, which confuses the frequentist probability from hypothesis testing with the subjective probability for belief in a fact.

The transpositional fallacy has a good pedigree, but that does not make it correct. Only a lawyer would suggest that a mistake once made was somehow binding upon future litigants. The following collection of citations and references illustrate how widespread the fundamental misunderstanding of statistical inference is, in the courts, in the academy, and at the bar. If courts cannot deliver fair, accurate adjudication of scientific facts, then it is time to reform the system.

Courts

U.S. Supreme Court

Vasquez v. Hillery, 474 U.S. 254, 259 n.3 (1986) (“the District Court . . . accepted . . . a probability of 2 in 1,000 that the phenomenon was attributable to chance”)

U.S. Court of Appeals

First Circuit

Fudge v. Providence Fire Dep’t, 766 F.2d 650, 658 (1st Cir. 1985) (“Widely accepted statistical techniques have been developed to determine the likelihood an observed disparity resulted from mere chance.”)

Second Circuit

Nat’l Abortion Fed. v. Ashcroft, 330 F. Supp. 2d 436 (S.D.N.Y. 2004), aff’d in part, 437 F.3d 278 (2d Cir. 2006), vacated, 224 Fed. App’x 88 (2d Cir. 2007) (reporting an expert witness’s interpretation of a p-value of 0.30 to mean that there was a 30% probability that the study results were due to chance alone)

Smith v. Xerox Corp., 196 F.3d 358, 366 (2d Cir. 1999) (“If an obtained result varies from the expected result by two standard deviations, there is only about a .05 probability that the variance is due to chance.”)

Waisome v. Port Auth., 948 F.2d 1370, 1376 (2d Cir. 1991) (“about one chance in 20 that the explanation for a deviation could be random”)

Ottaviani v. State Univ. of New York at New Paltz, 875 F.2d 365, 372 n.7 (2d Cir. 1989)

Murphy v. General Elec. Co., 245 F. Supp. 2d 459, 467 (N.D.N.Y. 2003) (“less than a 5% probability that age was related to termination by chance”)

Third Circuit

United States v. State of Delaware, 2004 WL 609331, *10 n.27 (D. Del. 2004) (“there is a 5% (or 1 in 20) chance that the relationship observed is purely random”)

Magistrini v. One Hour Martinizing Dry Cleaning, 180 F. Supp. 2d 584, 605 n.26 (D.N.J. 2002) (“only 5% probability that an observed association is due to chance”)

Fifth Circuit

EEOC v. Olson’s Dairy Queens, Inc., 989 F.2d 165, 167 (5th Cir. 1993) (“Dr. Straszheim concluded that the likelihood that [the] observed hiring patterns resulted from truly race-neutral hiring practices was less than one chance in ten thousand.”)

Capaci v. Katz & Besthoff, Inc., 711 F.2d 647, 652 (5th Cir. 1983) (“the highest probability of unbiased hiring was 5.367 × 10^-20”), cert. denied, 466 U.S. 927 (1984)

Rivera v. City of Wichita Falls, 665 F.2d 531, 545 n.22 (5th Cir. 1982)(” A variation of two standard deviations would indicate that the probability of the observed outcome occurring purely by chance would be approximately five out of 100; that is, it could be said with a 95% certainty that the outcome was not merely a fluke. Sullivan, Zimmer & Richards, supra n.9 at 74.”)

Vuyanich v. Republic Nat’l Bank, 505 F. Supp. 224, 272 (N.D.Tex. 1980) (“the chances are less than one in 20 that the true coefficient is actually zero”), judgement vacated, 723 F.2d 1195 (5th Cir. 1984).

Rivera v. City of Wichita Falls, 665 F.2d 531, 545 n.22 (5th Cir. 1982) (“the probability of the observed outcome occurring purely by chance would be approximately five out of 100; that is, it could be said with a 95% certainty that the outcome was not merely a fluke”)

Seventh Circuit

Adams v. Ameritech Services, Inc., 231 F.3d 414, 424, 427 (7th Cir. 2000) (“it is extremely unlikely (that is, there is less than a 5% probability) that the disparity is due to chance.”)

Sheehan v. Daily Racing Form, Inc., 104 F.3d 940, 941 (7th Cir. 1997) (“An affidavit by a statistician . . . states that the probability that the retentions . . . are uncorrelated with age is less than 5 percent.”)

Eighth Circuit

Craik v. Minnesota State Univ. Bd., 731 F.2d 465, 476n. 13 (8th Cir. 1984) (“Statistical significance is a measure of the probability that an observed disparity is not due to chance. Baldus & Cole, Statistical Proof of Discrimination § 9.02, at 290 (1980). A finding that a disparity is statistically significant at the 0.05 or 0.01 level means that there is a 5 per cent. or 1 per cent. probability, respectively, that the disparity is due to chance.

Ninth Circuit

Good v. Fluor Daniel Corp., 222 F.Supp. 2d 1236, 1241n.9 (E.D. Wash. 2002)(describing “statistical tools to calculate the probability that the difference seen is caused by random variation”)

D.C. Circuit

National Lime Ass’n v. EPA, 627 F.2d 416,453 (D.C. Cir. 1980)

FEDERAL CIRCUIT

Hodges v. Secretary Dep’t Health & Human Services, 9 F.3d 958, 967 (Fed. Cir. 1993) (Newman, J., dissenting) (“Scientists as well as judges must understand: ‘the reality that the law requires a burden of proof, or confidence level, other than the 95 percent confidence level that is often used by scientists to reject the possibility that chance alone accounted for observed differences’.”)(citing and quoting from the Report of the Carnegie Commission on Science, Technology, and Government, Science and Technology in Judicial Decision Making 28 (1993).

Regulatory Guidance

OSHA’s Guidance for Compliance with Hazard Communication Act:

“Statistical significance is a mathematical determination of the confidence in the outcome of a test. The usual criterion for establishing statistical significance is the p-value (probability value). A statistically significant difference in results is generally indicated by p < 0.05, meaning there is less than a 5% probability that the toxic effects observed were due to chance and were not caused by the chemical. Another way of looking at it is that there is a 95% probability that the effect is real, i.e., the effect seen was the result of the chemical exposure.”

U.S. Dep’t of Labor, Guidance for Hazard Determination for Compliance with the OSHA Hazard Communication Standard (29 CFR § 1910.1200) Section V (July 6, 2007).

Academic Commentators

Lucinda M. Finley, “Guarding the Gate to the Courthouse: How Trial Judges Are Using Their Evidentiary Screening Role to Remake Tort Causation Rules,” 336 DePaul L. Rev. 335, 348 n. 49 (1999):

“Courts also require that the risk ratio in a study be ‘statistically significant,’ which is a statistical measurement of the likelihood that any detected association has occurred by chance, or is due to the exposure. Tests of statistical significance are intended to guard against what are called ‘Type I’ errors, or falsely ascribing a relationship when there in fact is not one (a false positive). See SANDERS, supra note 5, at 51. The discipline of epidemiology is inherently conservative in making causal ascriptions, and regards Type I errors as more serious than Type II errors, or falsely assuming no association when in fact there is one (false negative). Thus, epidemiology conventionally requires a 95% level of statistical significance, i.e. that in statistical terms it is 95% likely that the association is due to exposure, rather than to chance. See id. at 50-52; Thompson, supra note 3, at 256-58. Despite courts’ use of statistical significance as an evidentiary screening device, this measurement has nothing to do with causation. It is most reflective of a study’s sample size, the relative rarity of the disease being studied, and the variance in study populations. Thompson, supra note 3, at 256.”

Erica Beecher-Monas, Evaluating Scientific Evidence: An Interdisciplinary Framework for Intellectual Due Process 42 n. 30 (2007):

“‘By rejecting a hypothesis only when the test is statistically significant, we have placed an upper bound, .05, on the chance of rejecting a true hypothesis’. Fienberg et al., p. 22. Another way of explaining this is that it describes the probability that the procedure produced the observed effect by chance.”

Professor Fienberg stated the matter corrrectly, but Beecher-Monas goes on to restate the matter in her own words, erroneously. Later, she repeats her incorrect interpretation:

“Statistical significance is a statement about the frequency with which a particular finding is likely to arise by chance.19”

Id. at 61 (citing a paper by Sander Greenland, who correctly stated the definition).

Mark G. Haug, “Minimizing Uncertainty in Scientific Evidence,” in Cynthia H. Cwik & Helen E. Witt, eds., Scientific Evidence Review: Current Issues at the Crossroads of Science, Technology, and the Law – Monograph No. 7, at 87 (2006)

Carl F. Cranor, Regulating Toxic Substances: A Philosophy of Science and the Law at 33-34(Oxford 1993)(One can think of α, β (the chances of type I and type II errors, respectively) and 1- β as measures of the “risk of error” or “standards of proof.”) See also id. at 44, 47, 55, 72-76.

Arnold Barnett, “An Underestimated Threat to Multiple Regression Analyses Used in Job Discrimination Cases, 5 Indus. Rel. L.J. 156, 168 (1982) (“The most common rule is that evidence is compelling if and only if the probability the pattern obtained would have arisen by chance alone does not exceed five percent.”)

David W. Barnes, Statistics as Proof: Fundamentals of Quantitative Evidence 162 (1983)(“Briefly, however, the findings of statistical significance at the P < .05, P < .04, and P < .02 levels indicate that the court can be 95%, 96%, and 98% certain, respectively, that the null hypotheses involved in the specific tests carried out … should be rejected.”)

Wayne Roth-Nelson & Kathey Verdeal, “Risk Evidence in Toxic Torts,” 2 Envt’l Lawyer 405,415-16 (1996) (confusing burden of proof with standard for hypothesis testint; and apparently endorsing the erroneous views given by Judge Newman, dissenting in Hodges). Caveat: Roth-Nelson is now a “forensic” toxicologist, who testifies in civil and criminal trials.

Steven R. Weller, “Book Review: Regulating Toxic Substances: A Philosophy of Science and Law,” 6 Harv. J. L. & Tech. 435, 436, 437-38 (1993) (“only when the statistical evidence gathered from studies shows that it is more than ninety-five percent likely that a test substance causes cancer will the substance be characterized scientifically as carcinogenic … to determine legal causality, the plaintiff need only establish that the probability with which it is true that the substance in question causes cancer is at least fifty percent, rather than the ninety-five percent to prove scientific causality”).

The Carnegie Commission on Science, Technology, and Government, Report on Science and Technology in Judicial Decision Making 28 (1993) (“The reality is that courts often decide cases not on the scientific merits, but on concepts such as burden of proof that operate differently in the legal and scientific realms. Scientists may misperceive these decisions as based on a misunderstanding of the science, when in actuality the decision may simply result from applying a different norm, one that, for the judiciary, is appropriate. Much, for instance, has been written about ‘junk science’ in the courtroom. But judicial decisions that appear to be based on ‘bad’ science may actually reflect the reality that the law requires a burden of proof, or confidence level, other than the 95 percent confidence level that is often used by scientists to reject the possibility that chance alone accounted for observed differences.”).

Plaintiffs’ Counsel

Steven Rotman, “Don’t Know Much About Epidemiology?” Trial (Sept. 2007) (Author’s question answered in the affirmative: “P values. These measure the probability that a reported association between a drug and condition was due to chance. A P-value of 0.05, which is generally considered the standard for statistical significance, means there is a 5 percent probability that the association was due to chance.”)

Defense Counsel

Bruce R. Parker & Anthony F. Vittoria, “Debunking Junk Science: Techniques for Effective Use of Biostatistics,” 65 Defense Csl. J. 35, 44 (2002) (“a P value of .01 means the researcher can be 99 percent sure that the result was not due to chance”).

Posted in Reference Manual on Scientific Evidence, Scientific Evidence, statistical evidence, Uncategorized | 2 Comments »

Meta-Analysis of Observational Studies in Non-Pharmaceutical Litigations

February 26th, 2012

Yesterday, I posted on several pharmaceutical litigations that have involved meta-analytic studies. Meta-analytic studies have also figured prominently in non-pharmaceutical product liability litigation, as well as in litigation over videogames, criminal recidivism, and eyewitness testimony. Some, but not all, of the cases in these other areas of litigation are collected below. In some cases, the reliability or validity of the meta-analyses were challenged; in some cases, the court fleetingly referred to meta-analyses relied upon the parties. Some of the courts’ treatments of meta-analysis are woefully inadequate or erroneous. The failure of the Reference Manual on Scientific Evidence to update its treatment of meta-analysis is telling. See “The Treatment of Meta-Analysis in the Third Edition of the Reference Manual on Scientific Evidence” (Nov. 14, 2011).

Abortion (Breast Cancer)

Christ’s Bride Ministries, Inc. v. Southeastern Pennsylvania Transportation Authority, 937 F.Supp. 425 (E.D. Pa. 1996), rev’d, 148 F.3d 242 (3d Cir. 1997)

Asbestos

In re Joint E. & S. Dist. Asbestos Litig., 827 F. Supp. 1014, 1042 (S.D.N.Y. 1993)(“adding a series of positive but statistically insignificant SMRs [standardized mortality ratios] together does not produce a statistically significant pattern”), rev’d, 52 F.3d 1124 (2d Cir. 1995).

In Re Asbestos Litigation, Texas Multi District Litigation Cause No. 2004-03964 (June 30, 2005)(Davidson, J.)(“The Defendants’ response was presented by Dr. Timothy Lash. I found him to be highly qualified and equally credible. He largely relied on the report submitted to the Environmental Protection Agency by Berman and Crump (“B&C”). He found the meta-analysis contained in B&C credible and scientifically based. B&C has not been published or formally accepted by the EPA, but it does perform a valuable study of the field. If the question before me was whether B&C is more credible than the Plaintiffs’ studies taken together, my decision might well be different.”)

Jones v. Owens-Corning Fiberglas, 288 N.J. Super. 258, 672 A.2d 230 (1996)

Berger v. Amchem Prods., 818 N.Y.S.2d 754 (2006)

Grenier v. General Motors Corp., 2009 WL 1034487 (Del.Super. 2009)

Benzene

Knight v. Kirby Inland Marine, Inc., 363 F. Supp. 2d 859 (N.D. Miss. 2005)(precluding proffered opinion that benzene caused bladder cancer and lymphoma; noting without elaboration or explanation, that meta-analyses are “of limited value in combining the results of epidemiologic studies based on observation”), aff’d, 482 F.3d 347 (5th Cir. 2007)

Baker v. Chevron USA, Inc., 680 F.Supp. 2d 865 (S.D. Ohio 2010)

Diesel Exhaust Exposure

King v. Burlington Northern Santa Fe Ry. Co., 277 Neb. 203, 762 N.W.2d 24 (2009)

Kennecott Greens Creek Mining Co. v. Mine Safety & Health Admin., 476 F.3d 946 (D.C. Cir. 2007)

Eyewitness Testimony

State of New Jersey v. Henderson, 208 N.J. 208, 27 A.3d 872 (2011)

Valle v. Scribner, 2010 WL 4671466 (C.D. Calif. 2010)

People v. Banks, 16 Misc.3d 929, 842 N.Y.S.2d 313 (2007)

Lead

Palmer Asarco Inc., 510 F.Supp.2d 519 (N.D. Okla. 2007)

PCBs

In re Paoli R.R. Yard PCB Litigation, 916 F.2d 829, 856-57 (3d Cir.1990) (‘‘There is some evidence that half the time you shouldn’t believe meta-analysis, but that does not mean that meta-analyses are necessarily in error. It means that they are, at times, used in circumstances in which they should not be.’’) (internal quotation marks and citations omitted), cert. denied, 499 U.S. 961 (1991)

Repetitive Stress

Allen v. International Business Machines Corp., 1997 U.S. Dist. LEXIS 8016 (D. Del. 1997)

Tobacco

Flue-Cured Tobacco Cooperative Stabilization Corp. v. United States Envt’l Protection Agency, 4 F.Supp.2d 435 (M.D.N.C. 1998), vacated by, 313 F.3d 852 (4th Cir. 2002)

Tocolytics – Medical Malpractice

Hurd v. Yaeger, 2009 WL 2516874 (M.D. Pa. 2009)

Toluene

Black v. Rhone-Poulenc, Inc., 19 F.Supp.2d 592 (S.D.W.Va. 1998)

Video Games (Violent Behavior)

Brown v. Entertainment Merchants Ass’n, ___ U.S.___, 131 S.Ct. 2729 (2011)

Entertainment Software Ass’n v. Blagojevich, 404 F.Supp.2d 1051 (N.D. Ill. 2005)

Entertainment Software Ass’n v. Hatch, 443 F.Supp.2d 1065 (D. Minn. 2006)

Video Software Dealers Ass’n v. Schwarzenegger, 556 F.3d 950 (9th Cir. 2009)

Vinyl Chloride

Taylor v. Airco, 494 F. Supp. 2d 21 (D. Mass. 2007)(permitting opinion testimony that vinyl chloride caused intrahepatic cholangiocarcinoma, without commenting upon the reasonableness of reliance upon the meta-analysis cited)

Welding

Cooley v. Lincoln Electric Co., 693 F.Supp.2d 767 (N.D. Ohio. 2010)

Posted in Meta-analysis, Reference Manual on Scientific Evidence, Rule 702, Scientific Evidence, statistical evidence | 103 Comments »

Meta-Analysis in Pharmaceutical Cases

February 25th, 2012

The Third Edition of the Reference Manual on Scientific Evidence attempts to cover a lot of ground to give the federal judiciary guidance on scientific, medical, and statistical, and engineering issues. It has some successes, and some failures. One of the major problems in coverage in the new Manual is its inconsistent, sparse, and at points out-dated treatment of meta-analysis. See “The Treatment of Meta-Analysis in the Third Edition of the Reference Manual on Scientific Evidence” (Nov. 14, 2011).

As I have pointed out elsewhere, the gaps and problems in the Manual‘s coverage are not “harmless error,” when some courts have struggled to deal with methodological and evaluative issues in connection with specific meta-analyses. See “Learning to Embrace Flawed Evidence – The Avandia MDL’s Daubert Opinion” (Jan. 10, 2011).

Perhaps the reluctance to treat meta-analysis more substantively comes from a perception that the technique for analyzing multiple studies does not come up frequently in litigation. If so, let me help dispel the notion. I have collected a partial list of drug and medical device cases that have confronted meta-analysis in one form or another. In some cases, such as the Avandia MDL, a meta-analysis was a key, or the key, piece of evidence. In other cases, meta-analysis may have been treated more peripherally. Still, there are over 20 pharmaceutical cases in the last two decades that have dealt with the statistical techniques involved in meta-analysis. In another post, I will collect the non-pharmaceutical cases as well.

Aredia – Zometa

Deutsch v. Novartis Pharm. Corp., 768 F. Supp. 2d 420 (E.D.N.Y. 2011)

Avandia

In re Avandia Marketing, Sales Practices and Product Liability Litigation, 2011 WL 13576, *12 (E.D. Pa. 2011)

Avon Pension Fund v. GlaxoSmithKline PLC, 343 Fed.Appx. 671 (2d Cir. 2009)

Baycol

In re Baycol Prods. Litig., 532 F.Supp. 2d 1029 (D. Minn. 2007)

Bendectin

Daubert v. Merrell Dow Pharm., 43 F.3d 1311 (9th Cir. 1995) (on remand from Supreme Court)

DePyper v. Navarro, 1995 WL 788828 (Mich.Cir.Ct. 1995)

Benzodiazepine

Vinitski v. Adler, 69 Pa. D. & C.4th 78, 2004 WL 2579288 (Phila. Cty. Ct. Common Pleas 2004)

Celebrex – Bextra

In re Bextra & Celebrex Marketing Sales Practices & Prod. Liab. Litig., 524 F.Supp.2d 1166 (2007)

E5 (anti-endotoxin monoclonal antibody for gram-negative sepsis)

Warshaw v. Xoma Corp., 74 F.3d 955 (1996)

Excedrin vs. Tylenol

McNeil-P.C.C., Inc. v. Bristol-Myers Squibb Co., 938 F.2d 1544 (2d Cir. 1991)

Fenfluramine, Phentermine

In re Diet Drugs Prod. Liab. Litig., 2000 WL 1222042 (E.D.Pa. 2000)

Fosamax

In re Fosamax Prods. Liab. Litig., 645 F.Supp.2d 164 (S.D.N.Y. 2009)

Gadolinium

In re Gadolinium-Based Contrast Agents Prod. Liab. Litig., 2010 WL 1796334 (N.D. Ohio 2010)

Neurontin

In re Neurontin Marketing, Sales Pracices, and Products Liab. Litig., 612 F.Supp.2d 116 (D. Mass. 2009)

Paxil (SSRI)

Tucker v. Smithkline Beecham Corp., 2010 U.S. Dist. LEXIS 30791 (S.D.Ind. 2010)

Prozac (SSRI)

Rimberg v. Eli Lilly & Co., 2009 WL 2208570 (D.N.M.)

Seroquel

In re Seroquel Products Liab. Litig., 2009 WL 3806434 *5 (M.D. Fla. 2009)

Silicone – Breast Implants

Allison v. McGhan Med. Corp., 184 F.3d 1300, 1315 n. 12 (11th Cir. 1999)(noting, in passing that the district court had found a meta-analysis (the “Kayler study”) unreliable “because it was a re-analysis of other studies that had found no statistical correlation between silicone implants and disease”)

Thimerosal – Vaccine

Salmond v. Sec’y Dep’t of Health & Human Services, 1999 WL 778528 (Fed.Cl. 1999)

Hennessey v. Sec’y Dep’t Health & Human Services, 2009 WL 1709053 (Fed.Cl. 2009)

Trasylol

In re Trasylol Prods. Liab. Litig., 2010 WL 1489793 (S.D. Fla. 2010)

Vioxx

Merck & Co., Inc. v. Ernst, 296 S.W.3d 81 (Tex. Ct. App. 2009)
Merck & Co., Inc. v. Garza, 347 S.W.3d 256 (Tex. 2011)

X-Ray Contrast Media (Nephrotoxicity of Visipaque versus Omnipaque)

Bracco Diagnostics, Inc. v. Amersham Health, Inc., 627 F.Supp.2d 384 (D.N.J. 2009)

Zestril

E.R. Squibb & Sons, Inc. v. Stuart Pharms., 1990 U.S. Dist. LEXIS 15788 (D.N.J. 1990)(Zestril versus Squibb’s competing product,
Capote)

Zoloft (SSRI)

Miller v. Pfizer, Inc., 356 F.3d 1326 (10th Cir. 2004)

Zymar

Senju Pharmaceutical Co. Ltd. v. Apotex Inc., 2011 WL 6396792 (D.Del. 2011)

Zyprexa

In re Zyprexa Products Liab. Litig., 489 F.Supp.2d 230 (E.D.N.Y. 2007) (Weinstein, J.)

Posted in Reference Manual on Scientific Evidence, Rule 702, statistical evidence | No Comments »

When There Is No Risk in Risk Factor

February 20th, 2012

Some of the terminology of statistics and epidemiology is not only confusing, but it is misleading. Consider the terms “effect size,” “random effects,” and “fixed effect,” which are all used to describe associations even if known to be non-causal. Biostatisticians and epidemiologists know that the terms are about putative or potential effects, but the sloppy, short-hand nomenclature can be misleading.

Although “risk” has a fairly precise meaning in scientific parlance, the usage for “risk factor” is fuzzy, loose, and imprecise. Journalists and plaintiffs’ lawyers use “risk factor,” much as they another frequently abused term in their vocabulary: “link.” Both “risk factor” and “link” sound as though they are “causes,” or at least as though they have something to do with causation. The reality is usually otherwise.

The business of exactly what “risk factor” means is puzzling and disturbing. The phrase seems to have gained currency because it is squishy and without a definite meaning. Like the use of “link” by journalists, the use of “risk factor” protects the speaker against contradiction, but appears to imply a scientifically valid conclusion. Plaintiffs’ counsel and witnesses love to throw this phrase around precisely because of its ambiguity. In journal articles, authors sometimes refer to any exposure inquired about in a case-control study to be a “risk factor,” regardless of the study result. So a risk factor can be merely an “exposure of interest,” or a possible cause, or a known cause.

The author’s meaning in using the phrase “risk factor” can often be discerned from context. When an article reports a case-control study, which finds an association with an exposure to some chemical the article will likely report in the discussion section that the study found that chemical to be a risk factor. The context here makes clear that the chemical was found to be associated with the outcome, and that chance was excluded as a likely explanation because the odds ratio was statistically significant. The context is equally clear that the authors did not conclude that the chemical was a cause of the outcome because they did not rule out bias or confounding; nor did they do any appropriate analysis to reach a causal conclusion and because their single study would not have justified reaching a causal association.

Sometimes authors qualify “risk factor” with an adjective to give more specific meaning to their usage. Some of the adjectives used in connection with the phrase include:

– putative, possible, potential, established, well-established, known, certain, causal, and causative

The use of the adjective highlights the absence of a precise meaning for “risk factor,” standing alone. Adjectives such as “established,” or “known” imply earlier similar findings, which are corroborated by the study at hand. Unless “causal” is used to modify “risk factor,” however, there is no reason to interpret the unqualified phrase to imply a cause.

Here is how the phrase “risk factor” is described in some noteworthy texts and treatises.

Legal Treatises

Professor David Faigman, and colleagues, with some understatement, note that the term “risk factor is loosely used”:

“Risk Factor An aspect of personal behavior or life-style, an environmental exposure, or an inborn or inherited characteristic, which on the basis of epidemiologic evidence is known to be associated with health-related condition(s) considered important to prevent. The term risk factor is rather loosely used, with any of the following meanings:

1. An attribute or exposure that is associated with an increased probability of a specified outcome, such as the occurrence of a disease. Not necessarily a causal factor.

2. An attribute or exposure that increases the probability of occurrence of disease or other specified outcome.

3. A determinant that can be modified by intervention, thereby reducing the probability of occurrence of disease or other specified outcomes.”

David L. Faigman, Michael J. Saks, Joseph Sanders, and Edward Cheng, Modern Scientific Evidence: The Law and Science of Expert Testimony 301, vol. 1 (2010)(emphasis added).

The Reference Manual on Scientific Evidence (2011) (RMSE3d) does not offer much in the way of meaningful guidance here. The chapter on statistics in the third edition provides a somewhat circular, and unhelpful definition. Here is the entry in that chapter’s glossary:

risk factor. See independent variable.

RMSE3d at 295. If the glossary defined “independent variable” as a simply a quantifiable variable that was being examined for some potential relationship with the outcome, or dependent, variable, the RMSE would have avoided error. Instead the chapter’s glossary, as well as its text, defines independent variables as “causes,” which begs the question why do a study to determine whether the “independent variable” is even a candidate for a causal factor? Here is how the statistics chapter’s glossary defines independent variable:

“Independent variables (also called explanatory variables, predictors, or risk factors) represent the causes and potential confounders in a statistical study of causation; the dependent variable represents the effect. ***. “

RMSE3d at 288. This is surely circular. Studies of causation are using independent variables that represent causes? There would be no reason to do the study if we already knew that the independent variables were causes.

The text of the RMSE chapter on statistics propagates the same confusion:

“When investigating a cause-and-effect relationship, the variable that represents the effect is called the dependent variable, because it depends on the causes. The variables that represent the causes are called independent variables. With a study of smoking and lung cancer, the independent variable would be smoking (e.g., number of cigarettes per day), and the dependent variable would mark the presence or absence of lung cancer. Dependent variables also are called outcome variables or response variables. Synonyms for independent variables are risk factors, predictors, and explanatory variables.”

FMSE3d at 219. In the text, the identification of causes with risk factors is explicit. Independent variables are the causes, and a synonym for an independent variable is “risk factor.” The chapter could have avoided this error simply by the judicious use of “putative,” or “candidate” in front of “causes.”

The chapter on epidemiology exercises more care by using “potential” to modify and qualify the risk factors that are considered in a study:

“In contrast to clinical studies in which potential risk factors can be controlled, epidemiologic investigations generally focus on individuals living in the community, for whom characteristics other than the one of interest, such as diet, exercise, exposure to other environmental agents, and genetic background, may distort a study’s results.”

FMSE3d at 556 (emphasis added).

Scientific Texts

Turning our attention to texts on epidemiology written for professionals rather than judges, we find that sometimes the term “risk factor” with a careful awareness of its ambiguity.

Herbert I. Weisberg is a statistician whose firm, Correlation Research Inc., specializes in the applied statistics in legal issues. Weisberg recently published an interesting book on bias and causation, which is recommended reading for lawyers who litigate claimed health effects. Weisberg’s book defines “risk factor” as merely an exposure of interest in a study that is looking for associations with a harmful outcome. He insightfully notes that authors use the phrase “risk factor” and similar phrases to avoid causal language:

“We will often refer to this factor of interest as a risk factor, although the outcome event is not necessarily something undesirable.”

Herbert I. Weisberg, Bias and Causation: Models and Judgment for Valid Comparisons 27 (2010).

“Causation is discussed elliptically if at all; statisticians typically employ circumlocutions such as ‘independent risk factor’ or ‘explanatory variable’ to avoid causal language.”

Id. at 35.

“Risk factor : The risk factor is the exposure of interest in an epidemiological study and often has the connotation that the outcome event is harmful or in some way undesirable.”

Id. at 317. This last definition is helpful in illustrating a balanced, fair definition that does not conflate risk factor with causation.

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Lemuel A. Moyé is an epidemiologist who testified in pharmaceutical litigation, mostly for plaintiffs. His text, Statistical Reasoning in Medicine: The Intuitive P-Value Primer, is in places a helpful source of guidance on key concepts. Moyé puts no stock in something’s being a risk factor unless studies show a causal relationship, established through a proper analysis. Accordingly, he uses “risk factor” to signify simply an exposure of interest:

“4.2.1 Association versus Causation

An associative relationship between a risk factor and a disease is one in which the two appear in the same patient through mere coincidence. The occurrence of the risk factor does not engender the appearance of the disease.

Causal relationships on the other hand are much stronger. A relationship is causal if the presence of the risk factor in an individual generates the disease. The causative risk factor excites the production of the disease. This causal relationship is tight, containing an embedded directionality in the relationship, i.e., (1) the disease is absence in the patient, (2) the risk factor is introduced, and (3) the risk factor’s presence produces the disease.

The declaration that a relationship is causal has a deeper meaning then the mere statement that a risk factor and disease are associated. This deeper meaning and its implications for healthcare require that the demonstration of a causal relationship rise to a higher standard than just the casual observation of the risk factor and disease’s joint occurrence.

Often limited by logistics and the constraints imposed by ethical research, the epidemiologist commonly cannot carry out experiments that identify the true nature of the risk factor–disease relationship. They have therefore become experts in observational studies. Through skillful use of observational research methods and logical thought, epidemiologists assess the strength of the links between risk factors and disease.”

Lemuel A. Moyé, Statistical Reasoning in Medicine: The Intuitive P-Value Primer 92 (2d ed. 2006)

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In A Dictionary of Epidemiology, which is put out by the International Epidemiology Association, a range of meanings is acknowledged, although the range is weighted toward causality:

“RISK FACTOR (Syn: risk indicator)

1. An aspect of personal behavior or lifestyle, an environmental exposure, or an inborn or inherited characteristic that, on the basis of scientific evidence, is known to be associated with meaningful health-related condition(s). In the twentieth century multiple cause era, a synonymous with determinant acting at the individual level.

2. An attribute or exposure that is associated with an increased probability of a specified outcome, such as the occurrence of a disease. Not necessarily a causal factor: it may be a risk marker.

3. A determinant that can be modified by intervention, thereby reducing the probability of occurrence of disease or other outcomes. It may be referred to as a modifiable risk factor, and logically must be a cause of the disease.

The term risk factor became popular after its frequent use by T. R. Dawber and others in papers from the Framingham study.³⁴⁶ The pursuit of risk factors has motivated the search for causes of chronic disease over the past half-century. Ambiguities in risk and in risk-related concepts, uncertainties inherent to the concept, and different legitimate meanings across cultures (even if within the same society) must be kept in mind in order to prevent medicalization of life and iatrogenesis.^{124–128,136,142,240}”

Miquel Porta, Sander Greenland, John M. Last, eds., A Dictionary of Epidemiology 218-19 (5^th ed. 2008). We might add that the uncertainties inherent in risk concepts should be kept in mind to prevent overcompensation for outcomes not shown to be caused by alleged tortogens.

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One introductory text uses “risk factor” as a term to describe the independent variable, while acknowledging that the variable does not become a risk factor until after the study shows an association between factor and the outcome of interest:

“A case-control study is one in which the investigator seeks to establish an association between the presence of a characteristic (a risk factor).”

Sylvia Wassertheil-Smoller, Biostatistics and Epidemiology: A Primer for Health and Biomedical Professionals 104 (3d ed. 2004). See also id. at 198 (“Here, also, epidemiology plays a central role in identifying risk factors, such as smoking for lung cancer”). Although it should be clear that much more must happen in order to show a risk factor is causally associated with an outcome, such as lung cancer, it would be helpful to spell this out. Some texts simply characterize risk factor as associations, not necessarily causal in nature. Another basic text provides:

“Analytical studies examine an association, i.e. the relationship between a risk factor and a disease in detail and conduct a statistical test of the corresponding hypothesis … .”

Wolfgang Ahrens & Iris Pigeot, eds., Handbook of Epidemiology 18 (2005). See also id. at 111 (Table describing the reasoning in a case-control study: “Increased prevalence of risk factor among diseased may indicate a causal relationship.”)(emphasis added).

These texts, both legal and scientific, indicate a wide range of usage and ambiguity for “risk factor.” There is a tremendous potential for the unscrupulous expert witness, or the uneducated lawyer, to take advantage of this linguistic latitude. Courts and counsel must be sensitive to the ambiguity and imprecision in usages of “risk factor,” and the mischief that may result. The Reference Manual on Scientific Evidence needs to sharpen and update its coverage of this and other statistical and epidemiologic issues.

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