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The Shmeta-Analysis in Paoli

July 11th, 2019

In the Paoli Railroad yard litigation, plaintiffs claimed injuries and increased risk of future cancers from environmental exposure to polychlorinated biphenyls (PCBs). This massive litigation showed up before federal district judge Hon. Robert F. Kelly,[1] in the Eastern District of Pennsylvania, who may well have been the first judge to grapple with a litigation attempt to use meta-analysis to show a causal association.

One of the plaintiffs’ expert witnesses was the late William J. Nicholson, who was a professor at Mt. Sinai School of Medicine, and a colleague of Irving Selikoff. Nicholson was trained in physics, and had no professional training in epidemiology. Nonetheless, Nicholson was Selikoff’s go-to colleague for performing epidemiologic studies. After Selikoff withdrew from active testifying for plaintiffs in tort litigation, Nicholson was one of his colleagues who jumped into the fray as a surrogate advocate for Selikoff.[2]

For his opinion that PCBs were causally associated with liver cancer in humans,[3] Nicholson relied upon a report he wrote for the Ontario Ministry of Labor. [cited here as “Report”].[4] Nicholson described his report as a “study of the data of all the PCB worker epidemiological studies that had been published,” from which he concluded that there was “substantial evidence for a causal association between excess risk of death from cancer of the liver, biliary tract, and gall bladder and exposure to PCBs.”[5]

The defense challenged the admissibility of Nicholson’s meta-analysis, on several grounds. The trial court decided the challenge based upon the Downing case, which was the law in the Third Circuit, before the Supreme Court decided Daubert.[6] The Downing case allowed some opportunity for consideration of reliability and validity concerns; there is, however, disappointingly little discussion of any actual validity concerns in the courts’ opinions.

The defense challenge to Nicholson’s proffered testimony on liver cancer turned on its characterization of meta-analysis as a “novel” technique, which is generally unreliable, and its claim that Nicholson’s meta-analysis in particular was unreliable. None of the individual studies that contributed data showed any “connection” between PCBs and liver cancer; nor did any individual study conclude that there was a causal association.

Of course, the appropriate response to this situation, with no one study finding a statistically significant association, or concluding that there was a causal association, should have been “so what?” One of the reasons to do a meta-analysis is that no available study was sufficiently large to find a statistically significant association, if one were there. As for drawing conclusions of causal associations, it is not the role or place of an individual study to synthesize all the available evidence into a principled conclusion of causation.

In any event, the trial court concluded that the proffered novel technique lacked sufficient reliability, that the meta-analysis would “overwhelm, confuse, or mislead the jury,” and that the proffered meta-analysis on liver cancer was not sufficiently relevant to the facts of the case (in which no plaintiff had developed, or had died of, liver cancer). The trial court noted that the Report had not been peer-reviewed, and that it had not been accepted or relied upon by the Ontario government for any finding or policy decision. The trial court also expressed its concern that the proffered testimony along the lines of the Report would possibly confuse the jury because it appeared to be “scientific” and because Nicholson appeared to be qualified.

The Appeal

The Court of Appeals for the Third Circuit, in an opinion by Judge Becker, reversed Judge Kelly’s exclusion of the Nicholson Report, in an opinion that is still sometimes cited, even though Downing is no longer good law in the Circuit or anywhere else.[7] The Court was ultimately not persuaded that the trial court had handled the exclusion of Nicholson’s Report and its meta-analysis correctly, and it remanded the case for a do-over analysis.

Judge Becker described Nicholson’s Report as a “meta-analysis,” which pooled or “combined the results of numerous epidemiologic surveys in order to achieve a larger sample size, adjusted the results for differences in testing techniques, and drew his own scientific conclusions.”[8] Through this method, Nicholson claimed to have shown that “exposure to PCBs can cause liver, gall bladder and biliary tract disorders … even though none of the individual surveys supports such a conclusion when considered in isolation.”[9]

Validity

The appellate court gave no weight to the possibility that a meta-analysis would confuse a jury, or that its “scientific nature” or Nicholson’s credentials would lead a jury to give it more weight than it deserved.[10] The Court of Appeals conceded, however, that exclusion would have been appropriate if the methodology used itself was invalid. The appellate opinion further acknowledged that the defense had offered opposition to Nicholson’s Report in which it documented his failure to include data that were inconsistent with his conclusions, and that “Nicholson had produced a scientifically invalid study.”[11]

Judge Becker’s opinion for a panel of the Third Circuit provided no details about the cherry picking. The opinion never analyzed why this charge of cherry-picking and manipulation of the dataset did not invalidate the meta-analytic method generally, or Nicholson’s method as applied. The opinion gave no suggestion that this counter-affidavit was ever answered by the plaintiffs.

Generally, Judge Becker’s opinion dodged engagement with the specific threats to validity in Nicholson’s Report, and took refuge in the indisputable fact that hundreds of meta-analyses were published annually, and that the defense expert witnesses did not question the general reliability of meta-analysis.[12] These facts undermined the defense claim that meta-analysis was novel.[13] The reality, however, was that meta-analysis was in its infancy in bio-medical research.

When it came to the specific meta-analysis at issue, the court did not discuss or analyze a single pertinent detail of the Report. Despite its lack of engagement with the specifics of the Report’s meta-analysis, the court astutely observed that prevalent errors and flaws do not mean that a particular meta-analysis is “necessarily in error.”[14] Of course, without bothering to look, the court would not know whether the proffered meta-analysis was “actually in error.”

The appellate court would have given Nicholson’s Report a “pass” if it was an application of an accepted methodology. The defense’s remedy under this condition would be to cross-examine the opinion in front of a jury. If, on the other hand, the Nicholson had altered an accepted methodology to skew its results, then the court’s gatekeeping responsibility under Downing would be invoked.

The appellate court went on to fault the trial court for failing to make sufficiently explicit findings as to whether the questioned meta-analysis was unreliable. From its perspective, the Court of Appeals saw the trial court as resolving the reliability issue upon the greater credibility of defense expert witnesses in branding the disputed meta-analysis as unreliability. Credibility determinations are for the jury, but the court left room for a challenge on reliability itself:[15]

“Assuming that Dr. Nicholson’s meta-analysis is the proper subject of Downing scrutiny, the district court’s decision is wanting, because it did not make explicit enough findings on the reliability of Dr. Nicholson’s meta-analysis to satisfy Downing. We decline to define the exact level at which a district court can exclude a technique as sufficiently unreliable. Reliability indicia vary so much from case to case that any attempt to define such a level would most likely be pointless. Downing itself lays down a flexible rule. What is not flexible under Downing is the requirement that there be a developed record and specific findings on reliability issues. Those are absent here. Thus, even if it may be possible to exclude Dr. Nicholson’s testimony under Downing, as an unreliable, skewed meta-analysis, we cannot make such a determination on the record as it now stands. Not only was there no hearing, in limine or otherwise, at which the bases for the opinions of the contesting experts could be evaluated, but the experts were also not even deposed. All of the expert evidence was based on affidavits.”

Peer Review

Understandably, the defense attacked Nicholson’s Report as not having been peer reviewed. Without any scrutiny of the scientific bona fides of the workers’ compensation agency, the appellate court acquiesced in Nicholson’s self-serving characterization of his Report as having been reviewed by “cooperating researchers” and the Panel of the Ontario Workers’ Compensation agency. Another partisan expert witness characterized Nicholson’s Report as a “balanced assessment,” and this seemed to appease the Third Circuit, which was wary of requiring peer review in the first place.[16]

Relevancy Prong

The defense had argued that Nicholson’s Report was irrelevant because no individual plaintiff claimed liver cancer.[17] The trial court largely accepted this argument, but the appellate court disagreed because of conclusory language in Nicholson’s affidavit, in which he asserted that “proof of an increased risk of liver cancer is probative of an increased risk of other forms of cancer.” The court seemed unfazed by the ipse dixit, asserted without any support. Indeed, Nicholson’s assertion was contradicted by his own Report, in which he reported that there were fewer cancers among PCB-exposed male capacitor manufacturing workers than expected,[18] and that the rate for all cancers for both men and women was lower than expected, with 132 observed and 139.40 expected.[19]

The trial court had also agreed with the defense’s suggestion that Nicholson’s report, and its conclusion of causality between PCB exposure and liver cancer, were irrelevant because the Report “could not be the basis for anyone to say with reasonable degree of scientific certainty that some particular person’s disease, not cancer of the liver, biliary tract or gall bladder, was caused by PCBs.”[20]

Analysis

It would likely have been lost on Judge Becker and his colleagues, but Nicholson presented SMRs (standardized mortality ratios) throughout his Report, and for the all cancers statistic, he gave an SMR of 95. What Nicholson clearly did in this, and in all other instances, was simply divide the observed number by the expected, and multiply by 100. This crude, simplistic calculation fails to present a standardized mortality ratio, which requires taking into account the age distribution of the exposed and the unexposed groups, and a weighting of the contribution of cases within each age stratum. Nicholson’s presentation of data was nothing short of false and misleading. And in case anyone remembers General Electric v. Joiner, Nicholson’s summary estimate of risk for lung cancer in men was below the expected rate.[21]

Nicholson’s Report was replete with many other methodological sins. He used a composite of three organs (liver, gall bladder, bile duct) without any biological rationale. His analysis combined male and female results, and still his analysis of the composite outcome was based upon only seven cases. Of those seven cases, some of the cases were not confirmed as primary liver cancer, and at least one case was confirmed as not being a primary liver cancer.[22]

Nicholson failed to standardize the analysis for the age distribution of the observed and expected cases, and he failed to present meaningful analysis of random or systematic error. When he did present p-values, he presented one-tailed values, and he made no corrections for his many comparisons from the same set of data.

Finally, and most egregiously, Nicholson’s meta-analysis was meta-analysis in name only. What he had done was simply to add “observed” and “expected” events across studies to arrive at totals, and to recalculate a bogus risk ratio, which he fraudulently called a standardized mortality ratio. Adding events across studies is not a valid meta-analysis; indeed, it is a well-known example of how to generate a Simpson’s Paradox, which can change the direction or magnitude of any association.[23]

Some may be tempted to criticize the defense for having focused its challenge on the “novelty” of Nicholson’s approach in Paoli. The problem of course was the invalidity of Nicholson’s work, but both the trial court’s exclusion of Nicholson, and the Court of Appeals’ reversal and remand of the exclusion decision, illustrate the problem in getting judges, even well-respected judges, to accept their responsibility to engage with questioned scientific evidence.

Even in Paoli, no amount of ketchup could conceal the unsavoriness of Nicholson’s scrapple analysis. When the Paoli case reached the Court Appeals again in 1994, Nicholson’s analysis was absent.[24] Apparently, the plaintiffs’ counsel had second thoughts about the whole matter. Today, under the revised Rule 702, there can be little doubt that Nicholson’s so-called meta-analysis should have been excluded.

[1] Not to be confused with the Judge Kelly of the same district, who was unceremoniously disqualified after attending an ex parte conference with plaintiffs’ lawyers and expert witnesses, at the invitation of Dr. Irving Selikoff.

[2] Pace Philip J. Landrigan & Myron A. Mehlman, “In Memoriam – William J. Nicholson,” 40 Am. J. Indus. Med. 231 (2001). Landrigan and Mehlman assert, without any support, that Nicholson was an epidemiologist. Their own description of his career, his undergraduate work at MIT, his doctorate in physics from the University of Washington, his employment at the Watson Laboratory, before becoming a staff member in Irving Selikoff’s department in 1969, all suggest that Nicholson brought little to no experience in epidemiology to his work on occupational and environmental exposure epidemiology.

[3] In re Paoli RR Yard Litig., 706 F. Supp. 358, 372-73 (E.D. Pa. 1988).

[4] William Nicholson, Report to the Workers’ Compensation Board on Occupational Exposure to PCBs and Various Cancers, for the Industrial Disease Standards Panel (ODP); IDSP Report No. 2 (Toronto, Ontario Dec. 1987).

[5] Id. at 373.

[6] United States v. Downing, 753 F.2d 1224 (3d Cir.1985)

[7] In re Paoli RR Yard PCB Litig., 916 F.2d 829 (3d Cir. 1990), cert. denied sub nom. General Elec. Co. v. Knight, 111 S.Ct. 1584 (1991).

[8] Id. at 845.

[9] Id.

[10] Id. at 841, 848.

[11] Id. at 845.

[12] Id. at 847-48.

[13] See, e.g., Robert Rosenthal, Judgment studies: Design, analysis, and meta-analysis (1987); Richard J. Light & David B. Pillemer, Summing Up: the Science of Reviewing Research (1984); Thomas A. Louis, Harvey V. Fineberg & Frederick Mosteller, “Findings for Public Health from Meta-Analyses,” 6 Ann. Rev. Public Health 1 (1985); Kristan A. L’abbé, Allan S. Detsky & Keith O’Rourke, “Meta-analysis in clinical research,” 107 Ann. Intern. Med. 224 (1987).

[14] Id. at 857.

[15] Id. at 858/

[16] Id. at 858.

[17] Id. at 845.

[18] Report, Table 16.

[19] Report, Table 18.

[20] In re Paoli, 916 F.2d at 847.

[21] See General Electric v. Joiner, 522 U.S. 136 (1997); NAS, “How Have Important Rule 702 Holdings Held Up With Time?” (March 20, 2015).

[22] Report, Table 22.

[23] James A. Hanley, Gilles Thériault, Ralf Reintjes and Annette de Boer, “Simpson’s Paradox in Meta-Analysis,” 11 Epidemiology 613 (2000); H. James Norton & George Divine, “Simpson’s paradox and how to avoid it,” Significance 40 (Aug. 2015); George Udny Yule, Notes on the theory of association of attributes in Statistics, 2 Biometrika 121 (1903).

[24] In re Paoli RR Yard Litig., 35 F.3d 717 (3d Cir. 1994).

Posted in Causation, Expert Witness Hall of Shame, Medical monitoring, Meta-analysis, Rule 702, Scientific Evidence | Comments Off on The Shmeta-Analysis in Paoli

Specious Claiming in Multi-District Litigation

May 2nd, 2019

In a recent article in an American Bar Association newsletter, Paul Rheingold notes with some concern that, in the last two years or so, there has been a rash of dismissals of entire multi-district litigations (MDLs) based upon plaintiffs’ failure to produce expert witnesses who can survive Rule 702 gatekeeping.[1] Paul D. Rheingold, “Multidistrict Litigation Mass Terminations for Failure to Prove Causation,” A.B.A. Mass Tort Litig. Newsletter (April 24, 2019) [cited as Rheingold]. According to Rheingold, judges historically involved in the MDL processing of products liability cases did not grant summary judgments across the board. In other words, federal judges felt that if plaintiffs’ lawyers aggregated a sufficient number of cases, then their judicial responsibility was to push settlements or to remand the cases to the transferor courts for trial.

Missing from Rheingold’s account is the prevalent judicial view, in the early going of MDL of products cases, which held that judges lacked the authority to consider Rule 702 motions for all cases in the MDL. Gatekeeping motions were considered extreme and best avoided by pushing them off to the transferor courts upon remand. In MDL 926, involving silicone gel breast implants, the late Judge Sam Pointer, who was a member of the Rules Advisory Committee, expressed the view that Rule 702 gatekeeping was a trial court function, for the trial judge who received the case on remand from the MDL.[2] Judge Pointer’s view was a commonplace in the 1990s. As mass tort litigation moved into MDL “camps,” judges more frequently adopted a managerial rather than a judicial role, and exerted great pressure on the parties, and the defense in particular, to settle cases. These judges frequently expressed their view that the two sides so stridently disagreed on causation that the truth must be somewhere in between, and even with “a little causation,” the defendants should offer a little compensation. These litigation managers thus eschewed dispositive motion practice, or gave it short shrift.

Rheingold cites five recent MDL terminations based upon “Daubert failure,” and he acknowledges other MDLs collapsed because of federal pre-emption issues (Eliquis, Incretins, and possibly Fosamax), and that other fatally weak causal MDL claims settled for nominal compensation (NuvaRing). He omits other MDLs, such as In re Silica, in which an entire MDL collapsed because of prevalent fraud in the screening and diagnosing of silicosis claimants by plaintiffs’ counsel and their expert witnesses.[3] Also absent from his reckoning is the collapse of MDL cases against Celebrex[4] and Viagra[5].

Rheingold does concede that the recent across-the-board dismissals of MDLs were due to very weak causal claims.[6] He softens his judgment by suggesting that the weaknesses were apparent “at least in retrospect,” but the weaknesses were clearly discernible before litigation by the refusal of regulatory agencies, such as the FDA, to accept the litigation-driven causal claims. Rheingold also tries to assuage fellow plaintiffs’ counsel by suggesting that plaintiffs’ lawyers somehow fell prey to the pressure to file cases because of internet advertising and the encouragement of records collection and analysis firms. This attribution of naiveté to Plaintiffs’ Steering Committee (PSC) members does not ring true given the wealth and resources of lawyers on PSCs. Furthermore, the suggestion that PSC member may be newcomers to the MDL playing fields does not hold water given that most of the lawyers involved are “repeat players,” with substantial experience and financial incentives to sort out invalid expert witness opinions.[7]

Rheingold offers the wise counsel that plaintiffs’ lawyers “should take [their] time and investigate for [themselves] the potential proof available for causation and adequacy of labeling.” If history is any guide, his advice will not be followed.

[1] Rheingold cites five MDLs that were “Daubert failures” in the recent times: (1) In re Lipitor (Atorvastatin Calcium) Marketing, Sales Practices & Prods. Liab. Litig. (MDL 2502), 892 F.3d 624 (4th Cir. 2018) (affirming Rule 702 dismissal of claims that atorvastatin use caused diabetes); (2) In re Mirena IUD Products Liab. Litig. (Mirena II, MDL 2767), 713 F. App’x 11 (2d Cir. 2017) (excluding expert witnesses’ opinion testimony that the intrauterine device caused embedment and perforation); (3) In re Mirena Ius Levonorgestrel-Related Prods. Liab. Litig., (Mirena II), 341 F. Supp. 3d 213 (S.D.N.Y. 2018) (affirming Rule 702 dismissal of claims that product caused pseudotumor cerebri); (4) In re Zoloft (Sertraline Hydrochloride) Prods. Liab. Litig., 858 F.3d 787 (3d Cir. 2017) (affirming MDL trial court’s Rule 702 exclusions of opinions that Zoloft is teratogenic); (5) Jones v. SmithKline Beecham, 652 F. App’x 848 (11th Cir. 2016) (affirming MDL court’s Rule 702 exclusions of expert witness opinions that denture adhesive creams caused metal deficiencies).

[2] Not only was Judge Pointer a member of the Rules committee, he was the principal author of the 1993 Amendments to the Federal Rules of Civil Procedure, as well as the editor-in-chief of the Federal Judicial Center’s Manual for Complex. At an ALI-ABA conference in 1997, Judge Pointer complained about the burden of gatekeeping. 3 Federal Discovery News 1 (Aug. 1997). He further opined that, under Rule 104(a), he could “look to decisions from the Southern District of New York and Eastern District of New York, where the same expert’s opinion has been offered and ruled upon by those judges. Their rulings are hearsay, but hearsay is acceptable. So I may use their rulings as a basis for my decision on whether to allow it or not.” Id. at 4. Even after Judge Jack Weinstein excluded plaintiffs’ expert witnesses’ causal opinions in the silicone litigation, however, Judge Pointer avoided having to make an MDL-wide decision with the scope of one of the leading judges from the Southern and Eastern Districts of New York. See In re Breast Implant Cases, 942 F. Supp. 958 (E. & S.D.N.Y. 1996). Judge Pointer repeated his anti-Daubert views three years later at a symposium on expert witness opinion testimony. See Sam C. Pointer, Jr., “Response to Edward J. Imwinkelried, the Taxonomy of Testimony Post-Kumho: Refocusing on the Bottom Lines of Reliability and Necessity,” 30 Cumberland L. Rev. 235 (2000).

[3] In re Silica Products Liab. Litig., MDL No. 1553, 398 F. Supp. 2d 563 (S.D. Tex. 2005).

[4] In re Bextra & Celebrex Marketing Sales Practices & Prod. Liab. Litig., 524 F. Supp. 2d 1166 (N.D. Calif. 2007) (excluding virtually all relevant expert witness testimony proffered to support claims that ordinary dosages of these COX-2 inhibitors caused cardiovascular events).

[5] In re Viagra Products Liab. Litig., 572 F. Supp. 2d 1071 (D. Minn. 2008) (addressing claims that sildenafil causes vision loss from non-arteritic anterior ischemic optic neuropathy (NAION)).

[6] Rheingold (“Examining these five mass terminations, at least in retrospect[,] it is apparent that they were very weak on causation.”)

[7] See Elizabeth Chamblee Burch & Margaret S. Williams, “Repeat Players in Multidistrict Litigation: The Social Network,” 102 Cornell L. Rev. 1445 (2017); Margaret S. Williams, Emery G. Lee III & Catherine R. Borden, “Repeat Players in Federal Multidistrict Litigation,” 5 J. Tort L. 141, 149–60 (2014).

Posted in Causation, Expert Witnesses, Rule 702, Scientific Evidence | Comments Off on Specious Claiming in Multi-District Litigation

Has the American Statistical Association Gone Post-Modern?

March 24th, 2019

Last week, the American Statistical Association (ASA) released a special issue of its journal, The American Statistician, with 43 articles addressing the issue of “statistical significance.” If you are on the ASA’s mailing list, you received an email announcing that

“the lead editorial calls for abandoning the use of ‘statistically significant’, and offers much (not just one thing) to replace it. Written by Ron Wasserstein, Allen Schirm, and Nicole Lazar, the co-editors of the special issue, ‘Moving to a World Beyond ‘p < 0.05’ summarizes the content of the issue’s 43 articles.”

In 2016, the ASA issued its “consensus” statement on statistical significance, in which it articulated six principles for interpreting p-values, and for avoiding erroneous interpretations. Ronald L. Wasserstein & Nicole A. Lazar, “The ASA’s Statement on p-Values: Context, Process, and Purpose,” 70 The American Statistician 129 (2016) [ASA Statement] In the final analysis, that ASA Statement really did not change very much, and could be read fairly only to state that statistical significance was not sufficient for causal inference.¹ Aside from overzealous, over-claiming lawyers and their expert witnesses, few scientists or statisticians had ever maintained that statistical significance was sufficient to support causal inference. Still, many “health effect claims” involve alleged causation that is really a modification of a base rate of a disease or disorder that happens without the allegedly harmful exposure, and which does not invariably happen even with the exposure. It is hard to imagine drawing an inference of such causation without ruling out random error, as well as bias and confounding.

According to the lead editorial for the special issue:

“The ASA Statement on P-Values and Statistical Significance stopped just short of recommending that declarations of ‘statistical significance’ be abandoned. We take that step here. We conclude, based on our review of the articles in this special issue and the broader literature, that it is time to stop using the term ‘statistically significant’ entirely. Nor should variants such as ‘significantly different’, ‘p < 0.05’, and ‘nonsignificant’ survive, whether expressed in words, by asterisks in a table, or in some other way.”²

The ASA (through Wasserstein and colleagues) appear to be condemning dichotomizing p-values, which are a continuum between zero and one. Presumably saying that a p-value is less than 5% is tantamount to dichotomizing, but providing the actual value of the p-value would cause no offense, as long as it was not labeled “significant.”

So although the ASA appears to have gone “whole hog,” the Wasserstein editorial does not appear to condemn assessing random error, or evaluating the extent of random error as part of assessing a study’s support for an association. Reporting p < 0.05 as opposed to p = a real number between zero and one is largely an artifact of statistical tables in the pre-computer era.

So what is the ASA affirmatively recommending? “Much, not just one thing?” Or too much of nothing, which we know makes a man feel ill at ease. Wasserstein’s editorial earnestly admits that there is no replacement for:

“the outsized role that statistical significance has come to play. The statistical community has not yet converged on a simple paradigm for the use of statistical inference in scientific research—and in fact it may never do so.”³

The 42 other articles in the special issue certainly do not converge on any unified, coherent response to the perceived crisis. Indeed, a cursory review of the abstracts alone suggests deep disagreements over an appropriate approach to statistical inference. The ASA may claim to be agnostic in the face of the contradictory recommendations, but there is one thing we know for sure: over-reaching litigants and their expert witnesses will exploit the real or apparent chaos in the ASA’s approach. The lack of coherent, consistent guidance will launch a thousand litigation ships, with no epistemic compass.⁴

1 “The American Statistical Association’s Statement on and of Significance” (March 17, 2016); “The American Statistical Association Statement on Significance Testing Goes to Court – Part I” (Nov. 13, 2018).

2 Ronald L. Wasserstein, Allen L. Schirm, and Nicole A. Lazar, “Editorial: Moving to a World Beyond ‘p < 0.05’,” 73 Am. Statistician S1, S2 (2019).

3 Id. at S2.

4 See, e.g., John P. A. Ioannidis, “Retiring statistical significance would give bias a free pass,” 567 Nature 461 (2019); Valen E. Johnson, “Raise the Bar Rather than Retire Significance,” 567 Nature 461 (2019).

Posted in Rule 702, statistical evidence | Comments Off on Has the American Statistical Association Gone Post-Modern?

Expert Witnesses Who Don’t Mean What They Say

March 24th, 2019

’Then you should say what you mean’, the March Hare went on.
‘I do’, Alice hastily replied; ‘at least–at least I mean what I say–that’s the same thing, you know’.
‘Not the same thing a bit!’ said the Hatter. ‘You might just as well say that “I see what I eat” is the same thing as “I eat what I see!”’

Lewis Carroll, Alice’s Adventures in Wonderland, Chapter VII (1865)

Anick Bérard is an epidemiologist at the Université de Montréal. Most of her publications involve birth outcomes and maternal medication use, but Dr. Bérard’s advocacy also involves social media (Facebook, YouTube) and expert witnessing in litigation against the pharmaceutical industry.

When the FDA issued its alert about cardiac malformations in children born to women who took Paxil (paroxetine) in their first trimesters of pregnancy, the agency characterized its assessment of the “early results of new studies for Paxil” as “suggesting that the drug increases the risk for birth defects, particularly heart defects, when women take it during the first three months of pregnancy.”¹ The agency also disclaimed any conclusion of “class effect” among the other selective serotonin reuptake inhibitors (SSRIs), such as Zoloft (sertraline), Celexa (citalopram), and Prozac (fluoxetine). Indeed, the FDA requested the manufacturer of paroxetine to undertake additional research to look at teratogenicity of paroxetine, as well as the possibility of class effects. That research never showed an SSRI teratogenicity class effect.

A “suggestion” from the FDA of an adverse effect is sufficient to launch a thousand litigation complaints, which were duly filed against GlaxoSmithKline. The plaintiffs’ counsel recruited Dr. Bérard to serve as an expert witness in support of a wide array of birth defects in Paxil cases. In her hands, the agency’s “suggestion” of causation became a conclusion. The defense challenged Bérard’s opinions, but the federal court motion to exclude her causal opinions were taken under advisement, without decision. Hayes v. SmithKline Beecham Corp., 2009 WL 4912178 (N.D. Okla. Dec. 14, 2009). One case in state court went to trial, with a verdict for plaintiffs.

Despite Dr. Bérard;s zealous advocacy for a causal association between Paxil and birth defects, she declined to assert any association between maternal use of the other, non-paroxetine SSRIs and birth defects. Here is an excerpt from her Rule 26 report in a paroxetine case:

“Taken together, the available scientific evidence makes it clear that Paxil use during the first trimester of pregnancy is an independent risk factor that at least doubles the risk of cardiovascular malformations in newborns at all commonly used doses. This risk has been consistent and was further reinforced by repeated observational study findings as well as meta-analyses results. No such associations were found with other types of SSRI exposures during gestation.”²

In her sworn testimony, Dr. Bérard made clear that she really meant what she had written in her report, about exculpating the non-paroxetine SSRIs of any association with birth defects:

“Q. Is it fair to say that you will not be offering an opinion that SSRIs as a class, or individual SSRIs other than Paxil increased the risk of cardiovascular malformations in newborns?

A. This is not what I was asked to do.

Q. But in fact you actually write in your report that you don’t believe there’s sufficient data to reach any conclusion about other SSRIs, true?

A. Correct.”³

In 2010, Dr. Bérard, along with two professional colleagues, published what they called a systematic review of antidepressant use in pregnancy and birth outcomes.⁴ In this review, Bérard specifically advised that paroxetine should be avoided by women of childbearing age, but she and her colleagaues affirmatively encouraged use of other SSRIs, such as fluoxetine, sertraline, and citalopram:

“Clinical Approach: A Brief Overview

“For women planning a pregnancy or when a treatment initiation during pregnancy is deemed necessary, the decision should rely not only on drug safety data but also on other factors such as the patient’s condition, previous response to other antidepressants, comorbidities, expected adverse effects and potential interactions with other current pharmacological treatments. Since there is a more extensive clinical experience with SSRIs such as fluoxetine, sertraline, and citalopram, these agents should be used as first-line therapies. Whenever possible, one should refrain from prescribing paroxetine to women of childbearing potential or planning a pregnancy. However, antenatal screening such as fetal echocardiography should be considered in a woman exposed prior to finding out about her pregnancy.”⁵

When Bérard wrote and published her systematic review, she was still actively involved as an expert witness for plaintiffs in lawsuits against the manufacturers of paroxetine. In her 2010 review, Dr. Bérard gave no acknowledgment of monies earned in her capacity as an expert witness, and her disclosure of potential conflicts of interest was limited to noting that she was “a consultant for a plaintiff in the litigation involving Paxil.”⁶ In fact, Bérard had submitted multiple reports, testified at deposition, and had been listed as a testifying expert witness in many cases involving Paxil or paroxetine.

Not long after the 2010 review article, Glaxo settled most of the pending paroxetine birth defect cases, and the plaintiffs’ bar pivoted to recast their expert witnesses’ opinions as causal teratogenic conclusions about the entire class of SSRIs. In 2012, the federal courts established a “multi-district litigation,” MDL 2342, for birth defect cases involving Zoloft (sertraline), in the Philadelphia courtroom of Judge Cynthia Rufe, in the Eastern District of Pennsylvania.

Notwithstanding her 2010 clinical advice that pregnant women with depression should use fluoxetine, sertraline, or citalopram, Dr. Bérard became actively involved in the new litigation against the other, non-Paxil SSRI manufacturers. By 2013, Dr. Bérard was on record as a party expert witness for plaintiffs, opining that setraline causes virtually every major congenital malformation.⁷

In the same year, 2013, Dr. Bérard published another review article on teratogens, but now she gave a more equivocal view of the other SSRIs, claiming that they were “known carcinogens,” but acknowledging in a footnote that teratogenicity of the SSRIs was “controversial.”⁸ Incredibly, this review article states that “Anick Bérard and Sonia Chaabane have no potential conflicts of interest to disclose.”⁹

Ultimately, Dr. Bérard could not straddle her own contradictory statements and remain upright, which encouraged the MDL court to examine her opinions closely for methodological shortcomings and failures. Although Bérard had evolved to claim a teratogenic “class effect” for all the SSRIs, the scientific support for her claim was somewhere between weak to absent.¹⁰ Perhaps even more distressing, many of the pending claims involving the other SSRIs arose from pregnancies and births that predated Bérard’s epiphany about class effect. Finding ample evidence of specious claiming, the federal court charged with oversight of the sertraline birth defect claims excluded Dr. Bérard’s causal opinions for failing to meet the requirements of Federal Rule of Evidence 702.¹¹

Plaintiffs sought to substitute Nicholas Jewell for Dr. Bérard, but Dr. Jewell fared no better, and was excluded for other methodological shenanigans.¹² Ultimately, a unanimous panel of the United States Court of Appeals, for the Third Circuit, upheld the expert witness exclusions.¹³

1 See “FDA Advising of Risk of Birth Defects with Paxil; Agency Requiring Updated Product Labeling,” P05-97 (Dec. 8, 2005) (emphasis added).

2 Bérard Report in Hayes v. SmithKline Beecham Corp, 2009 WL 3072955, at *4 (N.D. Okla. Feb. 4, 2009) (emphasis added).

3 Deposition Testimony of Anick Bérard, in Hayes v. SmithKline Beecham Corp., at 120:16-25 (N.D. Okla. April 2009).

4 Marieve Simoncelli, Brigitte-Zoe Martin & Anick Bérard, “Antidepressant Use During Pregnancy: A Critical Systematic Review of the Literature,” 5 Current Drug Safety 153 (2010).

5 Id. at 168b.

6 Id. at 169 (emphasis added).

7 See Anick Bérard, “Expert Report” (June 19, 2013).

8 Sonia Chaabanen & Anick Bérard, “Epidemiology of Major Congenital Malformations with Specific Focus on Teratogens,” 8 Current Drug Safety 128, 136 (2013).

9 Id. at 137b.

10 See, e.g., Nicholas Myles, Hannah Newall, Harvey Ward, and Matthew Large, “Systematic meta-analysis of individual selective serotonin reuptake inhibitor medications and congenital malformations,” 47 Australian & New Zealand J. Psychiatry 1002 (2013).

11 See In re Zoloft (Sertraline Hydrochloride) Prods. Liab. Litig., MDL No. 2342; 26 F.Supp. 3d 449 (E.D.Pa. 2014) (Rufe, J.). Plaintiffs, through their Plaintiffs’ Steering Committee, moved for reconsideration, but Judge Rufe reaffirmed her exclusion of Dr. Bérard. In re Zoloft (Sertraline Hydrochloride) Prods. Liab. Litig., MDL No. 2342; 12-md-2342, 2015 WL 314149 (E.D. Pa. Jan. 23, 2015) (Rufe, J.) (denying PSC’s motion for reconsideration). See “Zoloft MDL Relieves Matrixx Depression” (Jan. 30, 2015).

12 See In re Zoloft Prods. Liab. Litig., No. 12–md–2342, 2015 WL 7776911 (E.D. Pa. Dec. 2, 2015) (excluding Jewell’s opinions as scientifically unwarranted and methodologically flawed); In re Zoloft Prod. Liab. Litig., MDL NO. 2342, 12-MD-2342, 2016 WL 1320799 (E.D. Pa. April 5, 2016) (granting summary judgment after excluding Dr. Jewell). See also “The Education of Judge Rufe – The Zoloft MDL” (April 9, 2016).

13 In re Zoloft Prod. Liab. Litig., 858 F.3d 787 (3d Cir. 2017). See “WOE — Zoloft Escapes a MDL While Third Circuit Creates a Conceptual Muddle” (July 31, 2017).

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The Contrivance Standard for Gatekeeping

March 23rd, 2019

According to Google ngram, the phrase “junk science” made its debut circa 1975, lagging junk food by about five years. See “The Rise and Rise of Junk Science” (Mar. 8, 2014). I have never much like the phrase “junk science” because it suggests that courts need only be wary of the absurd and ridiculous in their gatekeeping function. Some expert witness opinions are, in fact, serious scientific contributions, just not worthy of being advanced as scientific conclusions. Perhaps better than “junk” would be patho-epistemologic opinions, or maybe even wissenschmutz, but even these terms might obscure that the opinion that needs to be excluded derives from serious scientific, only it is not ready to be held forth as a scientific conclusion that can be colorably called knowledge.

Another formulation of my term, patho-epistemology, is the Eleventh Circuit’s lovely “Contrivance Standard.” Rink v. Cheminova, Inc., 400 F.3d 1286, 1293 & n.7 (11th Cir. 2005). In Rink, the appellate court held that the district court had acted within its discretion to exclude expert witness testimony because it had properly confined its focus to the challenged expert witness’s methodology, not his credibility:

“In evaluating the reliability of an expert’s method, however, a district court may properly consider whether the expert’s methodology has been contrived to reach a particular result. See Joiner, 522 U.S. at 146, 118 S.Ct. at 519 (affirming exclusion of testimony where the methodology was called into question because an “analytical gap” existed “between the data and the opinion proffered”); see also Elcock v. Kmart Corp., 233 F.3d 734, 748 (3d Cir. 2000) (questioning the methodology of an expert because his “novel synthesis” of two accepted methodologies allowed the expert to ”offer a subjective judgment … in the guise of a reliable expert opinion”).”

Note the resistance, however, to the Supreme Court’s mandate of gatekeeping. District courts must apply the statutes, Rule of Evidence 702 and 703. There is no legal authority for the suggestion that a district court “may properly consider wither the expert’s methodology has been contrived.” Rink, 400 F.3d at 1293 n.7 (emphasis added).

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The Joiner Finale

March 23rd, 2019

“This is the end
Beautiful friend

This is the end
My only friend, the end”

Jim Morrison, “The End” (c. 1966)

The General Electric Co. v. Joiner, 522 U.S. 136 (1997), case was based upon polychlorinated biphenyl exposures (PCB), only in part. The PCB part did not hold up well legally in the Supreme Court; nor was the PCB lung cancer claim vindicated by later scientific evidence. See “How Have Important Rule 702 Holdings Held Up With Time?” (Mar. 20, 2015).

The Supreme Court in Joiner reversed and remanded the case to the 11^th Circuit, which then remanded the case back to the district court to address claims that Mr. Joiner had been exposed to furans and dioxins, and that these other chemicals had caused, or contributed to, his lung cancer, as well. Joiner v. General Electric Co., 134 F.3d 1457 (11th Cir. 1998) (per curiam). Thus the dioxins were left in the case even after the Supreme Court ruled.

After the Supreme Court’s decision, Anthony Roisman argued that the Court had addressed an artificial question when asked about PCBs alone because the case was really about an alleged mixture of exposures, and he held out hope that the Joiners would do better on remand. Anthony Z. Roisman, “The Implications of G.E. v. Joiner for Admissibility of Expert Testimony,” 1 Res Communes 65 (1999).

Many Daubert observers (including me) are unaware of the legal fate of the Joiners’ claims on remand. In the only reference I could find, the commentator simply noted that the case resolved before trial.[1] I am indebted to Michael Risinger, and Joseph Cecil, for pointing me to documents from PACER, which shed some light upon the Joiner “endgame.”

In February 1998, Judge Orinda Evans, who had been the original trial judge, and who had sustained defendants’ Rule 702 challenges and granted their motions for summary judgments, received and reopened the case upon remand from the 11th Circuit. In March, Judge Evans directed the parties to submit a new pre-trial order by April 17, 1998. At a status conference in April 1998, Judge Evans permitted the plaintiffs additional discovery, to be completed by June 17, 1998. Five days before the expiration of their additional discovery period, the plaintiffs moved for additional time; defendants opposed the request. In July, Judge Evans granted the requested extension, and gave defendants until November 1, 1998, to file for summary judgment.

Meanwhile, in June 1998, new counsel entered their appearances for plaintiffs – William Sims Stone, Kevin R. Dean, Thomas Craig Earnest, and Stanley L. Merritt. The docket does not reflect much of anything about the new discovery other than a request for a protective order for an unpublished study. But by October 6, 1998, the new counsel, Earnest, Dean, and Stone (but not Merritt) withdrew as attorneys for the Joiners, and by the end of October 1998, Judge Evans entered an order to dismiss the case, without prejudice.

A few months later, in February 1999, the parties filed a stipulation, approved by the Clerk, dismissing the action with prejudice, and with each party to bear its own coasts. Given the flight of plaintiffs’ counsel, the dismissals without and then with prejudice, a settlement seems never to have been involved in the resolution of the Joiner case. In the end, the Joiners’ case fizzled perhaps to avoid being Frye’d.

And what has happened since to the science of dioxins and lung cancer?

Not much.

In 2006, the National Research Council published a monograph on dioxin, which took the controversial approach of focusing on all cancer mortality rather than specific cancers that had been suggested as likely outcomes of interest. See David L. Eaton (Chairperson), Health Risks from Dioxin and Related Compounds – Evaluation of the EPA Reassessment (2006). The validity of this approach, and the committee’s conclusions, were challenged vigorously in subsequent publications. Paolo Boffetta, Kenneth A. Mundt, Hans-Olov Adami, Philip Cole, and Jack S. Mandel, “TCDD and cancer: A critical review of epidemiologic studies,” 41 Critical Rev. Toxicol. 622 (2011) (“In conclusion, recent epidemiological evidence falls far short of conclusively demonstrating a causal link between TCDD exposure and cancer risk in humans.”

In 2013, the Industrial Injuries Advisory Council (IIAC), an independent scientific advisory body in the United Kingdom, published a review of lung cancer and dioxin. The Council found the epidemiologic studies mixed, and declined to endorse the compensability of lung cancer for dioxin-exposed industrial workers. Industrial Injuries Advisory Council – Information Note on Lung cancer and Dioxin (December 2013). See also Mann v. CSX Transp., Inc., 2009 WL 3766056, 2009 U.S. Dist. LEXIS 106433 (N.D. Ohio 2009) (Polster, J.) (dioxin exposure case) (“Plaintiffs’ medical expert, Dr. James Kornberg, has opined that numerous organizations have classified dioxins as a known human carcinogen. However, it is not appropriate for one set of experts to bring the conclusions of another set of experts into the courtroom and then testify merely that they ‘agree’ with that conclusion.”), citing Thorndike v. DaimlerChrysler Corp., 266 F. Supp. 2d 172 (D. Me. 2003) (court excluded expert who was “parroting” other experts’ conclusions).

Last year, an industrial cohort, followed for two decades found no increased risk of lung cancer among workers exposed to dioxin. David I. McBride, James J. Collins, Thomas John Bender, Kenneth M Bodner, and Lesa L. Aylward, “Cohort study of workers at a New Zealand agrochemical plant to assess the effect of dioxin exposure on mortality,” 8 Brit. Med. J. Open e019243 (2018) (reporting SMR for lung cancer 0.95, 95%CI: 0.56 to 1.53)

[1] Morris S. Zedeck, Expert Witness in the Legal System: A Scientist’s Search for Justice 49 (2010) (noting that, after remand from the Supreme Court, Joiner v. General Electric resolved before trial)

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Lipitor Diabetes MDL’s Inexact Analysis of Fisher’s Exact Test

March 23rd, 2019

Muriel Bristol was a biologist who studied algae at the Rothamsted Experimental Station in England, after World War I. In addition to her knowledge of plant biology, Bristol claimed the ability to tell whether tea had been added to milk, or the tea poured first and then milk had been added. Bristol, as a scientist and a proper English woman, preferred the latter.

Ronald Fisher, who also worked at Rothamsted, expressed his skepticism over Dr. Bristol’s claim. Fisher set about to design a randomized experiment that would efficiently and effectively test her claim. Bristol was presented with eight cups of tea, four of which were prepared with milk added to tea, and four prepared with tea added to milk. Bristol, of course, was blinded to which was which, but was required to label each according to its manner of preparation. Fisher saw his randomized experiment as a 2 x 2 contingency table, from he could calculate the observed outcome (and ones more extreme if there were any more extreme outcomes) using the assumption of fixed marginal rates and the hypergeometric probability distribution. Fisher’s Exact Test was born at tea time.[1]

Fisher described the origins of his Exact Test in one of his early texts, but he neglected to report whether his experiment vindicated Bristol’s claim. According to David Salsburg, H. Fairfield Smith, one of Fisher’s colleagues, acknowledged that Bristol nailed Fisher’s Exact test, with all eight cups correctly identified. The test has gone on to become an important tool in the statistician’s armamentarium.

Fisher’s Exact, like any statistical test, has model assumptions and preconditions. For one thing, the test is designed for categorical data, with binary outcomes. The test allows us to evaluate whether two proportions are likely different by chance alone, by calculating the probability of the observed outcome, as well as more extreme outcomes.

The calculation of an exact attained significance probability, using Fisher’s approach, provides a one-sided p-value, with no unique solution to calculating a two-side attained significance probability. In discrimination cases, the one-sided p-value may well be more appropriate for the issue at hand. The Fisher’s Exact Test has thus played an important role in showing the judiciary that small sample size need not be an insuperable barrier to meaningful statistical analysis. In discrimination cases, the one-sided p-value provided by the test is not a particular problem.[2]

The difficulty of using Fisher’s Exact for small sample sizes is that the hypergeometric distribution, upon which the test is based, is highly asymmetric. The observed one-sided p-value does not measure the probability of a result equally extreme in the opposite direction. There are at least three ways to calculate the p-value:

Double the one-sided p-value.
Add the point probabilities from the opposite tail that are more extreme than the observed point probability.
Use the mid-P value; that is, add all values more extreme (smaller) than the observed point probability from both sides of the distribution, PLUS ½ of the observed point probability.

Some software programs will proceed in one of these ways by default, but their doing so does guarantee the most accurate measure of two-tailed significance probability.

In the Lipitor MDL for diabetes litigation, Judge Gergel generally used sharp analyses to cut through the rancid fat of litigation claims, to get to the heart of the matter. By and large, he appears to have done a splendid job. In course of gatekeeping under Federal Rule of Evidence 702, however, Judge Gergel may have misunderstood the nature of Fisher’s Exact Test.

Nicholas Jewell is a well-credentialed statistician at the University of California. In the courtroom, Jewell is a well-known expert witness for the litigation industry. He is no novice at generating unreliable opinion testimony. See In re Zoloft Prods. Liab. Litig., No. 12–md–2342, 2015 WL 7776911 (E.D. Pa. Dec. 2, 2015) (excluding Jewell’s opinions as scientifically unwarranted and methodologically flawed). In re Zoloft Prod. Liab. Litig., MDL NO. 2342, 12-MD-2342, 2016 WL 1320799 (E.D. Pa. April 5, 2016) (granting summary judgment after excluding Dr. Jewell). See “The Education of Judge Rufe – The Zoloft MDL” (April 9, 2016).

In the Lipitor cases, some of Jewell’s opinions seemed outlandish indeed, and Judge Gergel generally excluded them. See In re Lipitor Marketing, Sales Practices and Prods. Liab. Litig., 145 F.Supp. 3d 573 (D.S.C. 2015), reconsideration den’d, 2016 WL 827067 (D.S.C. Feb. 29, 2016). As Judge Gergel explained, Jewell calculated a relative risk for abnormal blood glucose in a Lipitor group to be 3.0 (95% C.I., 0.9 to 9.6), using STATA software. Also using STATA, Jewell obtained an attained significance probability of 0.0654, based upon Fisher’s Exact Test. Lipitor Jewell at *7.

Judge Gergel did not report whether Jewell’s reported p-value of 0.0654, was one- or two-sided, but he did state that the attained probability “indicates a lack of statistical significance.” Id. & n. 15. The rest of His Honor’s discussion of the challenged opinion, however, makes clear that of 0.0654 must have been a two-sided value. If it had been a one-sided p-value, then there would have been no way of invoking the mid-p to generate a two-sided p-value below 5%. The mid-p will always be larger than the one-tailed exact p-value generated by Fisher’s Exact Test.

The court noted that Dr. Jewell had testified that he believed that STATA generated this confidence interval by “flip[ping]” the Taylor series approximation. The STATA website notes that it calculates confidence intervals for odds ratios (which are different from the relative risk that Jewell testified he computed), by inverting the Fisher exact test.[3] Id. at *7 & n. 17. Of course, this description suggests that the confidence interval is not based upon exact methods.

STATA does not provide a mid p-value calculation, and so Jewell used an on-line calculator, to obtain a mid p-value of 0.04, which he declared statistically significant. The court took Jewell to task for using the mid p-value as though it were a different analysis or test. Id. at *8. Because the mid-p value will always be larger than the one-sided exact p-value from Fisher’s Exact Test, the court’s explanation does not really make sense:

“Instead, Dr. Jewell turned to the mid-p test, which would ‘[a]lmost surely’ produce a lower p-value than the Fisher exact test.”

Id. at *8. The mid-p test, however, is not different from the Fisher’s exact; rather it is simply a way of dealing with the asymmetrical distribution that underlies the Fisher’s exact, to arrive at a two-tailed p-value that more accurately captures the rate of Type I error.

The MDL court acknowledged that the mid-p approach, was not inherently unreliable, but questioned Jewell’s inconsistent, selective use of the approach for only one test.[4] Jewell certainly did not help the plaintiffs’ cause and his standing by having discarding the analyses that were not incorporated into his report, thus leaving the MDL court to guess at how much selection went on in his process of generating his opinions.. Id. at *9 & n. 19.

None of Jewell’s other calculated p-values involved the mid-p approach, but the court’s criticism begs the question whether the other p-values came from a Fisher’s Exact Test with small sample size, or other highly asymmetrical distribution. Id. at *8. Although Jewell had shown himself willing to engage in other dubious, result-oriented analyses, Jewell’s use of the mid-p for this one comparison may have been within acceptable bounds after all.

The court also noted that Jewell had obtained the “exact p-value and that this p-value was not significant.” Id. The court’s notation here, however, does not report the important detail whether that exact, unreported p-value was merely the doubled of the one-sided p-value given by the Fisher’s Exact Test. As the STATA website, cited by the MDL court, explains:

“The test naturally gives a one-sided p-value, and there are at least four different ways to convert it to a two-sided p-value (Agresti 2002, 93). One way, not implemented in Stata, is to double the one-sided p-value; doubling is simple but can result in p-values larger than one.”

Wesley Eddings, “Fisher’s exact test two-sided idiosyncrasy” (Jan. 2009) (citing Alan Agresti, Categorical Data Analysis 93 (2d ed. 2002)).

On plaintiffs’ motion for reconsideration, the MDL court reaffirmed its findings with respect to Jewell’s use of the mid-p. Lipitor Jewell Reconsidered at *3. In doing so, the court insisted that the one instance in which Jewell used the mid-p stood in stark contrast to all the other instances in which he had used Fisher’s Exact Test. The court then cited to the record to identify 21 other instances in which Jewell used a p-value rather than a mid-p value. The court, however, did not provide the crucial detail whether these 21 other instances actually involved small-sample applications of Fisher’s Exact Test. As result-oriented as Jewell can be, it seems safe to assume that not all his statistical analyses involved Fisher’s Exact Test, with its attendant ambiguity for how to calculate a two-tailed p-value.

[1] Sir Ronald A. Fisher, The Design of Experiments at chapter 2 (1935); see also Stephen Senn, “Tea for three: Of infusions and inferences and milk in first,” Significance 30 (Dec. 2012); David Salsburg, The Lady Tasting Tea: How Statistics Revolutionized Science in the Twentieth Century (2002).

[2] See, e.g., Dendy v. Washington Hosp. Ctr., 431 F. Supp. 873 (D.D.C. 1977) (denying preliminary injunction), rev’d, 581 F.2d 99 (D.C. Cir. 1978) (reversing denial of relief, and remanding for reconsideration). See also National Academies of Science, Reference Manual on Scientific Evidence 255 n.108 (3d ed. 2011) (“Well-known small sample techniques [for testing significance and calculating p-values] include the sign test and Fisher’s exact test.”).

[3] See Wesley Eddings, “Fisher’s exact test two-sided idiosyncrasy” (Jan. 2009), available at <http://www.stata.com/support/faqs/statistics/fishers-exact-test/>, last visited April 19, 2016 (“Stata’s exact confidence interval for the odds ratio inverts Fisher’s exact test.”). This article by Eddings contains a nice discussion of why the Fisher’s Exact Test attained significance probability disagrees with the calculated confidence interval. Eddings points out the asymmetry of the hypergeometric distribution, which complicates arriving at an exact p-value for a two-sided test.

[4] See Barber v. United Airlines, Inc., 17 Fed. Appx. 433, 437 (7th Cir. 2001) (“Because in formulating his opinion Dr. Hynes cherry-picked the facts he considered to render an expert opinion, the district court correctly barred his testimony because such a selective use of facts fails to satisfy the scientific method and Daubert.”).

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ASA Statement Goes to Court – Part 2

March 7th, 2019

It has been almost three years since the American Statistical Association (ASA) issued its statement on statistical significance. Ronald L. Wasserstein & Nicole A. Lazar, “The ASA’s Statement on p-Values: Context, Process, and Purpose,” 70 The American Statistician 129 (2016) [ASA Statement]. Before the ASA’s Statement, courts and lawyers from all sides routinely misunderstood, misstated, and misrepresented the meaning of statistical significance.¹ These errors were pandemic despite the efforts of the Federal Judicial Center and the National Academies of Science to educate judges and lawyers, through their Reference Manuals on Scientific Evidence and seminars. The interesting question is whether the ASA’s Statement has improved, or will improve, the unfortunate situation.²

The ASA Statement on Testosterone

“Ye blind guides, who strain out a gnat and swallow a camel!”
Matthew 23:24

To capture the state of the art, or the state of correct and flawed interpretations of the ASA Statement, reviewing a recent but now resolved, large so-called mass tort may be illustrative. Pharmaceutical products liability cases almost always turn on evidence from pharmaco-epidemiologic studies that compare the rate of an outcome of interest among patients taking a particular medication with the rate among similar, untreated patients. These studies compare the observed with the expected rates, and invariably assess the differences as either a “risk ratio,” or a “risk difference,” for both the magnitude of the difference and for “significance probability” of observing a rate at least as large as seen in the exposed group, given the assumptions that that the medication did not change the rate and that the data followed a given probability distribution. In these alleged “health effects” cases, claims and counterclaims of misuse of significance probability have been pervasive. After the ASA Statement was released, some lawyers began to modify their arguments to suggest that their adversaries’ arguments offend the ASA’s pronouncements.

One litigation that showcases the use and misuse of the ASA Statement arose from claims that AbbVie, Inc.’s transdermal testosterone medication (TRT) causes heart attacks, strokes, and venous thromboembolism. The FDA had reviewed the plaintiffs’ claims, made in a Public Citizen complaint, and resoundingly rejected the causal interpretation of two dubious observational studies, and an incomplete meta-analysis that used an off-beat composite end point.³ The Public Citizen petition probably did succeed in pushing the FDA to convene an Advisory Committee meeting, which again resulted in a rejection of the causal claims. The FDA did, however, modify the class labeling for TRT with respect to indication and a possible association with cardiovascular outcomes. And then the litigation came.

Notwithstanding the FDA’s determination that a causal association had not been shown, thousands of plaintiffs sued several companies, with most of the complaints falling on AbbVie, Inc., which had the largest presence in the market. The ASA Statement came up occasionally in pre-trial depositions, but became a major brouhaha, when AbbVie moved to exclude plaintiffs’ causation expert witnesses.⁴

The Defense’s Anticipatory Parry of the ASA Statement

As AbbVie described the situation:

“Plaintiffs’ experts uniformly seek to abrogate the established methods and standards for determining … causal factors in favor of precisely the kind of subjective judgments that Daubert was designed to avoid. Tests for statistical significance are characterized as ‘misleading’ and rejected [by plaintiffs’ expert witnesses] in favor of non-statistical ‘estimates’, ‘clinical judgment’, and ‘gestalt’ views of the evidence.”⁵

AbbVie’s brief in support of excluding plaintiffs’ expert witnesses barely mentioned the ASA Statement, but in a footnote, the defense anticipated the Plaintiffs’ opposition would be based on rejecting the importance of statistical significance testing and the claim that this rejection was somehow supported by the ASA Statement:

“The statistical community is currently debating whether scientists who lack expertise in statistics misunderstand p-values and overvalue significance testing. [citing ASA Statement] The fact that there is a debate among professional statisticians on this narrow issue does not validate Dr. Gerstman’s [plaintiffs’ expert witness’s] rejection of the importance of statistical significance testing, or undermine Defendants’ reliance on accepted methods for determining association and causation.”⁶

In its brief in support of excluding causation opinions, the defense took pains to define statistical significance, and managed to do so, painfully, or at least in ways that the ASA conferees would have found objectionable:

“Any association found must be tested for its statistical significance. Statistical significance testing measures the likelihood that the observed association could be due to chance variation among samples. Scientists evaluate whether an observed effect is due to chance using p-values and confidence intervals. The prevailing scientific convention requires that there be 95% probability that the observed association is not due to chance (expressed as a p-value < 0.05) before reporting a result as “statistically significant. * * * This process guards against reporting false positive results by setting a ceiling for the probability that the observed positive association could be due to chance alone, assuming that no association was actually present.”⁷

AbbVie’s brief proceeded to characterize the confidence interval as a tool of significance testing, again in a way that misstates the mathematical meaning and importance of the interval:

“The determination of statistical significance can be described equivalently in terms of the confidence interval calculated in connection with the association. A confidence interval indicates the level of uncertainty that exists around the measured value of the association (i.e., the OR or RR). A confidence interval defines the range of possible values for the actual OR or RR that are compatible with the sample data, at a specified confidence level, typically 95% under the prevailing scientific convention. Reference Manual, at 580 (Ex. 14) (“If a 95% confidence interval is specified, the range encompasses the results we would expect 95% of the time if samples for new studies were repeatedly drawn from the same population.”). * * * If the confidence interval crosses 1.0, this means there may be no difference between the treatment group and the control group, therefore the result is not considered statistically significant.”⁸

Perhaps AbbVie’s counsel should be permitted a plea in mitigation by having cited to, and quoted from, the Reference Manual on Scientific Evidence’s chapter on epidemiology, which was also wide of the mark in its description of the confidence interval. Counsel would have been better served by the Manual’s more rigorous and accurate chapter on statistics. Even so, the above-quoted statements give an inappropriate interpretation of random error as a probability about the hypothesis being tested.⁹ Particularly dangerous, in terms of failing to advance AbbVie’s own objectives, was the characterization of the confidence interval as measuring the level of uncertainty, as though there were no other sources of uncertainty other than random error in the measurement of the risk ratio.

The Plaintiffs’ Attack on Significance Testing

The Plaintiffs, of course, filed an opposition brief that characterized the defense position as an attempt to:

“elevate statistical significance, as measured by confidence intervals and so-called p-values, to the status of an absolute requirement to the establishment of causation.”¹⁰

Tellingly, the plaintiffs’ brief fails to point to any modern-era example of a scientific determination of causation based upon epidemiologic evidence, in which the pertinent studies were not assessed for, and found to show, statistical significance.

After citing a few judicial opinions that underplayed the importance of statistical significance, the Plaintiffs’ opposition turned to the ASA Statement for what it perceived to be support for its loosey-goosey approach to causal inference.¹¹ The Plaintiffs’ opposition brief quoted a series of propositions from the ASA Statement, without the ASA’s elaborations and elucidations, and without much in the way of explanation or commentary. At the very least, the Plaintiffs’ heavy reliance upon, despite their distortions of, the ASA Statement helped them to define key statistical concepts more carefully than had AbbVie in its opening brief.

The ASA Statement, however, was not immune from being misrepresented in the Plaintiffs’ opposition brief. Many of the quoted propositions were quite beside the points of the dispute over the validity and reliability of Plaintiffs’ expert witnesses’ conclusions of causation about testosterone and heart attacks, conclusions not reached or shared by the FDA, any consensus statement from medical organizations, or any serious published systematic review:

“P-values do not measure the probability that the studied hypothesis is true, … .”¹²

This proposition from the ASA Statement is true, but trivially true. (Of course, this ASA principle is relevant to the many judicial decisions that have managed to misstate what p-values measure.) The above-quoted proposition follows from the definition and meaning of the p-value; only someone who did not understand significance probability would confuse it with the probability of the truth of the studied hypothesis. P-values’ not measuring the probability of the null hypothesis, or any alternative hypothesis, is not a flaw in p-values, but arguably their strength.

“A p-value, or statistical significance, does not measure the size of an effect or the importance of a result.”¹³

Again, true, true, and immaterial. The existence of other importance metrics, such as the magnitude of an association or correlation, hardly detracts from the importance of assessing the random error in an observed statistic. The need to assess clinical or practical significance of an association or correlation also does not detract from the importance of the assessed random error in a measured statistic.

“By itself, a p-value does not provide a good measure of evidence regarding a model or hypothesis.”¹⁴

The Plaintiffs’ opposition attempted to spin the above ASA statement as a criticism of p-values involves an elenchi ignoratio. Once again, the p-value assumes a probability model and a null hypothesis, and so it cannot provide a “measure” or the model or hypothesis’ probability.

The Plaintiffs’ final harrumph on the ASA Statement was their claim that the ASA Statement’s conclusion was “especially significant” to the testosterone litigation:

“Good statistical practice, as an essential component of good scientific practice, emphasizes principles of good study design and conduct, a variety of numerical and graphical summaries of data, understanding of the phenomenon under study, interpretation of results in context, complete reporting and proper logical and quantitative understanding of what data summaries mean. No single index should substitute for scientific reasoning.”¹⁵

The existence of other important criteria in the evaluation and synthesis of a complex body of studies does not erase or supersede the importance of assessing stochastic error in the epidemiologic studies. Plaintiffs’ Opposition Brief asserted that the Defense had attempted to:

“to substitute the single index, the p-value, for scientific reasoning in the reports of Plaintiffs’ experts should be rejected.”¹⁶

Some of the defense’s opening brief could indeed be read as reducing causal inference to the determination of statistical significance. A sympathetic reading of the entire AbbVie brief, however, shows that it had criticized the threats to validity in the observational epidemiologic studies, as well as some of the clinical trials, and other rampant flaws in the Plaintiffs’ expert witnesses’ reasoning. The Plaintiffs’ citations to the ASA Statement’s “negative” propositions about p-values (to emphasize what they are not) appeared to be the stuffing of a strawman, used to divert attention from other failings of their own claims and proffered analyses. In other words, the substance of the Rule 702 application had much more to do with data quality and study validity than statistical significance.

What did the trial court make of this back and forth about statistical significance and the ASA Statement? For the most part, the trial court denied both sides’ challenges to proffered expert witness testimony on causation and statistical issues. In sorting the controversy over the ASA Statement, the trial court apparently misunderstood key statistical concepts and paid little attention to the threats to validity other than random variability in study results.¹⁷ The trial court summarized the controversy as follows:

“In arguing that the scientific literature does not support a finding that TRT is associated with the alleged injuries, AbbVie emphasize [sic] the importance of considering the statistical significance of study results. Though experts for both AbbVie and plaintiffs agree that statistical significance is a widely accepted concept in the field of statistics and that there is a conventional method for determining the statistical significance of a study’s findings, the parties and their experts disagree about the conclusions one may permissibly draw from a study result that is deemed to possess or lack statistical significance according to conventional methods of making that determination.”¹⁸

Of course, there was never a controversy presented to the court about drawing a conclusion from “a study.” By the time the briefs were filed, both sides had multiple observational studies, clinical trials, and meta-analyses to synthesize into opinions for or against causal claims.

Ironically, AbbVie might claim to have prevailed in having the trial court adopt its misleading definitions of p-values and confidence intervals:

“Statisticians test for statistical significance to determine the likelihood that a study’s findings are due to chance. *** According to conventional statistical practice, such a result *** would be considered statistically significant if there is a 95% probability, also expressed as a “p-value” of <0.05, that the observed association is not the product of chance. If, however, the p-value were greater than 0.05, the observed association would not be regarded as statistically significant, according to prevailing conventions, because there is a greater than 5% probability that the association observed was the result of chance.”¹⁹

The MDL court similarly appeared to accept AbbVie’s dubious description of the confidence interval:

“A confidence interval consists of a range of values. For a 95% confidence interval, one would expect future studies sampling the same population to produce values within the range 95% of the time. So if the confidence interval ranged from 1.2 to 3.0, the association would be considered statistically significant, because one would expect, with 95% confidence, that future studies would report a ratio above 1.0 – indeed, above 1.2.”²⁰

The court’s opinion clearly evidences the danger in stating the importance of statistical significance without placing equal emphasis on the need to exclude bias and confounding. Having found an observational study and one meta-analysis of clinical trial safety outcomes that were statistically significant, the trial court held that any dispute over the probativeness of the studies was for the jury to assess.

Some but not all of AbbVie’s brief might have encouraged this lax attitude by failing to emphasize study validity at the same time as emphasizing the importance of statistical significance. In any event, trial court continued with its précis of the plaintiffs’ argument that:

“a study reporting a confidence interval ranging from 0.9 to 3.5, for example, should certainly not be understood as evidence that there is no association and may actually be understood as evidence in favor of an association, when considered in light of other evidence. Thus, according to plaintiffs’ experts, even studies that do not show a statistically significant association between TRT and the alleged injuries may plausibly bolster their opinions that TRT is capable of causing such injuries.”²¹

Of course, a single study that reported a risk ratio greater than 1.0, with a confidence interval 0.9 to 3.5 might be reasonably incorporated into a meta-analysis that in turn could support, or not support a causal inference. In the TRT litigation, however, the well-conducted, most up-to-date meta-analyses did not report statistically significant elevated rates of cardiovascular events among users of TRT. The court’s insistence that a study with a confidence interval 0.9 to 3.5 cannot be interpreted as evidence of no association is, of course, correct. Equally correct would be to say that the interval shows that the study failed to show an association. The trial court never grappled with the reality that the best conducted meta-analyses failed to show statistically significant increases in the rates of cardiovascular events.

The American Statistical Association and its members would likely have been deeply disappointed by how both parties used the ASA Statement for their litigation objectives. AbbVie’s suggestion that the ASA Statement reflects a debate about “whether scientists who lack expertise in statistics misunderstand p-values and overvalue significance testing” would appear to have no support in the Statement itself or any other commentary to come out of the meeting leading up to the Statement. The Plaintiffs’ argument that p-values properly understood are unimportant and misleading similarly finds no support in the ASA Statement. Conveniently, the Plaintiffs’ brief ignored the Statement’s insistence upon transparency in pre-specification of analyses and outcomes, and in handling of multiple comparisons:

“P-values and related analyses should not be reported selectively. Conducting multiple analyses of the data and reporting only those with certain p-values (typically those passing a significance threshold) renders the reported p-values essentially uninterpretable. Cherrypicking promising findings, also known by such terms as data dredging, significance chasing, significance questing, selective inference, and ‘p-hacking’, leads to a spurious excess of statistically significant results in the published literature and should be vigorously avoided.”²²

Most if not all of the plaintiffs’ expert witnesses’ reliance materials would have been eliminated under this principle set forth by the ASA Statement.

1 See, e.g., In re Ephedra Prods. Liab. Litig., 393 F.Supp. 2d 181, 191 (S.D.N.Y. 2005). See also “Confidence in Intervals and Diffidence in the Courts” (March 4, 2012); “Scientific illiteracy among the judiciary” (Feb. 29, 2012).

2 “The American Statistical Association Statement on Significance Testing Goes to Court – Part I” (Nov. 13, 2018).

3Letter of Janet Woodcock, Director of FDA’s Center for Drug Evaluation and Research, to Sidney Wolfe, Director of Public Citizen’s Health Research Group (July 16, 2014) (denying citizen petition for “black box” warning).

4 Defendants’ (AbbVie, Inc.’s) Motion to Exclude Plaintiffs Expert Testimony on the Issue of Causation, and for Summary Judgment, and Memorandum of Law in Support, Case No. 1:14-CV-01748, MDL 2545, Document #: 1753, 2017 WL 1104501 (N.D. Ill. Feb. 20, 2017) [AbbVie Brief].

5 AbbVie Brief at 3; see also id. at 7-8 (“Depending upon the expert, even the basic tests of statistical significance are simply ignored, dismissed as misleading… .”) AbbVie’s definitions of statistical significance occasionally wandered off track and into the transposition fallacy, but generally its point was understandable.

6 AbbVie Brief at 63 n.16 (emphasis in original).

7 AbbVie Brief at 13 (emphasis in original).

8 AbbVie Brief at 13-14 (emphasis in original).

9 The defense brief further emphasized statistical significance almost as though it were a sufficient basis for inferring causality from observational studies: “Regardless of this debate, courts have routinely found the traditional epidemiological method—including bedrock principles of significance testing—to be the most reliable and accepted way to establish general causation. See, e.g., In re Zoloft, 26 F. Supp. 3d 449, 455; see also Rosen v. Ciba-Geigy Corp., 78 F.3d 316, 319 (7th Cir. 1996) (“The law lags science; it does not lead it.”). AbbVie Brief at 63-64 & n.16. The defense’s language about “including bedrock principles of significance testing” absolves it of having totally ignored other necessary considerations, but still the defense might have advantageously pointed out at the other needed considerations for causal inference at the same time.

10 Plaintiffs’ Steering Committee’ Memorandum of Law in Opposition to Motion of AbbVie Defendants to Exclude Plaintiffs’ Expert Testimony on the Issue of Causation, and for Summary Judgment at p.34, Case No. 1:14-CV-01748, MDL 2545, Document No. 1753 (N.D. Ill. Mar. 23, 2017) [Opp. Brief].

11 Id. at 35 (appending the ASA Statement and the commentary of more than two dozen interested commentators).

12 Id. at 38 (quoting from the ASA Statement at 131).

13 Id. at 38 (quoting from the ASA Statement at 132).

14 Id. at 38 (quoting from the ASA Statement at 132).

15 Id. at 38 (quoting from the ASA Statement at 132).

16 Id. at 38

17 In re Testosterone Replacement Therapy Prods. Liab. Litig., MDL No. 2545, C.M.O. No. 46, 2017 WL 1833173 (N.D. Ill. May 8, 2017) [In re TRT]

18 In re TRT at *4.

19 In re TRT at *4.

20 Id.

21 Id. at *4.

22 ASA Statement at 131-32.

Posted in Causation, Rule 702, Scientific Evidence, statistical evidence | Comments Off on ASA Statement Goes to Court – Part 2

Daubert Retrospective – Statistical Significance

January 5th, 2019

The holiday break was an opportunity and an excuse to revisit the briefs filed in the Supreme Court by parties and amici, in the Daubert case. The 22 amicus briefs in particular provided a wonderful basis upon which to reflect how far we have come, and also how far we have to go, to achieve real evidence-based fact finding in technical and scientific litigation. Twenty-five years ago, Rules 702 and 703 vied for control over errant and improvident expert witness testimony. With Daubert decided, Rule 702 emerged as the winner. Sadly, most courts seem to ignore or forget about Rule 703, perhaps because of its awkward wording. Rule 702, however, received the judicial imprimatur to support the policing and gatekeeping of dysepistemic claims in the federal courts.

As noted last week,¹ the petitioners (plaintiffs) in Daubert advanced several lines of fallacious and specious argument, some of which was lost in the shuffle and page limitations of the Supreme Court briefings. The plaintiffs’ transposition fallacy received barely a mention, although it did bring forth at least a footnote in an important and overlooked amicus brief filed by American Medical Association (AMA), the American College of Physicians, and over a dozen other medical specialty organizations,² all of which both emphasized the importance of statistical significance in interpreting epidemiologic studies, and the fallacy of interpreting 95% confidence intervals as providing a measure of certainty about the estimated association as a parameter. The language of these associations’ amicus brief is noteworthy and still relevant to today’s controversies.

The AMA’s amicus brief, like the brief filed by the National Academies of Science and the American Association for the Advancement of Science, strongly endorsed a gatekeeping role for trial courts to exclude testimony not based upon rigorous scientific analysis:

“The touchstone of Rule 702 is scientific knowledge. Under this Rule, expert scientific testimony must adhere to the recognized standards of good scientific methodology including rigorous analysis, accurate and statistically significant measurement, and reproducibility.”³

Having incorporated the term “scientific knowledge,” Rule 702 could not permit anything less in expert witness testimony, lest it pollute federal courtrooms across the land.

Elsewhere, the AMA elaborated upon its reference to “statistically significant measurement”:

“Medical researchers acquire scientific knowledge through laboratory investigation, studies of animal models, human trials, and epidemiological studies. Such empirical investigations frequently demonstrate some correlation between the intervention studied and the hypothesized result. However, the demonstration of a correlation does not prove the hypothesized result and does not constitute scientific knowledge. In order to determine whether the observed correlation is indicative of a causal relationship, scientists necessarily rely on the concept of “statistical significance.” The requirement of statistical reliability, which tends to prove that the relationship is not merely the product of chance, is a fundamental and indispensable component of valid scientific methodology.”⁴

And then again, the AMA spelled out its position, in case the Court missed its other references to the importance of statistical significance:

“Medical studies, whether clinical trials or epidemiologic studies, frequently demonstrate some correlation between the action studied … . To determine whether the observed correlation is not due to chance, medical scientists rely on the concept of ‘statistical significance’. A ‘statistically significant’ correlation is generally considered to be one in which statistical analysis suggests that the observed relationship is not the result of chance. A statistically significant correlation does not ‘prove’ causation, but in the absence of such a correlation, scientific causation clearly is not proven.⁹”⁵

In its footnote 9, in the above quoted section of the brief, the AMA called out the plaintiffs’ transposition fallacy, without specifically citing to plaintiffs’ briefs:

“It is misleading to compare the 95% confidence level used in empirical research to the 51% level inherent in the preponderance of the evidence standard.”⁶

Actually the plaintiffs’ ruse was much worse than misleading. The plaintiffs did not compare the two probabilities; they equated them. Some might call this ruse, an outright fraud on the court. In any event, the AMA amicus brief remains an available, citable source for opposing this fraud and the casual dismissal of the importance of statistical significance.

One other amicus brief touched on the plaintiffs’ statistical shanigans. The Product Liability Advisory Council, National Association of Manufacturers, Business Roundtable, and Chemical Manufacturers Association jointly filed an amicus brief to challenge some of the excesses of the plaintiffs’ submissions.⁷ Plaintiffs’ expert witness, Shanna Swan, had calculated type II error rates and post-hoc power for some selected epidemiologic studies relied upon by the defense. Swan’s complaint had been that some studies had only 20% probability (power) to detect a statistically significant doubling of limb reduction risk, with significance at p < 5%.⁸

The PLAC Brief pointed out that power calculations must assume an alternative hypothesis, and that the doubling of risk hypothesis had no basis in the evidentiary record. Although the PLAC complaint was correct, it missed the plaintiffs’ point that the defense had set exceeding a risk ratio of 2.0, as an important benchmark for specific causation attributability. Swan’s calculation of post-hoc power would have yielded an even lower probability for detecting risk ratios of 1.2 or so. More to the point, PLAC noted that other studies had much greater power, and that collectively, all the available studies would have had much greater power to have at least one study achieve statistical significance without dodgy re-analyses.

1 “The Advocates’ Errors in Daubert” (Dec. 28, 2018).

2 American Academy of Allergy and Immunology, American Academy of Dermatology, American Academy of Family Physicians, American Academy of Neurology, American Academy of Orthopaedic Surgeons, American Academy of Pain Medicine, American Association of Neurological Surgeons, American College of Obstetricians and Gynecologists, American College of Pain Medicine, American College of Physicians, American College of Radiology, American Society of Anesthesiologists, American Society of Plastic and Reconstructive Surgeons, American Urological Association, and College of American Pathologists.

3 Brief of the American Medical Association, et al., as Amici Curiae, in Support of Respondent, in Daubert v. Merrell Dow Pharmaceuticals, Inc., U.S. Supreme Court no. 92-102, 1993 WL 13006285, at *27 (U.S., Jan. 19, 1993)[AMA Brief].

4 AMA Brief at *4-*5 (emphasis added).

5 AMA Brief at *14-*15 (emphasis added).

6 AMA Brief at *15 & n.9.

7 Brief of the Product Liability Advisory Council, Inc., National Association of Manufacturers, Business Roundtable, and Chemical Manufacturers Association as Amici Curiae in Support of Respondent, as Amici Curiae, in Support of Respondent, in Daubert v. Merrell Dow Pharmaceuticals, Inc., U.S. Supreme Court no. 92-102, 1993 WL 13006288 (U.S., Jan. 19, 1993) [PLAC Brief].

8 PLAC Brief at *21.

Posted in Evidence, Expert Witnesses, Rule 702, Rule 703, statistical evidence, Statistical Power | Comments Off on Daubert Retrospective – Statistical Significance

The Advocates’ Errors in Daubert

December 28th, 2018

Over 25 years ago, the United States Supreme Court answered a narrow legal question about whether the so-called Frye rule was incorporated into Rule 702 of the Federal Rules of Evidence. Plaintiffs in Daubert v. Merrell Dow Pharmaceuticals, Inc., 509 U.S. 579 (1993), appealed a Ninth Circuit ruling that the Frye rule survived, and was incorporated into, the enactment of a statutory evidentiary rule, Rule 702. As most legal observers can now discern, plaintiffs won the battle and lost the war. The Court held that the plain language of Rule 702 does not memorialize Frye; rather the rule requires an epistemic warrant for the opinion testimony of expert witnesses.

Many of the sub-issues of the Daubert case are now so much water over the dam. The case involved claims of birth defects from maternal use of an anti-nausea medication, Bendectin. Litigation over Bendectin is long over, and the medication is now approved for use in pregnant women, on the basis of a full new drug application, supported by clinical trial evidence.

In revisiting Daubert, therefore, we might imagine that legal scholars and scientists would be interested in the anatomy of the errors that led Bendectin plaintiffs stridently to maintain their causal claims. The oral argument before the Supreme Court is telling with respect to some of the sources of error. Two law professors, Michael H. Gottesman, for plaintiffs, and Charles Fried, for the defense, squared off one Tuesday morning in March 1993. A review of Gottesman’s argument reveals several fallacious lines of argument, which are still relevant today:

A. Regulation is Based Upon Scientific Determinations of Causation

In his oral argument, Gottesman asserted that regulators (as opposed to the scientific community) are in charge of determining causation,¹ and environmental regulations are based upon scientific causation determinations.² By the time that the Supreme Court heard argument in the Daubert case, this conflation of scientific and regulatory standards for causal conclusions was fairly well debunked.³ Gottesman’s attempt to mislead the Court failed, but the effort continues in courtrooms around the United States.

B. Similar Chemical Structures Have the Same Toxicities

Gottesman asserted that human teratogenicity can be determined from similarity in chemical structures with other established teratogens.⁴ Close may count in horseshoes, but in chemical structural activities, small differences in chemical structures can result in huge differences in toxicologic or pharmacologic properties. A silly little methyl group on a complicated hydrocarbon ring structure can make a world of difference, as in the difference between estrogen and testosterone.

C. All Animals React the Same to Any Given Substance

Gottesman, in his oral argument, maintained that human teratogenicity can be determined from teratogenicity in non-human, non-primate, murine species.⁵ The Court wasted little time on this claim, the credibility of which has continued to decline in the last 25 years.

D. The Transposition Fallacy

Perhaps of greatest interest to me was Gottesman’s claim that the probability of the claimed causal association can be determined from the p-value or from the coefficient of confidence taken from the observational epidemiologic studies of birth defects among children of women who ingested Bendectin in pregancy; a.k.a. the transposition fallacy.⁶

All these errors are still in play in American courtrooms, despite efforts of scientists and scientific organizations to disabuse judges and lawyers. The transposition fallacy, which has been addressed in these pages and elsewhere at great length seems especially resilient to educational efforts. Still, the fallacy was as well recognized at the time of the Daubert argument as it is today, and it is noteworthy that the law professor who argued the plaintiffs’ case, in the highest court of the land, advanced this fallacious argument, and that the scientific and statistical community did little to nothing to correct the error.⁷

Although Professor Gottesman’s meaning in the oral argument is not entirely clear, on multiple occasions, he appeared to have conflated the coefficient of confidence, from confidence intervals, with the posterior probability that attaches to the alternative hypothesis of some association:

“What the lower courts have said was yes, but prove to us to a degree of statistical certainty which would give us 95 percent confidence that the human epidemiological data is reflective, that these higher numbers for the mothers who used Bendectin were not the product of random chance but in fact are demonstrating the linkage between this drug and the symptoms observed.”⁸

* * * * *

“… what was demonstrated by Shanna Swan was that if you used a degree of confidence lower than 95 percent but still sufficient to prove the point as likelier than not, the epidemiological evidence is positive… .”⁹

* * * * *

“The question is, how confident can we be that that is in fact probative of causation, not at a 95 percent level, but what Drs. Swan and Glassman said was applying the Rothman technique, a published technique and doing the arithmetic, that you find that this does link causation likelier than not.”¹⁰

Professor Fried’s oral argument for the defense largely refused or failed to engage with plaintiffs’ argument on statistical inference. With respect to the “Rothman” approach, Fried pointed out that plaintiffs’ statistical expert witness, Shanna swan, never actually employed “the Rothman principle.”¹¹

With respect to plaintiffs’ claim that individual studies had low power to detect risk ratios of two, Professor Fried missed the opportunity to point out that such post-hoc power calculations, whatever validity they might possess, embrace the concept of statistical significance at the customary 5% level. Fried did note that a meta-analysis, based upon all the epidemiologic studies, rendered plaintiffs’ power complaint irrelevant.¹²

Some readers may believe that judging advocates speaking extemporaneously about statistical concepts might be overly harsh. How well then did the lawyers explain and represent statistical concepts in their written briefs in the Daubert case?

Petitioners’ Briefs

Petitioners’ Opening Brief

The petitioners’ briefs reveal that Gottesman’s statements at oral argument represent a consistent misunderstanding of statistical concepts. The plaintiffs consistently conflated significance probability or the coefficient of confidence with the civil burden of proof probability:

“The crux of the disagreement between Merrell’s experts and those whose testimony is put forward by plaintiffs is that the latter are prepared to find causation more probable than not when the epidemiological evidence is strongly positive (albeit not at a 95% confidence level) and when it is buttressed with animal and chemical evidence predictive of causation, while the former are unwilling to find causation in the absence of an epidemiological study that satisfies the 95% confidence level.”¹³

After giving a reasonable fascimile of a definition of statistical significance, the plaintiffs’ brief proceeds to confuse the complement of alpha, or the coefficient of confidence (typically 95%), with probability that the observed risk ratio in a sample is the actual population parameter of risk:

“But in toxic tort lawsuits, the issue is not whether it is certain that a chemical caused a result, but rather whether it is likelier than not that it did. It is not self-evident that the latter conclusion would require eliminating the null hypothesis (i.e. non-causation) to a confidence level of 95%.³⁰” ¹⁴

The plaintiffs’ brief cited heavily to Rothman’s textbook, Modern Epidemiology, with the specious claim that the textbook supported the plaintiffs’ use of the coefficient of confidence to derive a posterior probability (> 50%) of the correctness of an elevated risk ratio for birth defects in children born to mothers who had taken Bendectin in their first trimesters of pregnancy:

“An alternative mechanism has been developed by epidemiologists in recent years to give a somewhat more informative picture of what the statistics mean. At any given confidence level (e.g. 95%) a confidence interval can be constructed. The confidence interval identifies the range of relative risks that collectively comprise the 95% universe. Additional confidence levels are then constructed exhibiting the range at other confidence levels, e.g., at 90%, 80%, etc. From this set of nested confidence intervals the epidemiologist can make assessments of how likely it is that the statistics are showing a true association. Rothman, Tab 9, pp. 122-25. By calculating nested confidence intervals for the data in the Bendectin studies, Dr. Swan was able to determine that it is far more likely than not that a true association exists between Bendectin and human limb reduction birth defects. Swan, Tab 12, at 3618-28.”¹⁵

The heavy reliance upon Rothman’s textbook at first blush appears confusing. Modern Epidemiology makes one limited mention of nested confidence intervals, and certainly never suggests that such intervals can provide a posterior probability of the correctness of the hypothesis. Rothman’s complaints about reliance upon “statistical significance,” however, are well-known, and Rothman himself submitted an amicus brief¹⁶ in Daubert, a brief that has its own problems.¹⁷

In direct response to the Rothman Brief,¹⁸ Professor Alvin Feinstein filed an amicus brief in Daubert, wherein he acknowledged that meta-analyses and re-analyses can be valid, but these techniques are subject to many sources of invalidity, and their employment by careful practitioners in some instances should not be a blank check to professional witnesses who are supported by plaintiffs’ counsel. Similarly, Feinstein acknowledged that standards of statistical significance:

“should be appropriately flexible, but they must exist if science is to preserve its tradition of intellectual discipline and high quality research.”¹⁹

Petitioners’ Reply Brief

The plaintiffs’ statistical misunderstandings are further exemplified in their Reply Brief, where they reassert the transposition fallacy and alternatively state that associations with p-values greater than 5%, or 95% confidence intervals that include the risk ratio of 1.0, do not show the absence of an association.²⁰ The latter point was, of course irrelevant in the Daubert case, in which plaintiffs had the burden of persuasion. As in their oral argument through Professor Gottesman, the plaintiffs’ appellate briefs misunderstand the crucial point that confidence intervals are conditioned upon the data observed from a particular sample, and do not provide posterior probabilities for the correctness of a claimed hypothesis.

Defense Brief

The defense brief spent little time on the statistical issue or plaintiffs’ misstatements, but dispatched the issue in a trenchant footnote:

“Petitioners stress the controversy some epidemiologists have raised about the standard use by epidemiologists of a 95% confidence level as a condition of statistical significance. Pet. Br. 8-10. See also Rothman Amicus Br. It is hard to see what point petitioners’ discussion establishes that could help their case. Petitioners’ experts have never developed and defended a detailed analysis of the epidemiological data using some alternative well-articulated methodology. Nor, indeed, do they show (or could they) that with some other plausible measure of confidence (say, 90%) the many published studies would collectively support an inference that Bendectin caused petitioners’ limb reduction defects. At the very most, all that petitioners’ theoretical speculations do is question whether these studies – as the medical profession and regulatory authorities in many countries have concluded – affirmatively prove that Bendectin is not a teratogen.”²¹

The defense never responded to the specious argument, stated or implied within the plaintiffs’ briefs, and in Gottesman’s oral argument, that a coefficient of confidence of 51% would have generated confidence intervals that routinely excluded the null hypothesis of risk ratio of 1.0. The defense did, however, respond to plaintiffs’ power argument by adverting to a meta-analysis that failed to find a statistically significant association.²²

The defense also advanced two important arguments to which the plaintiffs’ briefs never meaningfully responded. First, the defense detailed the “cherry picking” or selective reliance engaged in by plaintiffs’ expert witnesses.²³ Second, the defense noted that plaintiffs’ had a specific causation problem in that their expert witnesses had been attempting to infer specific causation based upon relative risks well below 2.0.²⁴

To some extent, the plaintiffs’ statistical misstatements were taken up by an amicus brief submitted by the United States government, speaking through the office of the Solicitor General.²⁵ Drawing upon the Supreme Court’s decisions in race discrimination cases,²⁶ the government asserted that epidemiologists “must determine” whether a finding of an elevated risk ratio “could have arisen due to chance alone.”²⁷

Unfortunately, the government’s brief butchered the meaning of confidence intervals. Rather than describe the confidence interval as showing what point estimates of risk ratios are reasonable compatible with the sample result, the government stated that confidence intervals show “how close the real population percentage is likely to be to the figure observed in the sample”:

“since there is a 95 percent chance that the ‘true’ value lies within two standard deviations of the sample figure, that particular ‘confidence interval’ (i.e., two standard deviations) is therefore said to have a ‘confidence level’ of about 95 percent.” ²⁸

The Solicitor General’s office seemed to have had some awareness that it was giving offense with the above definition because it quickly added:

“While it is customary (and, in many cases, easier) to speak of ‘a 95 percent chance’ that the actual population percentage is within two standard deviations of the figure obtained from the sample, ‘the chances are in the sampling procedure, not in the parameter’.”²⁹

Easier perhaps but clearly erroneous to speak that way, and customary only among the unwashed. The government half apologized for misleading the Court when it followed up with a better definition from David Freedman’s textbook, but sadly the government lawyers were not content to let the matter sit there. The Solicitor General office’s brief obscured the textbook definition with a further inaccurate and false précis:

“if the sampling from the general population were repeated numerous times, the ‘real’ population figure would be within the confidence interval 95 percent of the time. The ‘real’ figure would be outside that interval the remaining five percent of the time.”³⁰

The lawyers in the Solicitor General’s office thus made the rookie mistake of forgetting that in the long run, after numerous repeated samples, there would be numerous confidence intervals, not one. The 95% probability of containing the true population value belongs to the set of the numerous confidence intervals, not “the confidence interval” obtained in the first go around.

The Daubert case has been the subject of nearly endless scholarly comment, but few authors have chosen to revisit the parties’ briefs. Two authors have published a paper that reviewed the scientists’ amici briefs in Daubert.³¹ The Rothman brief was outlined in detail; the Feinstein rebuttal was not substantively discussed. The plaintiffs’ invocation of the transposition fallacy in Daubert has apparently gone unnoticed.

1 Oral Argument in Daubert v. Merrell Dow Pharmaceuticals, Inc., U.S. Supreme Court no. 92-102, 1993 WL 754951, *5 (Tuesday, March 30, 1993) [Oral Arg.]

2 Oral Arg. at *6.

3 In re Agent Orange Product Liab. Litig., 597 F. Supp. 740, 781 (E.D.N.Y.1984) (“The distinction between avoidance of risk through regulation and compensation for injuries after the fact is a fundamental one.”), aff’d in relevant part, 818 F.2d 145 (2d Cir. 1987), cert. denied sub nom. Pinkney v. Dow Chemical Co., 484 U.S. 1004 (1988).

4 Org. Arg. at *19.

5 Oral Arg. at *18-19.

6 Oral Arg. at *19.

7 See, e.g., “Sander Greenland on ‘The Need for Critical Appraisal of Expert Witnesses in Epidemiology and Statistics’” (Feb. 8, 2015) (noting biostatistician Sander Greenland’s publications, which selectively criticize only defense expert witnesses and lawyers for statistical misstatements); see also “Some High-Value Targets for Sander Greenland in 2018” (Dec. 27, 2017).

8 Oral Arg. at *19.

9 Oral Arg. at *20

10 Oral Arg. at *44. At the oral argument, this last statement was perhaps Gottesman’s clearest misstatement of statistical principles, in that he directly suggested that the coefficient of confidence translates into a posterior probability of the claimed association at the observed size.

11 Oral Arg. at *37.

12 Oral Arg. at *32.

13 Petitioner’s Brief in Daubert v. Merrell Dow Pharmaceuticals, Inc., U.S. Supreme Court No. 92-102, 1992 WL 12006442, *8 (U.S. Dec. 2, 1992) [Petitioiner’s Brief].

14 Petitioner’s Brief at *9.

15 Petitioner’s Brief at *n. 36.

16 Brief Amici Curiae of Professors Kenneth Rothman, Noel Weiss, James Robins, Raymond Neutra and Steven Stellman, in Support of Petitioners, 1992 WL 12006438, Daubert v. Merrell Dow Pharmaceuticals, Inc., U.S. S. Ct. No. 92-102 (Dec. 2, 1992).

17 See “The ‘Rothman’ Amicus Brief in Daubert v. Merrill Dow Pharmaceuticals” (Nov. 17, 2018).

18 Brief Amicus Curiae of Professor Alvan R. Feinstein in Support of Respondent, in Daubert v. Merrell Dow Pharmaceuticals, Inc., U.S. Supreme Court no. 92-102, 1993 WL 13006284, at *2 (U.S., Jan. 19, 1993) [Feinstein Brief].

19 Feinstein Brief at *19.

20 Petitioner’s Reply Brief in Daubert v. Merrell Dow Pharmaceuticals, Inc., U.S. Supreme Court No. 92-102, 1993 WL 13006390, at *4 (U.S., Feb. 22, 1993).

21 Respondent’s Brief in Daubert v. Merrell Dow Pharmaceuticals, Inc., U.S. Supreme Court No. 92-102, 1993 WL 13006277, at n. 32 (U.S., Jan. 19, 1993) [Respondent Brief].

22 Respondent Brief at *4.

23 Respondent Brief at *42 n.32 and 47.

24 Respondent Brief at *40-41 (citing DeLuca v. Merrell Dow Pharms., Inc., 911 F.2d 941, 958 (3d Cir. 1990)).

25 Brief for the United States as Amicus Curiae Supporting Respondent in Daubert v. Merrell Dow Pharmaceuticals, Inc., U.S. Supreme Court No. 92-102, 1993 WL 13006291 (U.S., Jan. 19, 1993) [U.S. Brief].

26 See, e.g., Hazelwood School District v. United States, 433 U.S. 299, 308-312

(1977); Castaneda v. Partida, 430 U.S. 482, 495-499 & nn.16-18 (1977) (“As a general rule for such large samples, if the difference between the expected value and the observed number is greater than two or three standard deviations, then the hypothesis that the jury drawing was random would be suspect to a social scientist.”).

27 U.S. Brief at *3-4. Over two decades later, when politically convenient, the United States government submitted an amicus brief in a case involving alleged securities fraud for failing to disclose adverse events of an over-the-counter medication. In Matrixx Initiatives Inc. v. Siracusano, 131 S. Ct. 1309 (2011), the securities fraud plaintiffs contended that they need not plead “statistically significant” evidence for adverse drug effects. The Solicitor General’s office, along with counsel for the Food and Drug Division of the Department of Health & Human Services, in their zeal to assist plaintiffs disclaimed the necessity, or even the importance, of statistical significance:

“[w]hile statistical significance provides some indication about the validity of a correlation between a product and a harm, a determination that certain data are not statistically significant … does not refute an inference of causation.”

Brief for the United States as Amicus Curiae Supporting Respondents, in Matrixx Initiatives, Inc. v. Siracusano, 2010 WL 4624148, at *14 (Nov. 12, 2010).

28 U.S. Brief at *5.

29 U.S. Brief at *5-6 (citing David Freedman, Freedman, R. Pisani, R. Purves & A. Adhikari, Statistics 351, 397 (2d ed. 1991)).

30 U.S. Brief at *6 (citing Freedman’s text at 351) (emphasis added).

31 See Joan E. Bertin & Mary S. Henifin, Science, Law, and the Search for Truth in the Courtroom: Lessons from Dauburt v. Menell Dow,” 22 J. Law, Medicine & Ethics 6 (1994); Joan E. Bertin & Mary Sue Henifin, “Scientists Talk to Judges: Reflections on Daubert v. Merrell Dow,” 4(3) New Solutions 3 (1994). The authors’ choice of the New Solutions journal is interesting and curious. New Solutions: A journal of Environmental and Occupational Health Policy was published by the Oil, Chemical and Atomic Workers International Union, under the control of Anthony Mazzocchi (June 13, 1926 – Oct. 5, 2002), who was the union’s secretary-treasurer. Anthony Mazzocchi, “Finding Common Ground: Our Commitment to Confront the Issues,” 1 New Solutions 3 (1990); see also Steven Greenhouse, “Anthony Mazzocchi, 76, Dies; Union Officer and Party Father,” N.Y. Times (Oct. 9, 2002). Even a cursory review of this journal’s contents reveals how concerned, even obsessed, the union was interested and invested in the litigation industry and that industry’s expert witnesses.

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