TORTINI

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

Good Night Styrene

April 18th, 2019

Perri Klass is a pediatrician who writes fiction and non-fiction. Her editorial article on “disruptive chemicals,” in this week’s Science Section of the New York Times contained large segments of fiction.[1]  The Times gives Dr. Klass, along with Nicholas Kristof and others, a generous platform to advance their chemophobic propaganda, on pesticides, phthalates, bisphenols, and flame retardants, without the bother of having to cite evidence. It has been just two weeks since the Times published another Klass fear piece on hormone disrupters.[2]

In her Science Times piece, Klass plugged Leonardo Trasande’s book, Sicker, Fatter, Poorer: The Urgent Threat of Hormone-Disrupting Chemicals to Our Health and Future . . . and What We Can Do About It (2019), to help wind up parents about chemical threats everywhere. Trasande, is “an internationally renowned leader in environmental health” expert; his website tells us so. Klass relies so extensively upon Trasande that it is difficult to discern whether she is presenting anything other than his opinions, which in some places she notes he has qualified as disputed and dependent upon correlational associations that have not established causal associations.

When it comes to recyclable plastic, number 6, Klass throws all journalistic caution and scientific scruple aside and tells us that “[a] number 6 denotes styrene, which is a known carcinogen.”[3] Known to whom? To Trasande? To Klass? To eco-zealots?

The first gaffe is that number 6 plastic, of course, is not styrene; rather it is polystyrene. Leaching of monomer certainly can occur,[4] and is worth noting, but equating polystyrene with styrene is simply wrong. The second gaffe, more serious yet, is that styrene is not a “known” carcinogen.

The International Agency for Research on Cancer, which has been known to engage in epistemic inflation about carcinogenicity, addressed styrene in its monograph 82.[5] Styrene was labeled a “2B” carcinogen, that is possible, not probable, and certainly not “known.” Last year, an IARC working group revisited the assessment of styrene, and in keeping with its current practice of grade inflation bumped styrene up to Group 2A, “probably carcinogenic to humans” based upon limited evidence in human being and sufficient evidence in rats and close relatives.[6] In any event, the IARC Monograph number 121, which will address styrene, is under preparation.

A responsible journalist, or scientist, regulator, or lawyer, is obligated however to note tha “probably” does not mean “more likely than not” in IARC-jargon.[7] Given that all empirical propositions have a probability of being true, somewhere between 0 and 100%, but never actually equal to 0 or 100%, the IARC classifications of “probably” causing cancer are probably not particularly meaningful.  Everything “probably” causes cancer, in this mathematical sense.[8]

In the meanwhile, what does the scientific community have to say about the carcinogenicity of styrene?

Recent reviews and systematic reviews of the styrene carcinogenicity issue have mostly concluded that there is no causal relationship between styrene exposure and any form of cancer in humans.[9] Of course, the “Lobby,” scientists in service to the litigation industry, disagree.[10]


[1]  Perri Klass, “Beware of Disruptive Chemicals,” N.Y. Times (April 16, 2019).

[2] Perri Klass, “How to Minimize Exposures to Hormone Disrupters,” N.Y. Times (April 1, 2019).

[3]  Klass (April 16, 2019), at D6, col. 3.

[4]  See, e.g., Despoina Paraskevopoulou, Dimitris Achiliasa, and Adamantini Paraskevopoulou, “Migration of styrene from plastic packaging based on polystyrene into food simulants,” 61 Polymers Internatl’l 141 (2012); J. R. Withey, “Quantitative Analysis of Styrene Monomerin Polystyrene and Foods Including Some Preliminary Studies of the Uptake and Pharmacodynamics of the Monomer in Rats,” 17 Envt’l Health Persp. 125 (1976).

[5]  IARC Monograph No. 82, at 437-78 (2002).

[6]  IARC Working Group, “Carcinogenicity of quinoline, styrene, and styrene-7,8-oxide,” 19 Lancet Oncology 728 (2018).

[7]  The IARC Preamble definition of probable reveals that “probable” does not mean greater than 50%. See also “The IARC Process is Broken” (May 4, 2016).

[8] See Ed Yong, “Beefing With the World Health Organization’s Cancer Warnings,” The Atlantic (Oct 26, 2015).

[9]  Boffetta, P., Adami, H. O., Cole, P., Trichopoulos, D. and Mandel, J. S., “Epidemiologic studies of styrene and cancer: a review of the literature,” 51 J. Occup. & Envt’l Med. 1275 (2009) (“The available epidemiologic evidence does not support a causal relationship between styrene exposure and any type of human cancer.”); James J. Collins & Elizabeth Delzell, “A systematic review of epidemiologic studies of styrene and cancer,” 48 Critical Revs. Toxicol. 443 (2018)  (“Consideration of all pertinent data, including substantial recent research, indicates that the epidemiologic evidence on the potential carcinogenicity of styrene is inconclusive and does not establish that styrene causes any form of cancer in humans.”).

[10] James Huff & Peter F. Infante, “Styrene exposure and risk of cancer,” 26 Mutagenesis 583 (2011).

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 alsoConfidence in Intervals and Diffidence in the Courts” (March 4, 2012); “Scientific illiteracy among the judiciary” (Feb. 29, 2012).

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.

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%.3014

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 offices 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 alsoSome 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).

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. 

 

The American Statistical Association Statement on Significance Testing Goes to Court – Part I

November 13th, 2018

It has been two and one-half 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]. When the ASA Statement was published, I commended it as a needed counterweight to the exaggerated criticisms of significance testing.1 Lawyers and expert witnesses for the litigation industry had routinely poo-poohed the absence of statistical significance, but over-endorsed its presence in poorly designed and biased studies. Courts and lawyers from all sides routinely misunderstand, misstated, and misrepresented the meaning of statistical significance.2

The ASA Statement had potential to help resolve judicial confusion. It is written in non-technical language, which is easily understood by non-statisticians. Still, the Statement has to be read with care. The principle of charity led me to believe that lawyers and judges would read the Statement carefully, and that it would improve judicial gatekeeping of expert witnesses’ opinion testimony that involved statistical evidence. I am less sanguine now about the prospect of progress.

No sooner had the ASA issued its Statement than the spinning started. One scientist, and an editor PLoS Biology, blogged that “the ASA notes, the importance of the p-value has been greatly overstated and the scientific community has become over-reliant on this one – flawed – measure.”3 Lawyers for the litigation industry were even less restrained in promoting wild misrepresentations about the Statement, with claims that the ASA had condemned the use of p-values, significance testing, and significance probabilities, as “flawed.”4 And yet, no where in the ASA’s statement does the group suggest that the the p-value was a “flawed” measure.

Criminal Use of the ASA Statement

Where are we now, two plus years out from the ASA Statement? Not surprisingly, the Statement has made its way into the legal arena. The Statement has been used in any number of depositions, relied upon in briefs, and cited in at least a couple of judicial decisions, in the last two years. The empirical evidence of how the ASA Statement has been used, or might be used in the future, is still sparse. Just last month, the ASA Statement was cited by the Washington State Supreme Court, in a ruling that held the death penalty unconstitutional. State of Washington v. Gregory, No. 88086-7, (Wash. S.Ct., Oct. 11, 2018) (en banc). Mr. Gregory, who was facing the death penalty, after being duly convicted or rape, robbery, and murder. The prosecution was supported by DNA matches, fingerprint identification, and other evidence. Mr. Gregory challenged the constitutionality of his imposed punishment, not on per se grounds of unconstitutionality, but on race disparities in the imposition of the death penalty. On this claim, the Washington Supreme Court commented on the empirical evidence marshalled on Mr. Gregory’s behalf:

The most important consideration is whether the evidence shows that race has a meaningful impact on imposition of the death penalty. We make this determination by way of legal analysis, not pure science. At the very most, there is an 11 percent chance that the observed association between race and the death penalty in Beckett’s regression analysis is attributed to random chance rather than true association. Commissioner’s Report at 56-68 (the p-values range from 0.048-0.111, which measures the probability that the observed association is the result of random chance rather than a true association).[8] Just as we declined to require ‘precise uniformity’ under our proportionality review, we decline to require indisputably true social science to prove that our death penalty is impermissibly imposed based on race.

Id. (internal citations omitted).

Whatever you think of the death penalty, or how it is imposed in the United States, you will have to agree that the Court’s discussion of statistics is itself criminal. In the above quotation from the Court’s opinion, the Court badly misinterpreted the p-values generated in various regression analyses that were offered to support claims of race disparity. The Court’s equating statistically significant evidence of race disparity in these regression analyses with “indisputably true social science” also reflects a rhetorical strategy that imputes ridiculously high certainty (indisputably true) to social science conclusions in order to dismiss the need for them in order to accept a causal race disparity claim on empirical evidence.5

Gregory’s counsel had briefed the Washington Court on statistical significance, and raised the ASA Statement as excuse and justification for not presenting statistically significant empirical evidence of race disparity.6 Footnote 8, in the above quote from the Gregory decision shows that the Court was aware of the ASA Statement, which makes the Court’s errors even more unpardonable: 

[8] The most common p-value used for statistical significance is 0.05, but this is not a bright line rule. The American Statistical Association (ASA) explains that the ‘mechanical “bright-line” rules (such as “p < 0.05”) for justifying scientific claims or conclusions can lead to erroneous beliefs and poor decision making’.”7

Conveniently, Gregory’s counsel did not cite to other parts of the ASA Statement, which would have called for a more searching review of the statistical regression analyses:

“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 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.”8

The Supreme Court of Washington first erred in its assessment of what scientific evidence requires in terms of a burden of proof. It then accepted spurious arguments to excuse the absence of statistical significance in the statistical evidence before it, on the basis of a distorted representation of the ASA Statement. Finally, the Court erred in claiming support from social science evidence, by ignoring other methodological issues in Gregory’s empirical claims. Ironically, the Court had made significance testing the end all and be all of its analysis, and when it dispatched statistical significance as a consideration, the Court jumped to the conclusion it wanted to reach. Clearly, the intended message of the ASA Statement had been subverted by counsel and the Court.

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

5 Moultrie v. Martin, 690 F.2d 1078, 1082 (4th Cir. 1982) (internal citations omitted) (“When a litigant seeks to prove his point exclusively through the use of statistics, he is borrowing the principles of another discipline, mathematics, and applying these principles to the law. In borrowing from another discipline, a litigant cannot be selective in which principles are applied. He must employ a standard mathematical analysis. Any other requirement defies logic to the point of being unjust. Statisticians do not simply look at two statistics, such as the actual and expected percentage of blacks on a grand jury, and make a subjective conclusion that the statistics are significantly different. Rather, statisticians compare figures through an objective process known as hypothesis testing.”).

6 Supplemental Brief of Allen Eugene Gregory, at 15, filed in State of Washington v. Gregory, No. 88086-7, (Wash. S.Ct., Jan. 22, 2018).

7 State of Washington v. Gregory, No. 88086-7, (Wash. S.Ct., Oct. 11, 2018) (en banc) (internal citations omitted).

8 ASA Statement at 132.