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Professor Lahav’s Radically Misguided Treatment of Chancy Tort Causation

September 27th, 2024

In the 19th and early 20th century, scientists and lay people usually conceptualized causation as “deterministic.” Their model of science was perhaps what was called Newtonian, in which observations were invariably described in terms of identifiable forces that acted upon antecedent phenomena. The universe was akin to a pool table, with the movement of the billiard balls fully explained by their previous positions, mass, and movements. There was little need for probability to describe events or outcomes in such a universe.

The 20th century ushered in probabilistic concepts and models in physics and biology. Because tort law is so focused on claims of bodily integrity and harms, I am focused here on claimed health effects. Departing from the Koch-Henle postulates and our understanding of pathogen-based diseases, the latter half of the 20th century saw the rise of observational epidemiology and scientific conclusions about stochastic processes and effects that could best be understood in terms of probabilities, with statistical inferences from samples of populations. The language of deterministic physics failed to do justice to epidemiologic evidence or conclusions. Modern medicine and biology invoked notions of base rates for chronic diseases, which rates might be modified by environmental exposures.

In the wake of the emerging science of epidemiology, the law experienced a new horizon on which many claimed tortogens did not involve exposures uniquely tied to the harms alleged. Rather, the harms asserted were often diseases of ordinary life, but with that suggested the harms were quantitatively more prevalent or incident among people exposed to the alleged tortogen. Of course, the backwaters of tort law saw reactionary world views on trial, as with claims of trauma-induced cancer cases, which are with us still. Nonetheless, slowly but not always steadily, the law came to grips with probability and statistical evidence.

In law, as in science, a key component of causal attribution is counterfactual analysis. If A causes B, then if in the same world, ceteris paribus, we do not have A, then we don’t have B. Counterfactual analysis applies as much to stochastic processes that are causally influenced by rate changes, as they apply to the Newtonian world of billiard balls. Some writers in the legal academy, however, would opportunistically use the advent of probabilistic analyses of health effects to dispose of science altogether. No one has more explicitly exploited the opportunity than Professor Alexandra Lahav.

In an essay published in 2022, Professor Lahav advanced extraordinary claims about probabilistic causation, or what she called “chancy causation.”[1] The proffered definition of chancy causation is bumfuzzling. Lahav provides an example of an herbicide that is “associated” with the type of cancer that the heavily exposed plaintiff developed. She tells us that:

“[t]here is a chance that the exposure caused his cancer, and a chance that it did not. Probability follows certain rules, or tendencies, but these regular laws do not abolish chance. This is a common problem in modern life, where much of what we know about medicines, interventions, and the chemicals to which we are exposed is probabilistic. Following the philosophical literature, I call this phenomenon chancy causation.”[2]

So the rules of probability do not abolish chance? It is hard to know what Lahav is trying to say here. Probability quantifies chance, and gives us an understanding of phenomena and their predictability. When we can model an empirical process with a probability distribution, such as one that is independent and identically distributed, we can often make and test quantitative inferences about the anticipated phenomena.

Lahav vaguely acknowledges that her term, “chancy causation” is borrowed, but she does not give credit to the many authors who have used it before.[3] Lahav does note that the concept of probabilistic causation used in modern-day risk factor epidemiology is different from the deterministic causal claims that dominated tort law in the 19th and the first half of the 20th century. Lahav claims that chancy causation is inconsistent with counterfactual analysis, but she cites no support for her claim, which is demonstrably false. If we previously saw the counterfactual of if A then B, as key to causality, we can readily restate the counterfactual as a probability: A probably causes B. On a counterfactual analysis, then if we do not have A as an antecedent, then we probably do not have B. For a classic tortogen such as tobacco smoking, we can say confidently that tobacco smoking probably causes lung cancer. And for a given instance of lung cancer, we can say based upon the entire evidentiary display, that if a person did not smoke tobacco, he would probably not have developed lung cancer. Of course, the correspondence is not 100 percent, which is only to say that it is probabilistic. There are highly penetrant genetic mutations that may be the cause of a given lung cancer case. We know, however, that such mutations do not cause or explain the large majority of lung cancer cases.

Contrary to Lahav’s ipse dixits, tort law can incorporate, and has accommodated, both general and specific causation in terms of probabilistic counterfactuals. The modification requires us, of course, to address the baseline situation as a rate or frequency of events, and the post-exposure world as one with a modified rate or frequency. Without confusion or embarrassment, we can say that the exposure is the cause of the change in event rates. Modern physics similarly addresses whether we must be content with probability statements, rather than precise deterministic “billiard ball” physics, which is so useful in a game of snooker, but less so in describing the position of sub-atomic particles. In the first half of the 20th century, the biological sciences learned with some difficulty that it must embrace probabilistic models, in genetic science, as well as in epidemiology. Many biological causation models are completely stated in terms of probabilities that are modified by specified conditions.

Lahav intends for her rejection of counterfactual causality to do a lot of work in her post-modern program. By falsely claiming that chancy causation has no factual basis, Lahav jumps to the conclusion that what the law calls for is nothing but “policy,”[4] and “normative decision.”[5] Having fabricated the demise of but-for causation in the context of probabilistic relationships, Lahav suggests that tort law can pretend that the causation question is nothing more than a normative analysis of the defendant’s conduct. (Perhaps it is more than a tad revealing that she does not see that the plaintiff’s conduct is involved in the normative judgment.) Of course, tort law already has ample room for policy and normative considerations built into the concepts of duty and breach of duty.

As we saw with the lung cancer example above, the claim that tobacco smoking probably caused the smoker to develop lung cancer can be entirely factual, and supported by a probabilistic judgment. Lahav calls her erroneous move “pragmatic,” although it has no relationship to the philosophical pragmatism of Peirce or Quine. Lahav’s move is an incorrect misrepresentation of probability and of epidemiologic science in the name of compensation free-for-alls. Obtaining a heads in the flip of a fair coin has a probability of 50%; that is a fact, not a normative decision, even though it is, to use Lahav’s vocabulary, “chancy.”

Lahav’s argument is not always easy to follow. In one place, she uses “chancy” to refer to the posterior probability of the correctness of the causal claim:

“the counterfactual standard can be successfully defended against by the introduction of chance. The more conflicting studies, the “more chancy” the causation. By that I do not mean proving a lower probability (although this is a good result from a defense point of view) but rather that more, different study results create the impression of irreducible chanciness, which in turn dictates that the causal relation cannot be definitively proven.”[6]

This usage, which clearly refers to the posterior probability of a claim, is not necessarily limited to so-called non-deterministic phenomena. People could refer to any conclusion, based upon conflicting evidence of deterministic phenomena, as “chancy.”

Lurking in her essay is a further confusion between the posterior probability we might assign to a claim, or to an inference from probabilistic evidence, and the probability of random error. In an interview conducted by Felipe Jiménez,[7] Lahav was more transparent in her confusion, and she explicitly commited the transpositional fallacy with her suggestion that customary statistical standards (statistical significance) ensure that even small increased risks, say of 30%, are known to a high degree of certainty.

Despite these confusions, it seems fairly clear that Lahav is concerned with stochastic causal processes, and most of her examples evidence that concern. Lahav poses a hypothetical in which epidemiologic studies show smokers have a 20% increased risk of developing lung cancer compared with non-smokers.[8] Given that typical smoking histories convey relative risks of 20 to 30, or increased risks of 2,000 to 3,000%, Lahav’s hypothetical may readers think she is shilling for tobacco compaies. In any event, in the face of a 20% increased risk (or relative rsk of 1.2), Lahav acknowledges that the probability of a smoker’s developing lung cancer is higher than that of a non-smoker, but “in any particular case the question whether a patient’s lung cancer was caused by smoking is uncertain.” This assertion, however, is untrue; the question is not “uncertain.” She has provided a certain quantification of the increased risk. Furthermore, her hypothetical gives us a good deal of information on which we can say that smoking probably did not result in the patient’s lung cancer. Causation may be chancy because it is based upon a probabilistic inference, but the chances are actual known, and they are low.

Lahav posits a more interesting hypothetical when she considers a case in which there is an 80% chance that a person’s lung cancer is attributable to smoking.[9] We can understand this hypothetical better if we reframe it as classic urn probability problem. In a given (large) population of non-smokers, we expect 100 lung cancers per year. In a population of smokers, otherwise just like the population of non-smokers, we observe 500 lung cancers. Of the observed number, 100 were “expected” because they happen without exposure to the putative causal agent, and 400 are “excess.”The relative risk would be 5, or 400% increased risk, and still well below the actual measure of risk from long-term smoking, but the attributable risk would be [(RR-1)/RR] or 0.8 (or 80%). If we imagine an urn with 100 white “expected” balls, and 400 red “excess” balls added, then any given draw from the urn, with replacement, yields an 80% probability of a red ball, or an excess case. Of course, if we can see the color, we may come to a consensus judgment that the ball is actually red. But on our analogy to discerning the cause of a given lung cancer, we have at present nothing by way of evidence with which to call the question, and so it remains “chancy” or probabilistic. The question is not, however, in any way normative. The answer is different quantitatively in the 20% and in the 400% hypotheticals.

Lahav asserts that we are in a state of complete ignorance once a smoker has lung cancer.[10] This is not, however, true. We have the basis for a probabilistic judgment that will probably be true. It may well be true that the probability of attribution will be affected by the probability that the relative risk = 5 is correct. If the posterior probability for the claim that smoking causes lung cancer by increasing its risk 400% is only 30%, then of course, we could not make the attribution in a given case with an 80% probability of correctness. In actual litigation, the argument is often framed on an assumption arguendo that the increased risk is greater than two, so that only the probability of attribution is involved. If the posterior probability of the claim that exposure to the tortogen increased risk by 400% or 20,000% was only 0.49, then the plaintiff would lose. If the posterior probability of the increased risk was greater than 0.5, the finder of fact could find that the specific causation claim had been carried if the magnitude of the relative risk, and the attributable risk, were sufficiently large. This inference on specific causation would not be a normative judgment; it would be guided by factual evidence about the magnitude of the relevant increased risk.

Lahav advances a perverse skepticism that any inferences about individuals can be drawn from information about rates or frequencies in groups of similar individuals.  Yes, there may always be some debate about what is “similar,” but successive studies may well draw the net tighter around what is the appropriate class. Lahav’s skepticism and her outright denialism about inferences from general causation to specific causation, are common among some in the legal academy, but it ignores that group to individual inferences are drawn in epidemiology in multiple contexts. Regressions for disease prediction are based upon individual data within groups, and the regression equations are then applied to future individuals to help predict those individuals’ probability of future disease (such as heart attack or breast cancer), or their probability of cancer-free survival after a specific therapy. Group to individual inferences are, of course, also the basis for prescribing decisions in clinical medicine.  These are not normative inferences; they are based upon evidence-based causal thinking about probabilistic inferences.

In the early tobacco litigation, defendants denied that tobacco smoking caused lung cancer, but they argued that even if it did, and the relative risk were 20, then the specific causation inference in this case was still insecure because the epidemiologic study tells us nothing about the particular case. Lahav seems to be channeling the tobacco-company argument, which has long since been rejected on the substantive law of causation. Indeed, as noted, epidemiologists do draw inferences about individual cases from population-based studies when they invoke clinical prediction models such as the Framingham cardiovascular risk event model, or the Gale breast cancer prediction model. Physicians base important clinical interventions, both pharmacologic and surgical, for individuals upon population studies. Lahav asserts, without evidence, that the only difference between an intervention based upon an 80% or a 30% probability is a “normative implication.”[11] The difference is starkly factual, not normative, and describes a long-term likelihood of success, as well as an individual probability of success.

Post-Modern Causation

What we have in Lahav’s essay is the ultimate post-modern program, which asserts, without evidence, that when causation is “chancy,” or indeterminate, courts leave the realm of science and step into the twilight zone of “normative decisions.” Lahav suggests that there is an extreme plasticity to the very concept of causation such that causation can be whatever judges want it to be. I for one sincerely doubt it. And if judges make up some Lahav-inspired concept of normative causation, the scientific community would rightfully scoff.

Establishing causation can be difficult, and many so-called mass tort litigations have failed for want of sufficient, valid evidence supporting causal claims. The late Professor Margaret Berger reacted to this difficulty in a more forthright way by arguing for the abandonment of general causation, or cause-in-fact, as an element of tort claims under the law.[12] Berger’s antipathy to requiring causation manifested in her hostility to judicial gatekeeping of the validity of expert witness opinions. Her animus against requiring causation and gatekeeping under Rule 702 was so strong that it exceeded her lifespan. Berger’s chapter in the third edition of the Reference Manual on Scientific Evidence, which came out almost one year after her death, embraced the First Circuit’s notorious anti-Daubert decision in Milward, which also post-dated her passing.[13]

Professor Lahav has previously expressed a distain for the causation requirement in tort law. In an earlier paper, “The Knowledge Remedy,” Lahav argued for an extreme, radical precautionary principle approach to causation.[14] Lahav believes that the likes of David Michaels have “demonstrated” that manufactured uncertainty is a genuine problem, but not one that affects her main claims. Remarkably, Lahav sees no problem with manufactured certainty in the advocacy science of many authors or the lawsuit industry.[15] In “Chancy Causation,” Lahav thus credulously repeats Michaels’ arguments, and goes so far as to describe Rule 702 challenges to causal claims as having the “negative effect” of producing “incentives to sow doubt about epidemiologic studies using methodological battles, a strategy pioneered by the tobacco companies … .”[16] Lahav’s agenda is revealed by the absence of any corresponding concern about the negative effect of producing incentives to overstate the findings, or the validity of inferences, in order to obtain an unwarranted and unsafe verdicts for claimants.

[1] Alexandra D. Lahav, “Chancy Causation in Tort,” 15 J. Tort L. 109 (2022) [hereafter Chancy Causation].

[2] Chancy Causation at 110.

[3] See, e.g., David K. Lewis, Philosophical Papers: Volume 2 175 (1986); Mark Parascandola, “Evidence and Association: Epistemic Confusion in Toxic Tort Law,” 63 Phil. Sci. S168 (1996).

[4] Chancy Causation at 109.

[5] Chancy Causation at 110-11.

[6] Chancy Causation at 129.

[7] Felipe Jiménez, “Alexandra Lahav on Chancy Causation in Tort,” The Private Law Podcast (Mar. 29, 2021).

[8] Chancy Causation at 115.

[9] Chancy Causation at 116-17.

[10] Chancy Causation at 117.

[11] Chancy Causation at 119.

[12] Margaret A. Berger, “Eliminating General Causation: Notes towards a New Theory of Justice and Toxic Torts,” 97 Colum. L. Rev. 2117 (1997).

[13] Milward v. Acuity Specialty Products Group, Inc., 639 F.3d 11 (1st Cir. 2011), cert. denied sub nom., U.S. Steel Corp. v. Milward, 132 S. Ct. 1002 (2012).

[14] Alexandra D. Lahav, “The Knowledge Remedy,” 98 Texas L. Rev. 1361 (2020). See “The Knowledge Remedy Proposal” Tortini (Nov. 14, 2020).

[15] Chancy Causation at 118 (citing plaintiffs’ expert witness David Michaels, The Triumph of Doubt: Dark Money and the Science of Deception (2020), among others).

[16] Chancy Causation at 129.

Posted in Causation, Evidence, Rule 702, statistical evidence | 1 Comment »

Zhang’s Glyphosate Meta-Analysis Succumbs to Judicial Scrutiny

August 5th, 2024

Back in March 2015, the International Agency for Research on Cancer (IARC) issued its working group’s monograph on glyphosate weed killer. The report classified glyphosate as a “probable carcinogen,” which is highly misleading. For IARC, the term “probable” does not mean more likely than not, or for that matter, probable does not have any quantitative meaning. The all-important statement of IARC methods, “The Preamble,” makes this clear.[1] 

In the case of glyphosate, the IARC working group concluded that the epidemiologic evidence for an association between glyphosate exposure and cancer (specifically non-Hodgkins lymphoma (NHL)), was limited, which is IARC’s euphemism for insuffcient. Instead of epidemiology, IARC’s glyphosate conclusion was based largely upon rodent studies, but even the animal evidence relied upon by IARC was dubious. The IARC working group cherry picked a few arguably “positive” rodent study results with increases in tumors, while ignoring exculpatory rodent studies with decreasing tumor yield.[2]

Although the IARC hazard classification was uncritically embraced by the lawsuit industry, most regulatory agencies, even indulging precautionary principle reasoning, rejected the claim of carcinogenicity. The United States  Environmental Protection Agency (EPA), European Food Safety Authority, Food and Agriculture Organization (in conjunction with World Health Organization, European Chemicals Agency, Health Canada, German Federal Institute for Risk Assessment, among others, found that the scientific evidence did not support the claim that glyphosate causes NHL. The IARC monograph very quickly after publication became the proximate cause of a huge litigation effort by the lawsuit industry against Monsanto.

The personal injury cases against Monsanto, filed in federal court, were aggregated for pre-trial hearing, before Judge Vince Chhabria, of the Northern District of California, as MDL 2741. Judge Chhabria denied Monsanto’s early Rule 702 motions, and thus cases proceeded to trial, with mixed results.

In 2019, the Zhang study, a curious meta-analysis of some of the available glyphosate epidemiologic studies appeared in Mutation Research / Reviews in Mutation Research, a toxicology journal that seemed an unlikely venue for a meta-analysis of epidemiologic studies. The authors combined selected results from one large cohort study, the Agricultural Health Study, along with five case-control studies, to reach a summary relative risk of 1.41 (95% confidence interval 1.13-1.75).[3] According to the authors, their “current meta-analysis of human epidemiological studies suggests a compelling link between exposures to GBHs [glyphosate] and increased risk for NHL.”

The Zhang meta-analysis was not well reviewed in regulatory and scientific circles. The EPA found that Zhang used inappropriate methods in her meta-analysis.[4] Academic authors also panned the Zhang meta-analysis in both scholarly,[5] and popular articles.[6] The senior author of the Zhang paper, Lianne Sheppard, a Professor in the University of Washington Departments of Environmental  and  Occupational Health Sciences, and Biostatistics, attempted to defend the study, in Forbes.[7] Professor Geoffrey Kabat very adeptly showed that this defense was futile.[8] Despite the very serious and real objections to the validity of the Zhang meta-analysis, plaintiffs’ expert witnesses, such as Beate Ritz, an epidemiologist with U.C.L.A. testified that she trusted and relied upon the analysis.[9]

For five years, the Zhang study was a debating point for lawyers and expert witnesses in the glyphosate litigation, without significant judicial gatekeeping. It took the entrance of Luoping Zhang herself as an expert witness in the glyphosate litigation, and the procedural oddity of her placing exclusive reliance upon her own meta-analysis, to bring the meta-analysis into the unforgiving light of judicial scrutiny.

Zhang is a biochemist and toxicologist, in the University of California, Berkeley. Along with two other co-authors of her 2019 meta-analysis paper, she had been a board member of the EPA’s 2016 scientific advisory panel on glyphosate. After plaintiffs’ counsel disclosed Zhang as an expert witness, she disclosed her anticipated testimony, as is required by Federal Rule of Civil Procedure 26, by attaching and adopting by reference the contents of two of her published papers. The first paper was her 2019 meta-analysis; the other paper discussed putative mechanisms. Neither paper concluded that glyphosate causes NHL. Zhang’s disclosure did not add materially to her 2019 published analysis of six epidemiologic studies on glyphosate and NHL.

The defense challenged the validity of Dr. Zhang’s proffered opinions, and her exclusive reliance upon her own 2019 meta-analysis required the MDL court to pay attention to the failings of that paper, which had previously escaped critical judicial scrutiny. In June 2024, after an oral hearing in Bulone v. Monsanto, at which Dr. Zhang testified, Judge Chhabria ruled that Zhang’s proffered testimony, and her reliance upon her own meta-analysis was “junk science.”[10]

Judge Chhabria, perhaps encouraged by the recently fortifying amendment to Rule 702, issued a remarkable opinion that paid close attention to the indicia of validity of an expert witness’s opinion and the underlying meta-analysis. Judge Chhabria quickly spotted the disconnect between Zhang’s published papers and what is required for an admissible causation opinion. The mechanism paper did not address the extant epidemiology, and both sides in the MDL had emphasized that the epidemiology was critically important for determining whether there was, or was not, causation.

Zhang’s meta-analysis did evaluate some, but not all, of the available epidemiology, but the paper’s conclusion stopped considerably short of the needed opinion on causation. Zhang and colleagues had concluded that there was a “compelling link” between exposures to [glyphosate-based herbicides] and increased risk for NHL. In their paper’s key figure, show casing the summary estimate of relative risk of 1.41 (95% C.I., 1.13 -1.75), Zhang and her co-authors concluded only that exposure was “associated with an increased risk of NHL.” According to Judge Chhabria, in incorporating her 2019 paper into her Rule 26 report, Zhang failed to add a proper holistic causation analysis, as had other expert witnesses who had considered the Bradford Hill predicates and considerations.

Judge Chhabria picked up on another problem that has both legal and scientific implications. A meta-analysis is out of date as soon as a subsequent epidemiologic study becomes available, which would have satisfied the inclusion criteria for the meta-analysis. Since publishing her meta-analysis in 2019, additional studies had in fact been published. At the hearing, Dr. Zhang acknowledged that several of them would qualify for inclusion in the meta-analysis, per her own stated methods. Her failure to update the meta-analysis made her report incomplete and inadmissible for a court matter in 2024.

Judge Chhabria might have stopped there, but he took a closer look at the meta-analysis to explore whether it was a valid analysis, on its own terms. Much as Chief Judge Nancy Rosenstengel had done with the made-for-litigation meta-analysis concocted by Martin Wells in the paraquat litigation,[11] Judge Chhabria examined whether Zhang had been faithful to her own stated methods. Like Chief Judge Rosenstengel’s analysis, Judge Chhabria’s analysis stands as a strong rebuttal to the uncharitable opinion of Professor Edward Cheng, who has asserted that judges lack the expertise to evaluate the “expert opinions” before them.[12]

Judge Chhabria accepted the intellectual challenge that Rule 702 mandates. With the EPA memorandum lighting the way, Judge Chhabria readily discerned that “the challenged meta-analysis was not reliably performed.” He declared that the Zhang meta-analysis was “junk science,” with “deep methodological problems.”

Zhang claimed that she was basing the meta-analysis on the subgroups of six studies with the heaviest glyphosate exposure. This claim was undermined by the absence of any exposure-response gradient in the study deemed by Zhang to be of the highest quality. Furthermore, of the remaining five studies, three studies failed to provide any exposure-dependent analysis other than a comparison of NHL rates among “ever” versus “never” glyphosate exposure. As a result of this heterogeneity, Zhang used all the data from studies without exposure characterizations, but only limited data from the other studies that analyzed NHL by exposure levels. And because the highest quality study was among those that provided exposure level correlations, Zhang’s meta-analysis used only some of the data from it.

The analytical problems created by Zhang’s meta-analytical approach were compounded by the included studies’ having measured glyphosate exposures differently, with different cut-points for inclusion as heavily exposed. Some of the excluded study participants would have heavier exposure than those included in the summary analysis.

In the universe of included studies, some provided adjusted results from multi-variate analyses that included other pesticide exposures. Other studies reported only unadjusted results. Even though Zhang’s method stated a preference for adjusted analyses, she inexplicably failed to use adjusted data in the case of one study that provided both adjusted and unadjusted results.

As shown in Judge Chhabria’s review, Zhang’s methodological errors created an incoherent analysis, with methods that could not be justified. Even accepting its own stated methodology, the meta-analysis was an exercise in cherry picking. In the court’s terms, it was, without qualification, “junk science.”

After the filing of briefs, Judge Chhabria provided the parties an oral hearing, with an opportunity for viva voce testimony. Dr. Zhang thus had a full opportunity to defend her meta-analysis. The hearing, however, did not go well for her. Zhang could not talk intelligently about the studies included, or how they defined high exposure. Zhang’s lack of familiarity with her own opinion and published paper was yet a further reason for excluding her testimony.

As might be expected, plaintiffs’ counsel attempted to hide behind peer review. Plaintiffs’ counsel attempted to shut down Rule 702 scrutiny of the Zhang meta-analysis by suggesting that the trial court had no business digging into validity concerns given that Zhang had published her meta-analysis in what apparently was a peer reviewed journal. Judge Chhabria would have none of it. In his opinion, publication in a peer-reviewed journal cannot obscure the glaring methodological defects of the relied upon meta-analysis. The court observed that “[p]re-publication editorial peer review, just by itself, is far from a guarantee of scientific reliability.”[13] The EPA memorandum was thus a more telling indicator of the validity issues than the publication in a nominally peer-reviewed journal.

Contrary to some law professors who are now seeking to dismantle expert witness gatekeeping as beyond a judge’s competence, Judge Chhabria dismissed the suggestion that he lacked the expertise to adjudicate the validity issues. Indeed, he displayed a better understanding of the meta-analytic process than did Dr. Zhang. As the court observed, one of the goals of MDL assignments was to permit a single trial judge to have time to engage with the scientific issues and to develop “fluency” in the relevant scientific studies. Indeed, when MDL judges have the fluency in the scientific concepts to address Rule 702 or 703 issues, it would be criminal for them to ignore it.

The Bulone opinion should encourage lawyers to get “into the weeds” of expert witness opinions. There is nothing that a little clear thinking – and glyphosate – cannot clear away. Indeed, now that the weeds of Zhang’s meta-analysis are cleared away, it is hard to fathom that any other expert witness can rely upon it without running afoul of both Federal Rules of Evidence 702 and 703.

There were a few issues not addressed in Bulone. As seen in her oral hearing testimony, Zhang probably lacked the qualifications to proffer the meta-analysis. The bar for qualification as an expert witness, however, is sadly very low. One other issue that might well have been addressed is Zhang’s use of a fixed effect model for her meta-analysis. Considering that she was pooling data from cohort and case-control studies, some with and some without adjustments for confounders, with different measures of exposure, and some with and some without exposure-dependent analyses, Zhang and her co-authors were not justified in using a fixed effect model for arriving at a summary estimate of relative risk. Admittedly, this error could easily have been lost in the flood of others.

Postscript

Glyphosate is not merely a scientific issue. Its manufacturer, Monsanto, is the frequent target of media outlets (such as Telesur) from autocratic countries, such as Communist China and its client state, Venezuela.[14]

天安门广场英雄万岁

[1] “The IARC-hy of Evidence – Incoherent & Inconsistent Classifications of Carcinogenicity,” Tortini (Sept. 19, 2023).

[2] Robert E Tarone, “On the International Agency for Research on Cancer classification of glyphosate as a probable human carcinogen,” 27 Eur. J. Cancer Prev. 82 (2018).

[3] Luoping Zhang, Iemaan Rana, Rachel M. Shaffer, Emanuela Taioli, Lianne Sheppard, “Exposure to glyphosate-based herbicides and risk for non-Hodgkin lymphoma: A meta-analysis and supporting evidence,” 781 Mutation Research/Reviews in Mutation Research 186 (2019).

[4] David J. Miller, Acting Chief Toxicology and Epidemiology Branch Health Effects Division, U.S. Environmental Protection Agency, Memorandum to Christine Olinger, Chief Risk Assessment Branch I, “Glyphosate: Epidemiology Review of Zhang et al. (2019) and Leon et al. (2019) publications for Response to Comments on the Proposed Interim Decision” (Jan. 6, 2020).

[5] Geoffrey C. Kabat, William J. Price, Robert E. Tarone, “On recent meta-analyses of exposure to glyphosate and risk of non-Hodgkin’s lymphoma in humans,” 32 Cancer Causes & Control 409 (2021).

[6] Geoffrey Kabat, “Paper Claims A Link Between Glyphosate And Cancer But Fails To Show Evidence,” Science 2.0 (Feb. 18, 2019).

[7] Lianne Sheppard, “Glyphosate Science is Nuanced. Arguments about it on the Internet? Not so much,” Forbes (Feb. 20, 2020).

[8] Geoffrey Kabat, “EPA Refuted A Meta-Analysis Claiming Glyphosate Can Cause Cancer And Senior Author Lianne Sheppard Doubled Down,” Science 2.0 (Feb. 26, 2020).

[9] Maria Dinzeo, “Jurors Hear of New Study Linking Roundup to Cancer,” Courthouse News Service (April 8, 2019).

[10] Bulone v. Monsanto Co., Case No. 16-md-02741-VC, MDL 2741 (N.D. Cal. June 20, 2024). See Hank Campbell, “Glyphosate legal update: Meta-study used by ambulance-chasing tort lawyers targeting Bayer’s Roundup as carcinogenic deemed ‘junk science nonsense’ by trial judge,” Genetic Literacy Project (June 24, 2024).

[11] In re Paraquat Prods. Liab. Litig., No. 3:21-MD-3004-NJR, 2024 WL 1659687 (S.D. Ill. Apr. 17, 2024) (opinion sur Rule 702 motion), appealed sub nom., Fuller v. Syngenta Crop Protection, LLC, No. 24-1868 (7th Cir. May 17, 2024). See “Paraquat Shape-Shifting Expert Witness Quashed,” Tortini (April 24, 2024).

[12] Edward K. Cheng, “The Consensus Rule: A New Approach to Scientific Evidence,” 75 Vanderbilt L. Rev. 407 (2022). See “Cheng’s Proposed Consensus Rule for Expert Witnesses,” Tortini (Sept. 15, 2022); “Further thoughts on Cheng’s Consensus Rule,” Tortini (Oct. 3, 2022).

[13] Bulone, citing Valentine v. Pioneer Chlor Alkali Co., 921 F. Supp. 666, 674-76 (D. Nev. 1996), for its distinction between “editorial peer review” and “true peer review,” with the latter’s inclusion of post-publication assessment of a paper as really important for Rule 702 purposes.

[14] Anne Applebaum, Autocracy, Inc.: The Dictators Who Want to Run the World 66 (2024).

Posted in Causation, Confounding, Expert Witnesses, Meta-analysis, Rule 702, Rule 703, statistical evidence | 15 Comments »

STEM-ing the Tide of Scientific & Mathematical Illiteracy in the Law

July 31st, 2024

I will blame the heat of this summer for reducing my blog posts to a trickle, but I have written elsewhere. The James G. Martin Center for Academic Renewal invited me to write a piece about the need for science and mathematics literacy in law school, and among lawyers and judges. I have touched on the subject before, but I agreed to submit a short essay that is now published as “STEM-ing the Tide of Scientific and Mathematical Illiteracy in the Law: Attorneys need to understand how numbers work. It’s time we teach them,” James G. Martin Center (July 26, 2024).

Although I was delighted to receive the invitation, I was initially skeptical of the organization. The James G. Martin Center for Academic Renewal (previously known as the Pope Center for Higher Education Policy) is a group that has criticized and sought reforms in higher education from a right-of-center perspective. I have given up calling such groups “conservative,” because the term no longer has any clear meaning. While I continue to view Burke and Oakeshott as having something important to say about our current crises, their counsel has no sway among self-styled conservatives in the Republican party, where neo-cons, theo-cons, paleo-cons, fascismo-cons, crypto-cons, techno-cons, ignoratio-cons, and plain ol’ con-cons have pitched one large ignominious tent.

Still, as a group that describes itself as particularly concerned especially with free markets, limited constitutional government, and personal responsibility, the Martin Center has much to commend it. Although I cannot agree with everything promoted on the Center’s website, which has articles from many authors, the group’s publications seemed sufficiently heterodox to me to consider it as a publishing venue.

My piece focused on the need for a modicum of scientific and statistical acumen and training among lawyers, and the ethical lapses that can result from lack of training. I chose to use real world examples of lawyers whose pronouncements in public and in court caused them to look either untutored or unethical. There were no lack of examples, but perhaps as a test of the Martin Center’s bona fides, I focused on three high-profile “conservative” lawyers, Alan Dershowitz, Ken Paxton, and John Eastman. Of course, the last of these lawyers has now had his license suspended, pending an appeal to the California Supreme Court. I was gratified that the Martin Center received and enthusiastically published my short article, which is now online at the Center’s website.

Posted in statistical evidence | No Comments »

Paraquat Shape-Shifting Expert Witness Quashed

April 24th, 2024

Another multi-district litigation (MDL) has hit a jarring speed bump. Claims for Parkinson’s disease (PD), allegedly caused by exposure to paraquat dichloride (paraquat), were consolidated, in June 2021, for pre-trial coordination in MDL No. 3004, in the Southern District of Illinois, before Chief Judge Nancy J. Rosenstengel. Like many health-effects litigation claims, the plaintiffs’ claims in these paraquat cases turn on epidemiologic evidence. To make their causation case in the first MDL trial cases, plaintiffs’ counsel nominated a statistician, Martin T. Wells, to present their causation case. Last week, Judge Rosenstengel found Wells’ opinion so infected by invalid methodologies and inferences as to be inadmissible under the most recent version of Rule 702.[1] Summary judgment in the trial cases followed.[2]

Back in the 1980s, paraquat gained some legal notoriety in one of the most retrograde Rule 702 decisions.[3] Both the herbicide and Rule 702 survived, however, and they both remain in wide use. For the last two decades, there has been a widespread challenges to the safety of paraquat, and in particular there have been claims that paraquat can cause PD or parkinsonism under some circumstances.  Despite this background, the plaintiffs’ counsel in MDL 3004 began with four problems.

First, paraquat is closely regulated for agricultural use in the United States. Under federal law, paraquat can be used to control the growth of weeds only “by or under the direct supervision of a certified applicator.”[4] The regulatory record created an uphill battle for plaintiffs.[5] Under the Federal Insecticide, Fungicide, and Rodenticide Act (“FIFRA”), the U.S. EPA has regulatory and enforcement authority over the use, sale, and labeling of paraquat.[6] As part of its regulatory responsibilities, in 2019, the EPA systematically reviewed available evidence to assess whether there was an association between paraquat and PD. The agency’s review concluded that “there is limited, but insufficient epidemiologic evidence at this time to conclude that there is a clear associative or causal relationship between occupational paraquat exposure and PD.”[7] In 2021, the EPA issued its Interim Registration Review Decision, and reapproved the registration of paraquat. In doing so, the EPA concluded that “the weight of evidence was insufficient to link paraquat exposure from pesticidal use of U.S. registered products to Parkinson’s disease in humans.”[8]

Second, beyond the EPA, there were no other published reviews, systematic or otherwise, which reached a conclusion that paraquat causes PD.[9]

Third, the plaintiffs claims faced another serious impediment. Their counsel placed their reliance upon Professor Martin Wells, a statistician on the faculty of Cornell University. Unfortunately for plaintiffs, Wells has been known to operate as a “cherry picker,” and his methodology has been previously reviewed in an unfavorable light. Another MDL court, which reviewed a review and meta-analysis propounded by Wells, found that his reports “were marred by a selective review of data and inconsistent application of inclusion criteria.”[10]

Fourth, the plaintiffs’ claims were before Chief Judge Nancy J. Rosenstengel, who was willing to do the hard work required under Rule 702, specially as it has been recently amended for clarification and emphasis of the gatekeeper’s responsibilities to evaluate validity issues in the proffered opinions of expert witnesses. As her 97 page decision evinces, Judge Rosenstengel conducted four days of hearings, which included viva voce testimony from Martin Wells, and she obviously read the underlying papers, reviews, as well as the briefs and the Reference Manual on Scientific Evidence, with great care. What followed did not go well for Wells or the plaintiffs’ claims.[11] Judge Rosenstengel has written an opinion that may be the first careful judicial consideration of the basic requirements of systematic review.

The court noted that systematic reviewers carefully define a research question and what kinds of empirical evidence will be reviewed, and then collect, summarize, and, if feasible, synthesize the available evidence into a conclusion.[12] The court emphasized that systematic reviewers should “develop a protocol for the review before commencement and adhere to the protocol regardless of the results of the review.”[13]

Wells proffered a meta-analysis, and a “weight of the evidence” (WOE) review from which he concluded that paraquat causes PD and nearly triples the risk of the disease among workers exposed to the herbicide.[14] In his reports, Wells identified a universe of at least 36 studies, but included seven in his meta-analysis. The defense had identified another two studies that were germane.[15]

Chief Judge Rosenstengel’s opinion is noteworthy for its fine attention to detail, detail that matters to the validity of the expert witness’s enterprise. Martin Wells set out to do a meta-analysis, which was all fine and good. With a universe of 36 studies, with sub-findings, alternative analyses, and changing definitions of relevant exposure, the devil lay in the details.

The MDL court was careful to point out that it was not gainsaying Wells’ decision to limit his meta-analysis to case-control studies, or to his grading of any particular study as being of low quality. Systematic reviews and meta-analyses are generally accepted techniques that are part of a scientific approach to causal inference, but each has standards, predicates, and requirements for valid use. Expert witnesses must not only use a reliable methodology, Rule 702(d) requires that they must reliably apply their chosen methodology to the facts at hand in reaching their conclusions.[16]

The MDL court concluded that Wells’ meta-analysis was not sufficiently reliable under Rule 702 because he failed faithfully and reliably to apply his own articulated methodology. The court followed Wells’ lead in identifying the source and content of his chosen methodology, and simply examined his proffered opinion for compliance with that methodology.[17] The basic principles of validity for conducting meta-analyses were not, in any event, really contested. These principles and requirements were clearly designed to ensure and enhance the reliability of meta-analyses by pre-empting results-driven, reverse-engineered summary estimates of association.

The court found that Wells failed clearly to pre-specify his eligibility criteria. He then proceeded to redefine exposure criteria and study inclusion or eligibility criteria, and study quality criteria, after looking at the evidence. He also inconsistently applied his stated criteria, all in an apparently desired effort to exclude less favorable study outcomes. These ad hoc steps were some of Wells’ deviations from the standards to which he played lip service.

The court did not exclude Wells because it disagreed with his substantive decisions to include or exclude any particular study, or his quality grading of any study. Rather, Dr. Wells’ meta-analysis does not pass muster under Rule 702 because its methodology was unclear, inconsistently applied, not replicable, and at times transparently reverse-engineered.[18]

The court’s evaluation of Wells was unflinchingly critical. Wells’ proffered opinions “required several methodological contortions and outright violations of the scientific standards he professed to apply.”[19] From his first involvement in this litigation, Wells had violated the basic rules of conducting systematic reviews and meta-analyses.[20] His definition of “occupational” exposure meandered to suit his desire to include one study (with low variance) that might otherwise have been excluded.[21] Rather than pre-specifying his review process, his study inclusion criteria, and his quality scores, Wells engaged in an unwritten “holistic” review process, which he conceded was not objectively replicable. Wells’ approach left him free to include studies he wanted in his meta-analysis, and then provide post hoc justifications.[22] His failure to identify his inclusion/exclusion criteria was a “methodological red flag” in Dr. Wells’ meta-analysis, which suggested his reverse engineering of the whole analysis, the “very antithesis of a systematic review.”[23]

In what the court described as “methodological shapeshifting,” Wells blatantly and inconsistently graded studies he wanted to include, and had already decided to include in his meta-analysis, to be of higher quality.[24] The paraquat MDL court found, unequivocally, that Wells had “failed to apply the same level of intellectual rigor to his work in the four trial selection cases that would be required of him and his peers in a non-litigation setting.”[25]

It was also not lost upon the MDL court that Wells had shifted from a fixed effect to a random effects meta-analysis, between his principal and rebuttal reports.[26] Basic to the meta-analytical enterprise is a predicate systematic review, properly done, with pre-specification of inclusion and exclusion criteria for what studies would go into any meta-analysis. The MDL court noted that both sides had cited Borenstein’s textbook on meta-analysis,[27] and that Wells had himself cited the Cochrane Handbook[28] for the basic proposition that that objective and scientifically valid study selection criteria should be clearly stated in advance to ensure the objectivity of the analysis.

There was of course legal authority for this basic proposition about prespecification. Given that the selection of studies that go into a systematic review and meta-analysis can be dispositive of its conclusion, undue subjectivity or ad hoc inclusion can easily arrange a desired outcome.[29] Furthermore, meta-analysis carries with it the opportunity to mislead a lay jury with a single (and inflated) risk ratio,[30] which is obtained by the operator’s manipulation of inclusion and exclusion criteria. This opportunity required the MDL court to examine the methodological rigor of the proffered meta-analysis carefully to evaluate whether it reflects a valid pooling of data or it was concocted to win a case.[31]

Martin Wells had previously acknowledged the dangers of manipulation and subjective selectivity inherent in systematic reviews and meta-analyses. The MDL court quoted from Wells’ testimony in Martin v. Actavis:

QUESTION: You would certainly agree that the inclusion-exclusion criteria should be based upon objective criteria and not simply because you were trying to get to a particular result?

WELLS: No, you shouldn’t load the – sort of cook the books.

QUESTION: You should have prespecified objective criteria in advance, correct?

WELLS: Yes.[32]

The MDL court also picked up on a subtle but important methodological point about which odds ratio to use in a meta-analysis when a study provides multiple analyses of the same association. In his first paraquat deposition, Wells cited the Cochrane Handbook, for the proposition that if a crude risk ratio and a risk ratio from a multivariate analysis are both presented in a given study, then the adjusted risk ratio (and its corresponding measure of standard error seen in its confidence interval) is generally preferable to reduce the play of confounding.[33] Wells violated this basic principle by ignoring the multivariate analysis in the study that dominated his meta-analysis (Liou) in favor of the unadjusted bivariate analysis. Given that Wells accepted this basic principle, the MDL court found that Wells likely selected the minimally adjusted odds ratio over the multiviariate adjusted odds ratio for inclusion in his meta-analysis in order to have the smaller variance (and thus greater weight) from the former. This maneuver was disqualifying under Rule 702.[34]

All in all, the paraquat MDL court’s Rule 702 ruling was a convincing demonstration that non-expert generalist judges, with assistance from subject-matter experts, treatises, and legal counsel, can evaluate and identify deviations from methodological standards of care.

[1] In re Paraquat Prods. Prods. Liab. Litig., Case No. 3:21-md-3004-NJR, MDL No. 3004, Slip op., ___ F.3d ___ (S.D. Ill. Apr. 17, 2024) [Slip op.]

[2] In re Paraquat Prods. Prods. Liab. Litig., Op. sur motion for judgment, Case No. 3:21-md-3004-NJR, MDL No. 3004 (S.D. Ill. Apr. 17, 2024). See also Brendan Pierson, “Judge rejects key expert in paraquat lawsuits, tosses first cases set for trial,” Reuters (Apr. 17, 2024); Hailey Konnath, “Trial-Ready Paraquat MDL Cases Tossed After Testimony Axed,” Law360 (Apr. 18, 2024).

[3] Ferebee v. Chevron Chem. Co., 552 F. Supp. 1297 (D.D.C. 1982), aff’d, 736 F.2d 1529 (D.C. Cir.), cert. denied, 469 U.S. 1062 (1984). See “Ferebee Revisited,” Tortini (Dec. 28, 1017).

[4] See 40 C.F.R. § 152.175.

[5] Slip op. at 31.

[6] 7 U.S.C. § 136w; 7 U.S.C. § 136a(a); 40 C.F.R. § 152.175. The agency must periodically review the registration of the herbicide. 7 U.S.C. § 136a(g)(1)(A). See Ruckelshaus v. Monsanto Co., 467 U.S. 986, 991-92 (1984).

[7] See Austin Wray & Aaron Niman, Memorandum, Paraquat Dichloride: Systematic review of the literature to evaluate the relationship between paraquat dichloride exposure and Parkinson’s disease at 35 (June 26, 2019).

[8] See also Jeffrey Brent and Tammi Schaeffer, “Systematic Review of Parkinsonian Syndromes in Short- and Long-Term Survivors of Paraquat Poisoning,” 53 J. Occup. & Envt’l Med. 1332 (2011) (“An analysis the world’s entire published experience found no connection between high-dose paraquat exposure in humans and the development of parkinsonism.”).

[9] Douglas L. Weed, “Does paraquat cause Parkinson’s disease? A review of reviews,” 86 Neurotoxicology 180, 180 (2021).

[10] In re Incretin-Based Therapies Prods. Liab. Litig., 524 F.Supp. 3d 1007, 1038, 1043 (S.D. Cal. 2021), aff’d, No. 21-55342, 2022 WL 898595 (9th Cir. Mar. 28, 2022) (per curiam). See “Madigan’s Shenanigans and Wells Quelled in Incretin-Mimetic Cases” Tortini (July 15, 2022).

[11] The MDL court obviously worked hard to learn the basics principles of epidemiology. The court relied extensively upon the epidemiology chapter in the Reference Manual on Scientific Evidence. Much of that material is very helpful, but its exposition on statistical concepts is at times confused and erroneous. It is unfortunate that courts do not pay more attention to the more precise and accurate exposition in the chapter on statistics. Citing the epidemiology chapter, the MDL court gave an incorrect interpretation of the p-value: “A statistically significant result is one that is unlikely the product of chance. Slip op. at 17 n. 11. And then again, citing the Reference Manual, the court declared that “[a] p-value of .1 means that there is a 10% chance that values at least as large as the observed result could have been the product of random error. Id.” Id. Similarly, the MDL court gave an incorrect interpretation of the confidence interval. In a footnote, the court tells us that “[r]esearchers ordinarily assert a 95% confidence interval, meaning that ‘there is a 95% chance that the “true” odds ratio value falls within the confidence interval range’. In re Zoloft (Sertraline Hydrochloride) Prod. Liab. Litig., MDL No. 2342, 2015 WL 7776911, at *2 (E.D. Pa. Dec. 2, 2015).” Slip op. at 17n.12.  Citing another court for the definition of a statistical concept is a risky business.

[12] Slip op. at 20, citing Lisa A. Bero, “Evaluating Systematic Reviews and Meta-Analyses,” 14 J.L. & Pol’y 569, 570 (2006).

[13] Slip op. at 21, quoting Bero, at 575.

[14] Slip op. at 3.

[15] The nine studies at issue were as follows: (1) H.H. Liou, et al., “Environmental risk factors and Parkinson’s disease; A case-control study in Taiwan,” 48 Neurology 1583 (1997); (2) Caroline M. Tanner, et al., “Rotenone, Paraquat and Parkinson’s Disease,” 119 Envt’l Health Persps. 866 (2011) (a nested case-control study within the Agricultural Health Study (“AHS”)); (3) Clyde Hertzman, et al., “A Case-Control Study of Parkinson’s Disease in a Horticultural Region of British Columbia,” 9 Movement Disorders 69 (1994); (4) Anne-Maria Kuopio, et al., “Environmental Risk Factors in Parkinson’s Disease,” 14 Movement Disorders 928 (1999); (5) Katherine Rugbjerg, et al., “Pesticide exposure and risk of Parkinson’s disease – a population-based case-control study evaluating the potential for recall bias,” 37 Scandinavian J. of Work, Env’t & Health 427 (2011); (6) Jordan A. Firestone, et al., “Occupational Factors and Risk of Parkinson’s Disease: A Population-Based Case-Control Study,” 53 Am. J. of Indus. Med. 217 (2010); (7) Amanpreet S. Dhillon,“Pesticide / Environmental Exposures and Parkinson’s Disease in East Texas,” 13 J. of Agromedicine 37 (2008); (8) Marianne van der Mark, et al., “Occupational exposure to pesticides and endotoxin and Parkinson’s disease in the Netherlands,” 71 J. Occup. & Envt’l Med. 757 (2014); (9) Srishti Shrestha, et al., “Pesticide use and incident Parkinson’s disease in a cohort of farmers and their spouses,” Envt’l Research 191 (2020).

[16] Slip op. at 75.

[17] Slip op. at 73.

[18] Slip op. at 75, citing In re Mirena IUS Levonorgestrel-Related Prod. Liab. Litig. (No. II), 341 F. Supp. 3d 213, 241 (S.D.N.Y. 2018) (“Opinions that assume a conclusion and reverse-engineer a theory to fit that conclusion are . . . inadmissible.”) (internal citation omitted), aff’d, 982 F.3d 113 (2d Cir. 2020); In re Zoloft (Sertraline Hydrochloride) Prod. Liab. Litig., No. 12-md-2342, 2015 WL 7776911, at *16 (E.D. Pa. Dec. 2, 2015) (excluding expert’s opinion where he “failed to consistently apply the scientific methods he articulat[ed], . . . deviated from or downplayed certain well established principles of his field, and . . . inconsistently applied methods and standards to the data so as to support his a priori opinion.”), aff’d, 858 F.3d 787 (3d Cir. 2017).

[19] Slip op. at 35.

[20] Slip op. at 58.

[21] Slip op. at 55.

[22] Slip op. at 41, 64.

[23] Slip op. at 59-60, citing In re Lipitor (Atorvastatin Calcium) Mktg., Sales Pracs. & Prod. Liab. Litig., 892 F.3d 624, 634 (4th Cir. 2018) (“Result-driven analysis, or cherry-picking, undermines principles of the scientific method and is a quintessential example of applying methodologies (valid or otherwise) in an unreliable fashion.”).

[24] Slip op. at 67, 69-70, citing In re Zoloft (Sertraline Hydrochloride) Prod. Liab. Litig., 858 F.3d 787, 795-97 (3d Cir. 2017) (“[I]f an expert applies certain techniques to a subset of the body of evidence and other techniques to another subset without explanation, this raises an inference of unreliable application of methodology.”); In re Bextra and Celebrex Mktg. Sales Pracs. & Prod. Liab. Litig., 524 F. Supp. 2d 1166, 1179 (N.D. Cal. 2007) (excluding an expert witness’s causation opinion because of his result-oriented, inconsistent evaluation of data sources).

[25] Slip op. at 40.

[26] Slip op. at 61 n.44.

[27] Michael Borenstein, Larry V. Hedges, Julian P. T. Higgins, and Hannah R. Rothstein, Introduction to Meta-Analysis (2d ed. 2021).

[28] Jacqueline Chandler, James Thomas, Julian P. T. Higgins, Matthew J. Page, Miranda Cumpston, Tianjing Li, Vivian A. Welch, eds., Cochrane Handbook for Systematic Reviews of Interventions (2ed 2023).

[29] Slip op. at 56, citing In re Zimmer Nexgen Knee Implant Prod. Liab. Litig., No. 11 C 5468, 2015 WL 5050214, at *10 (N.D. Ill. Aug. 25, 2015).

[30] Slip op. at 22. The court noted that the Reference Manual on Scientific Evidence cautions that “[p]eople often tend to have an inordinate belief in the validity of the findings when a single number is attached to them, and many of the difficulties that may arise in conducting a meta-analysis, especially of observational studies such as epidemiological ones, may consequently be overlooked.” Id., quoting from Manual, at 608.

[31] Slip op. at 57, citing Deutsch v. Novartis Pharms. Corp., 768 F. Supp. 2d 420, 457-58 (E.D.N.Y. 2011) (“[T]here is a strong risk of prejudice if a Court permits testimony based on an unreliable meta-analysis because of the propensity for juries to latch on to the single number.”).

[32] Slip op. at 64, quoting from Notes of Testimony of Martin Wells, in In re Testosterone Replacement Therapy Prod. Liab. Litig., Nos. 1:14-cv-1748, 15-cv-4292, 15-cv-426, 2018 WL 7350886 (N.D. Ill. Apr. 2, 2018).

[33] Slip op. at 70.

[34] Slip op. at 71-72, citing People Who Care v. Rockford Bd. of Educ., 111 F.3d 528, 537-38 (7th Cir. 1997) (“[A] statistical study that fails to correct for salient explanatory variables . . . has no value as causal explanation and is therefore inadmissible in federal court.”); In re Roundup Prod. Liab. Litig., 390 F. Supp. 3d 1102, 1140 (N.D. Cal. 2018). Slip op. at 17 n. 12.

Posted in Causation, Confounding, Expert Witnesses, Meta-analysis, Reference Manual on Scientific Evidence, Rule 702, statistical evidence | 44 Comments »

Peer Review, Protocols, and QRPs

April 3rd, 2024

In Daubert, the Supreme Court decided a legal question about the proper interpretation of a statute, Rule 702, and then remanded the case to the Ninth Circuit of the Court of Appeals for further proceedings. The Court did, however, weigh in with dicta about some several considerations in admissibility decisions.  In particular, the Court identified four non-dispositive factors: whether the challenged opinion has been empirically tested, published and peer reviewed, and whether the underlying scientific technique or method supporting the opinion has an acceptable rate of error, and has gained general acceptance.[1]

The context in which peer review was discussed in Daubert is of some importance to our understanding its holding peer review out as a consideraton. One of the bases for the defense challenges to some of the plaintiffs’ expert witnesses’ opinions in Daubert was their reliance upon re-analyses of published studies to suggest that there was indeed an increased risk of birth defects if only the publication authors had used some other control group, or taken some other analytical approach. Re-analyses can be important, but these reanalyses of published Bendectin studies were post hoc, litigation driven, and obviously result oriented. The Court’s discussion of peer review reveals that it was not simply creating a box to be checked before a trial court could admit an expert witness’s opinions. Peer review was suggested as a consideration because:

“submission to the scrutiny of the scientific community is a component of “good science,” in part because it increases the likelihood that substantive flaws in methodology will be detected. The fact of publication (or lack thereof) in a peer reviewed journal thus will be a relevant, though not dispositive, consideration in assessing the scientific validity of a particular technique or methodology on which an opinion is premised.”[2]

Peer review, or the lack thereof, for the challenged expert witnesses’ re-analyses was called out because it raised suspicions of lack of validity. Nothing in Daubert, or in later decisions, or more importantly in Rule 702 itself, supports admitting expert witness testimony just because the witness relied upon peer-reviewed studies, especially when the studies are invalid or are based upon questionable research practices. The Court was careful to point out that peer-reviewed publication was “not a sine qua non of admissibility; it does not necessarily correlate with reliability, … .”[3] The Court thus showed that it was well aware that well-ground (and thus admissible) opinions may not have been previously published, and that the existence of peer review was simply a potential aid in answering the essential question, whether the proponent of a proffered opinion has shown “the scientific validity of a particular technique or methodology on which an opinion is premised.”[4]

Since 1993, much has changed in the world of bio-science publishing. The wild proliferation of journals, including predatory and “pay-to-play” journals, has disabused most observers that peer review provides evidence of validity of methods. Along with the exponential growth in publications has come an exponential growth in expressions of concern and out-right retractions of articles, as chronicled and detailed at Retraction Watch.[5] Some journals encourage authors to nominate the peer reviewers for their manuscripts; some journals let authors block some scientists as peer reviewers of their submitted manuscripts. If the Supreme Court were writing today, it might well note that peer review is often a feature of bad science, advanced by scientists who know that peer-reviewed publication is the price of admission to the advocacy arena.

Since the Supreme Court decided Daubert, the Federal Judicial Center and National Academies of Science have provided a Reference Manual for Scientific Evidence, now in its third edition, and with a fourth edition on the horizon, to assist judges and lawyers involved in the litigation of scientific issues. Professor Goodstein, in his chapter “How Science Works,” in the third edition, provides the most extensive discussion of peer review in the Manual, and emphasizes that peer review “works very poorly in catching cheating or fraud.”[6]  Goodstein invokes his own experience as a peer reviewer to note that “peer review referees and editors limit their assessment of submitted articles to such matters as style, plausibility, and defensibility; they do not duplicate experiments from scratch or plow through reams of computer-generated data in order to guarantee accuracy or veracity or certainty.”[7] Indeed, Goodstein’s essay in the Reference Manual characterizes the ability of peer review to warrant study validity as a “myth”:

“Myth: The institution of peer review assures that all published papers are sound and dependable.

Fact: Peer review generally will catch something that is completely out of step with majority thinking at the time, but it is practically useless for catching outright fraud, and it is not very good at dealing with truly novel ideas. … It certainly does not ensure that the work has been fully vetted in terms of the data analysis and the proper application of research methods.”[8]

Goodstein’s experience as a peer reviewer is hardly idiosyncratic. One standard text on the ethical conduct of research reports that peer review is often ineffective or incompetent, and that it may not even catch simple statistical or methodological errors.[9] According to the authors, Shamoo and Resnik:

“[p]eer review is not good at detecting data fabrication or falsification partly because reviewers usually do not have access to the material they would need to detect fraud, such as the original data, protocols, and standard operating procedures.”[10]

Indeed, without access to protocols, statistical analysis plans, and original data, peer review often cannot identify good faith or negligent deviations from the standard of scientific care. There is some evidence to support this negative assessment of peer review from testing of the counter-factual. Reviewers were able to detect questionable, selective reporting when they had access to the study authors’ research protocols.[11]

Study Protocol

The study protocol provides the scientific rationale for a study, clearly defines the research question, the data collection process, defines the key exposure and outcomes, and describes the methods to be applied, before commencing data collection.[12] The protocol also typically pre-specifies the statistical data analysis. The epidemiology chapter of the current edition of the Reference Manual for Scientific Evidence offers blandly only that epidemiologists attempt to minimize bias in observational studies with “data collection protocols.”[13] Epidemiologists and statisticians are much clearer in emphasizing the importance, indeed the necessity, of having a study protocol before commencing data collection. Back in 1988, John Bailar and Frederick Mosteller explained that it was critical in reporting statistical analyses to inform readers about how and when the authors devised the study design, and whether they set the design criteria out in writing before they began to collect data.[14]

The necessity of a study protocol is “self-evident,”[15] and essential to research integrity.[16] The International Society of Pharmacoepidemiology has issued Guidelines for “Good Pharmacoepidemiology Practices,”[17] which calls for every study to have a written protocol. Among the requirements set out in this set of guidelines are descriptions of the research method, study design, operational definitions of exposure and outcome variables, and projected study sample size. The Guidelines provide that a detailed statistical analysis plan may be specified after data collection begins, but before any analysis commences.

Expert witness opinions on health effects are built upon studies, and so it behooves legal counsel to identify the methodological strengths and weaknesses of key studies through questioning whether they have protocols, whether the protocols were methodologically appropriate, and whether the researchers faithfully followed their protocols and their statistical analysis plans. Determining the peer review status of a publication, on the other hand, will often not advance a challenge based upon improvident methodology.

In some instances, a published study will have sufficiently detailed descriptions of methods and data that readers, even lawyers, can evaluate their scientific validity or reliability (vel non). In some cases, however, readers will be no better off than the peer reviewers who were deprived of access to protocols, statistical analysis plans, and original data. When a particular study is crucial support for an adversary’s expert witness, a reasonable litigation goal may well be to obtain the protocol and statistical analysis plan, and if need be, the original underlying data. The decision to undertake such discovery is difficult. Discovery of non-party scientists can be expensive and protracted; it will almost certainly be contentious. When expert witnesses rely upon one or a few studies, which telegraph internal validity, this litigation strategy may provide the strongest evidence against the study’s being reasonably relied upon, or its providing “sufficient facts and data” to support an admissible expert witness opinion.

[1] Daubert v. Merrell Dow Pharms., Inc., 509 U.S. 579, 593-594 (1993).

[2] Id. at 594 (internal citations omitted) (emphasis added).

[3] Id.

[4] Id. at 593-94.

[5] Retraction Watch, at https://retractionwatch.com/.

[6] Reference Manual on Scientific Evidence at 37, 44-45 (3rd ed. 2011) [Manual].

[7] Id. at 44-45 n.11.

[8] Id. at 48 (emphasis added).

[9] Adil E. Shamoo and David B. Resnik, Responsible Conduct of Research 133 (4th ed. 2022).

[10] Id.

[11] An-Wen Chan, Asbjørn Hróbjartsson, Mette T. Haahr, Peter C. Gøtzsche, and David G. Altman, D. G. “Empirical evidence for selective reporting of outcomes in randomized trials: Comparison of protocols to published articles,” 291 J. Am. Med. Ass’n 2457 (2004).

[12] Wolfgang Ahrens & Iris Pigeot, eds., Handbook of Epidemiology 477 (2nd ed. 2014).

[13] Michael D. Green, D. Michal Freedman, and Leon Gordis, “Reference Guide on Epidemiology,” in Reference Manual on Scientific Evidence 573 (3rd ed. 2011) 573 (“Study designs are developed before they begin gathering data.”).

[14] John Bailar & Frederick Mosteller, “Guidelines for Statistical Reporting in Articles for Medical Journals,” 108 Ann. Intern. Med. 2266, 268 (1988).

[15] Wolfgang Ahrens & Iris Pigeot, eds., Handbook of Epidemiology 477 (2nd ed. 2014).

[16] Sandra Alba, et al., “Bridging research integrity and global health epidemiology statement: guidelines for good epidemiological practice,” 5 BMJ Global Health e003236, at p.3 & passim (2020).

[17] See “The ISPE Guidelines for Good Pharmacoepidemiology Practices (GPP),” available at <https://www.pharmacoepi.org/resources/policies/guidelines-08027/>.

Posted in Data Sharing, Expert Witness Discovery, Rule 702, Rule 703, statistical evidence, Underlying Data | 12 Comments »

Reference Manual – Desiderata for 4th Edition – Part IV – Confidence Intervals

February 10th, 2023

Putting aside the idiosyncratic chapter by the late Professor Berger, most of the third edition of the Reference Manual presented guidance on many important issues.  To be sure, there are gaps, inconsistencies, and mistakes, but the statistics chapter should be a must-read for federal (and state) judges. On several issues, especially statistical in nature, the fourth edition could benefit from an editor to ensure that the individual chapters, written by different authors, actually agree on key concepts.  One such example is the third edition’s treatment of confidence intervals.[1]

The “DNA Identification” chapter noted that the meaning of a confidence interval is subtle,[2] but I doubt that the authors, David Kaye and George Sensabaugh, actually found it subtle or difficult. In the third edition’s chapter on statistics, David Kaye and co-author, the late David A. Freedman, gave a reasonable definition of confidence intervals in their glossary:

“confidence interval. An estimate, expressed as a range, for a parameter. For estimates such as averages or rates computed from large samples, a 95% confidence interval is the range from about two standard errors below to two standard errors above the estimate. Intervals obtained this way cover the true value about 95% of the time, and 95% is the confidence level or the confidence coefficient.”[3]

Intervals, not the interval, which is correct. This chapter made clear that it was the procedure of obtaining multiple samples with intervals that yielded the 95% coverage. In the substance of their chapter, Kaye and Freedman are explicit about how intervals are constructed, and that:

“the confidence level does not give the probability that the unknown parameter lies within the confidence interval.”[4]

Importantly, the authors of the statistics chapter named names; that is, they cited some cases that butchered the concept of the confidence interval.[5] The fourth edition will have a more difficult job because, despite the care taken in the statistics chapter, many more decisions have misstated or misrepresented the meaning of a confidence interval.[6] Citing more cases perhaps will disabuse federal judges of their reliance upon case law for the meaning of statistical concepts.

The third edition’s chapter on multiple regression defined confidence interval in its glossary:

“confidence interval. An interval that contains a true regression parameter with a given degree of confidence.”[7]

The chapter avoided saying anything obviously wrong only by giving a very circular definition. When the chapter substantively described a confidence interval, it ended up giving an erroneous one:

“In general, for any parameter estimate b, the expert can construct an interval around b such that there is a 95% probability that the interval covers the true parameter. This 95% confidence interval is given by: b ± 1.96 (SE of b).”[8]

The formula provided is correct, but the interpretation of a 95% probability that the interval covers the true parameter is unequivocably wrong.[9]

The third edition’s chapter by Shari Seidman Diamond on survey research, on the other hand, gave an anodyne example and a definition:

“A survey expert could properly compute a confidence interval around the 20% estimate obtained from this sample. If the survey were repeated a large number of times, and a 95% confidence interval was computed each time, 95% of the confidence intervals would include the actual percentage of dentists in the entire population who would believe that Goldgate was manufactured by the makers of Colgate.

                 *  *  *  *

Traditionally, scientists adopt the 95% level of confidence, which means that if 100 samples of the same size were drawn, the confidence interval expected for at least 95 of the samples would be expected to include the true population value.”[10]

Similarly, the third edition’s chapter on epidemiology correctly defined the confidence interval operationally as a process of iterative intervals that collectively cover the true value in 95% of all the intervals:

“A confidence interval provides both the relative risk (or other risk measure) found in the study and a range (interval) within which the risk likely would fall if the study were repeated numerous times.”[11]

Not content to leave it well said, the chapter’s authors returned to the confidence interval and provided another, more problematic definition, a couple of pages later in the text:

“A confidence interval is a range of possible values calculated from the results of a study. 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.”[12]

The first sentence refers to “a study”; that is, one study, one range of values. The second sentence then tells us that “the range” (singular, presumably referring back to the single “a study”), will capture 95% of the results from many resamplings from the same population. Now the definition is not framed with respect to the true population parameter, but the results from many other samples. The authors seem to have given the first sample’s confidence interval the property of including 95% of all future studies, and that is incorrect. From reviewing the case law, courts remarkably have gravitated to the second, incorrect definition.

The glossary to the third edition’s epidemiology chapter clearly, however, runs into the ditch:

“confidence interval. A range of values calculated from the results of a study within which the true value is likely to fall; the width of the interval reflects random error. Thus, if a confidence level of .95 is selected for a study, 95% of similar studies would result in the true relative risk falling within the confidence interval.”[13]

Note that the sentence before the semicolon talked of “a study” with “a range of values,” and that there is a likelihood of that range including the “true value.” This definition thus used the singular to describe the study and to describe the range of values.  The definition seemed to be saying, clearly but wrongly, that a single interval from a single study has a likelihood of containing the true value. The second full sentence ascribed a probability, 95%, to the true relative risk’s falling within “the interval.” To point out the obvious, “the interval,” is singular, and refers back to “a study,” also singular. At best, this definition was confusing; at worst, it was wrong.

The Reference Manual has a problem beyond its own inconsistencies, and the refractory resistance of the judiciary to statistical literacy. There are any number of law professors and even scientists who have held out incorrect definitions and interpretations of confidence intervals.  It would be helpful for the fourth edition to caution its readers, both bench and bar, to the prevalent misunderstandings.

Here, for instance, is an example of a well-credentialed statistician, who gave a murky definition in a declaration filed in federal court:

“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.”[14]

The expert witness correctly identifies the repeated sampling, but specifies a 95% probability to “the range,” which leaves unclear whether it is the range of all intervals or “a 95% confidence interval,” which is in the antecedent of the statement.

Much worse was a definition proffered in a recent law review article by well-known, respected authors:

“A 95% confidence interval, in contrast, is a one-sided or two-sided interval from a data sample with 95% probability of bounding a fixed, unknown parameter, for which no nondegenerate probability distribution is conceived, under specified assumptions about the data distribution.”[15]

The phrase “for which no nondegenerate probability distribution is conceived,” is unclear as to whether the quoted phrase refers to the confidence interval or to the unknown parameter. It seems that the phrase modifies the noun closest to it in the sentence, the “fixed, unknown parameter,” which suggests that these authors were simply trying to emphasize that they were giving a frequentist interpretation and not conceiving of the parameter as a random variable as Bayesians would. The phrase “no nondegenerate” appears to be a triple negative, since a degenerate distribution is one that does not have a variation. The phrase makes the definition obscure, and raises questions what is being excluded by the phrase.

The more concerning aspect of the quoted footnote is its obfuscation of the important distinction between the procedure of repeatedly calculating confidence intervals (which procedure has a 95% success rate in the long run) and the probability that any given instance of the procedure, in a single confidence interval, contains the parameter. The latter probability is either zero or one.

The definition’s reference to “a” confidence interval, based upon “a” data sample, actually leaves the reader with no way of understanding the definition to be referring to the repeated process of sampling, and the set of resulting intervals. The upper and lower interval bounds are themselves random variables that need to be taken into account, but by referencing a single interval from a single data sample, the authors misrepresent the confidence interval and invite a Bayesian interpretation.[16]

Sadly, there is a long tradition of scientists and academics in giving errant definitions and interpretations of the confidence interval.[17] Their error is not harmless because they invite the attribution of a high level of probability to the claim that the “true” population measure is within the reported confidence interval. The error encourages readers to believe that the confidence interval is not conditioned upon the single sample result, and it misleads readers into believing that not only random error, but systematic and data errors are accounted for in the posterior probability.[18] 

[1] “Confidence in Intervals and Diffidence in the Courts” (Mar. 4, 2012).

[2] David H. Kaye & George Sensabaugh, “Reference Guide on DNA Identification Evidence” 129, 165 n.76.

[3] David H. Kaye & David A. Freedman, “Reference Guide on Statistics” 211, 284-5 (Glossary).

[4] Id. at 247.

[5] Id. at 247 n.91 & 92 (citing DeLuca v. Merrell Dow Pharms., Inc., 791 F. Supp. 1042, 1046 (D.N.J. 1992), aff’d, 6 F.3d 778 (3d Cir. 1993); SmithKline Beecham Corp. v. Apotex Corp., 247 F. Supp. 2d 1011, 1037 (N.D. Ill. 2003), aff’d on other grounds, 403 F.3d 1331 (Fed. Cir. 2005); In re Silicone Gel Breast Implants Prods. Liab. Litig, 318 F. Supp. 2d 879, 897 (C.D. Cal. 2004) (“a margin of error between 0.5 and 8.0 at the 95% confidence level . . . means that 95 times out of 100 a study of that type would yield a relative risk value somewhere between 0.5 and 8.0.”).

[6] See, e.g., Turpin v. Merrell Dow Pharm., Inc., 959 F.2d 1349, 1353–54 & n.1 (6th Cir. 1992) (erroneously describing a 95% CI of 0.8 to 3.10, to mean that “random repetition of the study should produce, 95 percent of the time, a relative risk somewhere between 0.8 and 3.10”); American Library Ass’n v. United States, 201 F.Supp. 2d 401, 439 & n.11 (E.D.Pa. 2002), rev’d on other grounds, 539 U.S. 194 (2003); Ortho–McNeil Pharm., Inc. v. Kali Labs., Inc., 482 F.Supp. 2d 478, 495 (D.N.J.2007) (“Therefore, a 95 percent confidence interval means that if the inventors’ mice experiment was repeated 100 times, roughly 95 percent of results would fall within the 95 percent confidence interval ranges.”) (apparently relying party’s expert witness’s report), aff’d in part, vacated in part, sub nom. Ortho McNeil Pharm., Inc. v. Teva Pharms Indus., Ltd., 344 Fed.Appx. 595 (Fed. Cir. 2009); Eli Lilly & Co. v. Teva Pharms, USA, 2008 WL 2410420, *24 (S.D. Ind. 2008) (stating incorrectly that “95% percent of the time, the true mean value will be contained within the lower and upper limits of the confidence interval range”); Benavidez v. City of Irving, 638 F.Supp. 2d 709, 720 (N.D. Tex. 2009) (interpreting a 90% CI to mean that “there is a 90% chance that the range surrounding the point estimate contains the truly accurate value.”); Pritchard v. Dow Agro Sci., 705 F. Supp. 2d 471, 481, 488 (W.D. Pa. 2010) (excluding Dr. Bennet Omalu who assigned a 90% probability that an 80% confidence interval excluded relative risk of 1.0), aff’d, 430 F. App’x 102 (3d Cir.), cert. denied, 132 S. Ct. 508 (2011); Estate of George v. Vermont League of Cities and Towns, 993 A.2d 367, 378 n.12 (Vt. 2010) (erroneously describing a confidence interval to be a “range of values within which the results of a study sample would be likely to fall if the study were repeated numerous times”); Garcia v. Tyson Foods, 890 F. Supp. 2d 1273, 1285 (D. Kan. 2012) (quoting expert witness Robert G. Radwin, who testified that a 95% confidence interval in a study means “if I did this study over and over again, 95 out of a hundred times I would expect to get an average between that interval.”); In re Chantix (Varenicline) Prods. Liab. Litig., 889 F. Supp. 2d 1272, 1290n.17 (N.D. Ala. 2012); In re Zoloft Products, 26 F. Supp. 3d 449, 454 (E.D. Pa. 2014) (“A 95% confidence interval means that there is a 95% chance that the ‘‘true’’ ratio value falls within the confidence interval range.”), aff’d, 858 F.3d 787 (3d Cir. 2017); Duran v. U.S. Bank Nat’l Ass’n, 59 Cal. 4th 1, 36, 172 Cal. Rptr. 3d 371, 325 P.3d 916 (2014) (“Statisticians typically calculate margin of error using a 95 percent confidence interval, which is the interval of values above and below the estimate within which one can be 95 percent certain of capturing the ‘true’ result.”); In re Accutane Litig., 451 N.J. Super. 153, 165 A.3d 832, 842 (2017) (correctly quoting an incorrect definition from the third edition at p.580), rev’d on other grounds, 235 N.J. 229, 194 A.3d 503 (2018); In re Testosterone Replacement Therapy Prods. Liab., No. 14 C 1748, MDL No. 2545, 2017 WL 1833173, *4 (N.D. Ill. May 8, 2017) (“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.”); Maldonado v. Epsilon Plastics, Inc., 22 Cal. App. 5th 1308, 1330, 232 Cal. Rptr. 3d 461 (2018) (“The 95 percent ‘confidence interval’, as used by statisticians, is the ‘interval of values above and below the estimate within which one can be 95 percent certain of capturing the “true” result’.”); Escheverria v. Johnson & Johnson, 37 Cal. App. 5th 292, 304, 249 Cal. Rptr. 3d 642 (2019) (quoting uncritically and with approval one of plaintiff’s expert witnesses, Jack Siemiatycki, who gave the jury an example of a study with a relative risk of 1.2, with a “95 percent probability that the true estimate is between 1.1 and 1.3.” According to the court, Siemiatycki went on to explain that this was “a pretty tight interval, and we call that a confidence interval. We call it a 95 percent confidence interval when we calculate it in such a way that it covers 95 percent of the underlying relative risks that are compatible with this estimate from this study.”); In re Viagra (Sildenafil Citrate) & Cialis (Tadalafil) Prods. Liab. Litig., 424 F.Supp.3d 781, 787 (N.D. Cal. 2020) (“For example, a given study could calculate a relative risk of 1.4 (a 40 percent increased risk of adverse events), but show a 95 percent “confidence interval” of .8 to 1.9. That confidence interval means there is 95 percent chance that the true value—the actual relative risk—is between .8 and 1.9.”); Rhyne v. United States Steel Corp., 74 F. Supp. 3d 733, 744 (W.D.N.C. 2020) (relying upon, and quoting, one of the more problematic definitions given in the third edition at p.580: “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 population.”); Wilant v. BNSF Ry., C.A. No. N17C-10-365 CEB, (Del. Super. Ct. May 13, 2020) (citing third edition at p.573, “a confidence interval provides ‘a range (interval) within which the risk likely would fall if the study were repeated numerous times’.”; “[s]o a 95% confidence interval indicates that the range of results achieved in the study would be achieved 95% of the time when the study is replicated from the same population.”); Germaine v. Sec’y Health & Human Servs., No. 18-800V, (U.S. Fed. Ct. Claims July 29, 2021) (giving an incorrect definition directly from the third edition, at p.621; “[a] “confidence interval” is “[a] range of values … within which the true value is likely to fall[.]”).

[7] Daniel Rubinfeld, “Reference Guide on Multiple Regression” 303, 352.

[8] Id. at 342.

[9] See Sander Greenland, Stephen J. Senn, Kenneth J. Rothman, John B. Carlin, Charles Poole, Steven N. Goodman, and Douglas G. Altman, “Statistical tests, P values, confidence intervals, and power: a guide to misinterpretations,” 31 Eur. J. Epidemiol. 337, 343 (2016).

[10] Shari Seidman Diamond, “Reference Guide on Survey Research” 359, 381.

[11] Michael D. Green, D. Michal Freedman, and Leon Gordis, “Reference Guide on Epidemiology,” 549, 573.

[12] Id. at 580.

[13] Id. at 621.

[14] In re Testosterone Replacement Therapy Prods. Liab. Litig., Declaration of Martin T. Wells, Ph.D., at 2-3 (N.D. Ill., Oct. 30, 2016). 

[15] Joseph Sanders, David Faigman, Peter Imrey, and A. Philip Dawid, “Differential Etiology: Inferring Specific Causation in the Law from Group Data in Science,” 63 Arizona L. Rev. 851, 898 n.173 (2021).

[16] The authors are well-credentialed lawyers and scientists. Peter Imrey, was trained in, and has taught, mathematical statistics, biostatistics, and epidemiology. He is a professor of medicine in the Cleveland Clinic Lerner College of Medicine. A. Philip Dawid is a distinguished statistician, an Emeritus Professor of Statistics, Cambridge University, Darwin College, and a Fellow of the Royal Society. David Faigman is the Chancellor & Dean, and the John F. Digardi Distinguished Professor of Law at the University of California Hastings College of the Law. Joseph Sanders is the A.A. White Professor, at the University of Houston Law Center. I have previously pointed this problem in these authors’ article. “Differential Etiologies – Part One – Ruling In” (June 19, 2022).

[17] See, e.g., Richard W. Clapp & David Ozonoff, “Environment and Health: Vital Intersection or Contested Territory?” 30 Am. J. L. & Med. 189, 210 (2004) (“Thus, a RR [relative risk] of 1.8 with a confidence interval of 1.3 to 2.9 could very likely represent a true RR of greater than 2.0, and as high as 2.9 in 95 out of 100 repeated trials.”); Erica Beecher-Monas, Evaluating Scientific Evidence: An Interdisciplinary Framework for Intellectual Due Process 60-61 n. 17 (2007) (quoting Clapp and Ozonoff with obvious approval); Déirdre Dwyer, The Judicial Assessment of Expert Evidence 154-55 (Cambridge Univ. Press 2008) (“By convention, scientists require a 95 per cent probability that a finding is not due to chance alone. The risk ratio (e.g. ‘2.2’) represents a mean figure. The actual risk has a 95 per cent probability of lying somewhere between upper and lower limits (e.g. 2.2 ±0.3, which equals a risk somewhere between 1.9 and 2.5) (the ‘confidence interval’).”); Frank C. Woodside, III & Allison G. Davis, “The Bradford Hill Criteria: The Forgotten Predicate,” 35 Thomas Jefferson L. Rev. 103, 110 (2013) (“A confidence interval provides both the relative risk found in the study and a range (interval) within which the risk would likely fall if the study were repeated numerous times.”); Christopher B. Mueller, “Daubert Asks the Right Questions:  Now Appellate Courts Should Help Find the Right Answers,” 33 Seton Hall L. Rev. 987, 997 (2003) (describing the 95% confidence interval as “the range of outcomes that would be expected to occur by chance no more than five percent of the time”); Arthur H. Bryant & Alexander A. Reinert, “The Legal System’s Use of Epidemiology,” 87 Judicature 12, 19 (2003) (“The confidence interval is intended to provide a range of values within which, at a specified level of certainty, the magnitude of association lies.”) (incorrectly citing the first edition of Rothman & Greenland, Modern Epidemiology 190 (Philadelphia 1998);  John M. Conley & David W. Peterson, “The Science of Gatekeeping: The Federal Judicial Center’s New Reference Manual on Scientific Evidence,” 74 N.C.L.Rev. 1183, 1212 n.172 (1996) (“a 95% confidence interval … means that we can be 95% certain that the true population average lies within that range”).

[18] See Brock v. Merrill Dow Pharm., Inc., 874 F.2d 307, 311–12 (5th Cir. 1989) (incorrectly stating that the court need not resolve questions of bias and confounding because “the studies presented to us incorporate the possibility of these factors by the use of a confidence interval”). Bayesian credible intervals can similarly be misleading when the interval simply reflects sample results and sample variance, but not the myriad other ways the estimate may be wrong.

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An Opinion to SAVOR

November 11th, 2022

The saxagliptin medications are valuable treatments for type 2 diabetes mellitus (T2DM). The SAVOR (Saxagliptin Assessment of Vascular Outcomes Recorded in Patients with Diabetes Mellitus) study was a randomized controlled trial, undertaken by manufacturers at the request of the FDA.[1] As a large (over sixteen thousand patients randomized) double-blinded cardiovascular outcomes trial, SAVOR collected data on many different end points in patients with T2DM, at high risk of cardiovascular disease, over a median of 2.1 years. The primary end point was a composite end point of cardiac death, non-fatal myocardial infarction, and non-fatal stroke. Secondary end points included each constituent of the composite, as well as hospitalizations for heart failure, coronary revascularization, or unstable angina, as well as other safety outcomes.

The SAVOR trial found no association between saxagliptin use and the primary end point, or any of the constituents of the primary end point.  The trial did, however, find a modest association between saxagliptin and one of the several secondary end points, hospitalization for heart failure (hazard ratio, 1.27; 95% C.I., 1.07 to 1.51; p = 0.007). The SAVOR authors urged caution in interpreting their unexpected finding for heart failure hospitalizations, given the multiple end points considered.[2] Notwithstanding the multiplicity, in 2016, the FDA, which does not require a showing of causation for adding warnings to a drug’s labeling, added warnings about the “risk” of hospitalization for heart failure from the use of saxagliptin medications.

And the litigation came.

The litigation evidentiary display grew to include, in addition to SAVOR, observational studies, meta-analyses, and randomized controlled trials of other DPP-4 inhibitor medications that are in the same class as saxagliptin. The SAVOR finding for heart failure was not supported by any of the other relevant human study evidence. The lawsuit industry, however, armed with an FDA warning, pressed its cases. A multi-district litigation (MDL 2809) was established. Rule 702 motions were filed by both plaintiffs’ and defendants’ counsel.

When the dust settled in this saxagliptin litigation, the court found that the defendants’ expert witnesses satisfied the relevance and reliability requirements of Rule 702, whereas the proferred opinions of plaintiff’s expert witness, Dr. Parag Goyal, a cardiologist at Cornell-Weill Hospital in New York, did not satisfy Rule 702.[3] The court’s task was certainly made easier by the lack of any other expert witness or published opinion that saxagliptin actually causes heart failure serious enough to result in hospitalization. 

The saxagliptin litigation presented an interesting array of facts for a Rule 702 show down. First, there was an RCT that reported a nominally statistically significant association between medication use and a harm, hospitalization for heart failure. The SAVOR finding, however, was in a secondary end point, and its statistical significance was unimpressive when considered in the light of the multiple testing that took place in the context of a cardiovascular outcomes trial.

Second, the heart failure increase was not seen in the original registration trials. Third, there was an effort to find corroboration in observational studies and meta-analyses, without success. Fourth, there was no apparent mechanism for the putative effect. Fifth, there was no support from trials or observational studies of other medications in the class of DPP-4 inhibitors.

Dr. Goyal testified that the heart failure finding in SAVOR “should be interpreted as cause and effect unless there is compelling evidence to prove otherwise.” On this record, the MDL court excluded Dr. Goyal’s causation opinions. Dr. Goyal purported to conduct a Bradford Hill analysis, but the MDL court appeared troubled by his glib dismissal of the threat to validity in SAVOR from multiple testing, and his ignoring the consistency prong of the Hill factors. SAVOR was the only heart failure finding in humans, with the remaining observational studies, meta-analyses, and other trials of DPP-4 inhibitors failing to provide supporting evidence.

The challenged defense expert witnesses defended the validity of their opinions, and ultimately the MDL court had little concern in permitting them through the judicial gate. The plaintiffs’ challenges to Suneil Koliwad, a physician with a doctorate in molecular physiology, Eric Adler, a cardiologist, and Todd Lee, a pharmaco-epidemiologist, were all denied. The plaintiffs challenged, among other things, whether Dr. Adler was qualified to apply a Bonferroni correction to the SAVOR results, and whether Dr. Lee was obligated to obtain and statistically analyze the data from the trials and studies ab initio. The MDL court quickly dispatched these frivolous challenges.

The saxagliptin MDL decision is an important reminder that litigants should remain vigilant about inaccurate assertions of “statistical significance,” even in premier, peer-reviewed journals. Not all journals are as careful as the New England Journal of Medicine in requiring qualification of claims of statistical significance in the face of multiple testing.

One legal hiccup in the court’s decision was its improvident citation to Daubert, for the proposition that the gatekeeping inquiry must focus “solely on principles and methodology, not on the conclusions they generate.”[4] That piece of obiter dictum did not survive past the Supreme Court’s 1997 decision in Joiner,[5] and it was clearly superseded by statute in 2000. Surely it is time to stop citing Daubert for this dictum.

[1] Benjamin M. Scirica, Deepak L. Bhatt, Eugene Braunwald, Gabriel Steg, Jaime Davidson, et al., for the SAVOR-TIMI 53 Steering Committee and Investigators, “Saxagliptin and Cardiovascular Outcomes in Patients with Type 2 Diabetes Mellitus,” 369 New Engl. J. Med. 1317 (2013).

[2] Id. at 1324.

[3] In re Onglyza & Kombiglyze XR Prods. Liab. Litig., MDL 2809, 2022 WL 43244 (E.D. Ken. Jan. 5, 2022).

[4] Daubert v. Merrell Dow Pharms., Inc., 509 U.S. 579, 595 (1993).

[5] General Electric Co. v. Joiner, 522 U.S. 136 (1997).

Posted in Causation, Meta-analysis, Rule 702, Scientific Evidence, statistical evidence | No Comments »

Amicus Curious – Gelbach’s Foray into Lipitor Litigation

August 25th, 2022

Professor Schauer’s discussion of statistical significance, covered in my last post,[1] is curious for its disclaimer that “there is no claim here that measures of statistical significance map easily onto measures of the burden of proof.” Having made the disclaimer, Schauer proceeds to falls into the transposition fallacy, which contradicts his disclaimer, and, generally speaking, is not a good thing for a law professor eager to advance the understanding of “The Proof,” to do.

Perhaps more curious than Schauer’s error is his citation support for his disclaimer.[2] The cited paper by Jonah B. Gelbach is one of several of Gelbach’s papers that advances the claim that the p-value does indeed map onto posterior probability and the burden of proof. Gelbach’s claim has also been the center piece in his role as an advocate in support of plaintiffs in the Lipitor (atorvastatin) multi-district litigation (MDL) over claims that ingestion of atorvastatin causes diabetes mellitus.

Gelbach’s intervention as plaintiffs’ amicus is peculiar on many fronts. At the time of the Lipitor litigation, Sonal Singh was an epidemiologist and Assistant Professor of Medicine, at the Johns Hopkins University. The MDL trial court initially held that Singh’s proffered testimony was inadmissible because of his failure to consider daily dose.[3] In a second attempt, Singh offered an opinion for 10 mg daily dose of atorvastatin, based largely upon the results of a clinical trial known as ASCOT-LLA.[4]

The ASCOT-LLA trial randomized 19,342 participants with hypertension and at least three other cardiovascular risk factors to two different anti-hypertensive medications. A subgroup with total cholesterol levels less than or equal to 6.5 mmol./l. were randomized to either daily 10 mg. atorvastatin or placebo.  The investigators planned to follow up for five years, but they stopped after 3.3 years because of clear benefit on the primary composite end point of non-fatal myocardial infarction and fatal coronary heart disease. At the time of stopping, there were 100 events of the primary pre-specified outcome in the atorvastatin group, compared with 154 events in the placebo group (hazard ratio 0.64 [95% CI 0.50 – 0.83], p = 0.0005).

The atorvastatin component of ASCOT-LLA had, in addition to its primary pre-specified outcome, seven secondary end points, and seven tertiary end points.  The emergence of diabetes mellitus in this trial population, which clearly was at high risk of developing diabetes, was one of the tertiary end points. Primary, secondary, and tertiary end points were reported in ASCOT-LLA without adjustment for the obvious multiple comparisons. In the treatment group, 3.0% developed diabetes over the course of the trial, whereas 2.6% developed diabetes in the placebo group. The unadjusted hazard ratio was 1.15 (0.91 – 1.44), p = 0.2493.[5] Given the 15 trial end points, an adjusted p-value for this particular hazard ratio, for diabetes, might well exceed 0.5, and even approach 1.0.

On this record, Dr. Singh honestly acknowledged that statistical significance was important, and that the diabetes finding in ASCOT-LLA might have been the result of low statistical power or of no association at all. Based upon the trial data alone, he testified that “one can neither confirm nor deny that atorvastatin 10 mg is associated with significantly increased risk of type 2 diabetes.”[6] The trial court excluded Dr. Singh’s 10mg/day causal opinion, but admitted his 80mg/day opinion. On appeal, the Fourth Circuit affirmed the MDL district court’s rulings.[7]

Jonah Gelbach is a professor of law at the University of California at Berkeley. He attended Yale Law School, and received his doctorate in economics from MIT.

Professor Gelbach entered the Lipitor fray to present a single issue: whether statistical significance at conventionally demanding levels such as 5 percent is an appropriate basis for excluding expert testimony based on statistical evidence from a single study that did not achieve statistical significance.

Professor Gelbach is no stranger to antic proposals.[8] As amicus curious in the Lipitor litigation, Gelbach asserts that plaintiffs’ expert witness, Dr. Singh, was wrong in his testimony about not being able to confirm the ASCOT-LLA association because he, Gelbach, could confirm the association.[9] Ultimately, the Fourth Circuit did not discuss Gelbach’s contentions, which is not surprising considering that the asserted arguments and alleged factual considerations were not only dehors the record, but in contradiction of the record.

Gelbach’s curious claim is that any time a risk ratio, for an exposure and an outcome of interest, is greater than 1.0, with a p-value < 0.5,[10] the evidence should be not only admissible, but sufficient to support a conclusion of causation. Gelbach states his claim in the context of discussing a single randomized controlled trial (ASCOT-LLA), but his broad pronouncements are carelessly framed such that others may take them to apply to a single observational study, with its greater threats to internal validity.

Contra Kumho Tire

To get to his conclusion, Gelbach attempts to remove the constraints of traditional standards of significance probability. Kumho Tire teaches that expert witnesses must “employ[] in the courtroom the same level of intellectual rigor that characterizes the practice of an expert in the relevant field.”[11] For Gelbach, this “eminently reasonable admonition” does not impose any constraints on statistical inference in the courtroom. Statistical significance at traditional levels (p < 0.05) is for elitist scholarly work, not for the “practical” rent-seeking work of the tort bar. According to Gelbach, the inflation of the significance level ten-fold to p < 0.5 is merely a matter of “weight” and not admissibility of any challenged opinion testimony.

Likelihood Ratios and Posterior Probabilities

Gelbach maintains that any evidence that has a likelihood ratio (LR > 1) greater than one is relevant, and should be admissible under Federal Rule of Evidence 401.[12] This argument ignores the other operative Federal Rules of Evidence, namely 702 and 703, which impose additional criteria of admissibility for expert witness opinion testimony.

With respect to variance and random error, Gelbach tells us that any evidence that generates a LR > 1, should be admitted when “the statistical evidence is statistically significant below the 50 percent level, which will be true when the p-value is less than 0.5.”[13]

At times, Gelbach seems to be discussing the admissibility of the ASCOT-LLA study itself, and not the proffered opinion testimony of Dr. Singh. The study itself would not be admissible, although it is clearly the sort of hearsay an expert witness in the field may consider. If Dr. Singh were to have reframed and recalculated the statistical comparisons, then the Rule 703 requirement of “reasonable reliance” by scientists in the field of interest may not have been satisfied.

Gelbach also generates a posterior probability (0.77), which is based upon his calculations from data in the ASCOT-LLA trial, and not the posterior probability of Dr. Singh’s opinion. The posterior probability, as calculated, is problematic on many fronts.

Gelbach does not present his calculations – for the sake of brevity he says – but he tells us that the ASCOT-LLA data yield a likelihood ratio of roughly 1.9, and a p-value of 0.126.[14] What the clinical trialists reported was a hazard ratio of 1.15, which is a weak association on most researchers’ scales, with a two-sided p-value of 0.25, which is five times higher than the usual 5 percent. Gelbach does not explain how or why his calculated p-value for the likelihood ratio is roughly half the unadjusted, two-sided p-value for the tertiary outcome from ASCOT-LLA.

As noted, the reported diabetes hazard ratio of 1.15 was a tertiary outcome for the ASCOT trial, one of 15 calculated by the trialists, with p-values unadjusted for multiple comparisons.  The failure to adjust is perhaps excusable in that some (but certainly not all) of the outcome variables are overlapping or correlated. A sophisticated reader would not be misled; only when someone like Gelbach attempts to manufacture an inflated posterior probability without accounting for the gross underestimate in variance is there an insult to statistical science. Gelbach’s recalculated p-value for his LR, if adjusted for the multiplicity of comparisons in this trial, would likely exceed 0.5, rendering all his arguments nugatory.

Using the statistics as presented by the published ASCOT-LLA trial to generate a posterior probability also ignores the potential biases (systematic errors) in data collection, the unadjusted hazard ratios, the potential for departures from random sampling, errors in administering the participant recruiting and inclusion process, and other errors in measurements, data collection, data cleaning, and reporting.

Gelbach correctly notes that there is nothing methodologically inappropriate in advocating likelihood ratios, but he is less than forthcoming in explaining that such ratios translate into a posterior probability only if he posits a prior probability of 0.5.[15] His pretense to having simply stated “mathematical facts” unravels when we consider his extreme, unrealistic, and unscientific assumptions.

The Problematic Prior

Gelbach’s glibly assumes that the starting point, the prior probability, for his analysis of Dr. Singh’s opinion is 50%. This is an old and common mistake,[16] long since debunked.[17] Gelbach’s assumption is part of an old controversy, which surfaced in early cases concerning disputed paternity. The assumption, however, is wrong legally and philosophically.

The law simply does not hand out 0.5 prior probability to both parties at the beginning of a trial. As Professor Jaffee noted almost 35 years ago:

“In the world of Anglo-American jurisprudence, every defendant, civil and criminal, is presumed not liable. So, every claim (civil or criminal) starts at ground zero (with no legal probability) and depends entirely upon proofs actually adduced.”[18]

Gelbach assumes that assigning “equal prior probability” to two adverse parties is fair, because the fact-finder would not start hearing evidence with any notion of which party’s contentions are correct. The 0.5/0.5 starting point, however, is neither fair nor is it the law.[19] The even odds prior is also not good science.

The defense is entitled to a presumption that it is not liable, and the plaintiff must start at zero.  Bayesians understand that this is the death knell of their beautiful model.  If the prior probability is zero, then Bayes’ Theorem tells us mathematically that no evidence, no matter how large a likelihood ratio, can move the prior probability of zero towards one. Bayes’ theorem may be a correct statement about inverse probabilities, but still be an inadequate or inaccurate model for how factfinders do, or should, reason in determining the ultimate facts of a case.

We can see how unrealistic and unfair Gelbach’s implied prior probability is if we visualize the proof process as a football field.  To win, plaintiffs do not need to score a touchdown; they need only cross the mid-field 50-yard line. Rather than making plaintiffs start at the zero-yard line, however, Gelbach would put them right on the 50-yard line. Since one toe over the mid-field line is victory, the plaintiff is spotted 99.99+% of its burden of having to present evidence to build up 50% probability. Instead, plaintiffs are allowed to scoot from the zero yard line right up claiming success, where even the slightest breeze might give them winning cases. Somehow, in the model, plaintiffs no longer have to present evidence to traverse the first half of the field.

The even odds starting point is completely unrealistic in terms of the events upon which the parties are wagering. The ASCOT-LLA study might have shown a protective association between atorvastatin and diabetes, or it might have shown no association at all, or it might have show a larger hazard ratio than measured in this particular sample. Recall that the confidence interval for hazard ratios for diabetes ran from 0.91 to 1.44. In other words, parameters from 0.91 (protective association) to 1.0 (no association), to 1.44 (harmful association) were all reasonably compatible with the observed statistic, based upon this one study’s data. The potential outcomes are not binary, which makes the even odds starting point inappropriate.[20]

[1] “Schauer’s Long Footnote on Statistical Significance” (Aug. 21, 2022).

[2] Frederick Schauer, The Proof: Uses of Evidence in Law, Politics, and Everything Else 54-55 (2022) (citing Michelle M. Burtis, Jonah B. Gelbach, and Bruce H. Kobayashi, “Error Costs, Legal Standards of Proof, and Statistical Significance,” 25 Supreme Court Economic Rev. 1 (2017).

[3] In re Lipitor Mktg., Sales Practices & Prods. Liab. Litig., MDL No. 2:14–mn–02502–RMG, 2015 WL 6941132, at *1  (D.S.C. Oct. 22, 2015).

[4] Peter S. Sever, et al., “Prevention of coronary and stroke events with atorvastatin in hypertensive patients who have average or lower-than-average cholesterol concentrations, in the Anglo-Scandinavian Cardiac Outcomes Trial Lipid Lowering Arm (ASCOT-LLA): a multicentre randomised controlled trial,” 361 Lancet 1149 (2003). [cited here as ASCOT-LLA]

[5] ASCOT-LLA at 1153 & Table 3.

[6][6] In re Lipitor Mktg., Sales Practices & Prods. Liab. Litig., 174 F.Supp. 3d 911, 921 (D.S.C. 2016) (quoting Dr. Singh’s testimony).

[7] In re Lipitor Mktg., Sales Practices & Prods. Liab. Litig., 892 F.3d 624, 638-39 (2018) (affirming MDL trial court’s exclusion in part of Dr. Singh).

[8] See “Expert Witness Mining – Antic Proposals for Reform” (Nov. 4, 2014).

[9] Brief for Amicus Curiae Jonah B. Gelbach in Support of Plaintiffs-Appellants, In re Lipitor Mktg., Sales Practices & Prods. Liab. Litig., 2017 WL 1628475 (April 28, 2017). [Cited as Gelbach]

[10] Gelbach at *2.

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

[12] Gelbach at *5.

[13] Gelbach at *2, *6.

[14] Gelbach at *15.

[15] Gelbach at *19-20.

[16] See Richard A. Posner, “An Economic Approach to the Law of Evidence,” 51 Stanford L. Rev. 1477, 1514 (1999) (asserting that the “unbiased fact-finder” should start hearing a case with even odds; “[I]deally we want the trier of fact to work from prior odds of 1 to 1 that the plaintiff or prosecutor has a meritorious case. A substantial departure from this position, in either direction, marks the trier of fact as biased.”).

[17] See, e.g., Richard D. Friedman, “A Presumption of Innocence, Not of Even Odds,” 52 Stan. L. Rev. 874 (2000). [Friedman]

[18] Leonard R. Jaffee, “Prior Probability – A Black Hole in the Mathematician’s View of the Sufficiency and Weight of Evidence,” 9 Cardozo L. Rev. 967, 986 (1988).

[19] Id. at p.994 & n.35.

[20] Friedman at 877.

Posted in Causation, Evidence, Expert Witnesses, Rule 702, Scientific Evidence, statistical evidence | No Comments »

Schauer’s Long Footnote on Statistical Significance

August 21st, 2022

One of the reasons that, in 2016, the American Statistical Association (ASA) issued, for the first time in its history, a consensus statement on p-values, was the persistent and sometimes deliberate misstatements and misrepresentations about the meaning of the p-value. Indeed, of the six principles articulated by the ASA, several were little more than definitional, designed to clear away misunderstandings.  Notably, “Principle Two” addresses one persistent misunderstanding and states:

“P-values do not measure the probability that the studied hypothesis is true, or the probability that the data were produced by random chance alone.

Researchers often wish to turn a p-value into a statement about the truth of a null hypothesis, or about the probability that random chance produced the observed data. The p-value is neither. It is a statement about data in relation to a specified hypothetical explanation, and is not a statement about the explanation itself.”[1]

The ASA consensus statement followed on the heels of an important published article, written by seven important authors in the fields of statistics and epidemiology.[2] One statistician,[3] who frequently shows up as an expert witness for multi-district litigation plaintiffs, described the article’s authors as the “A-Team” of statistics. In any event, the seven prominent thought leaders identified common statistical misunderstandings, including the belief that:

“2. The P value for the null hypothesis is the probability that chance alone produced the observed association; for example, if the P value for the null hypothesis is 0.08, there is an 8% probability that chance alone produced the association. No!”[4]

This is all basic statistics.

Frederick Schauer is the David and Mary Harrison Distinguished Professor of Law at the University of Virginia. Schauer has had contributed prolifically to legal scholarship, and his publications are often well written and thoughtful analyses. Schauer’s recent book, The Proof: Uses of Evidence in Law, Politics, and Everything Else, published by the Harvard University Press is a contribution to the literature of “legal epistemology,” and the foundations of evidence that lie beneath many of our everyday and courtroom approaches to resolving disputes.[5] Schauer’s book might be a useful addition to an undergraduate’s reading list for a course in practical epistemology, or for a law school course on evidence. The language of The Proof is clear and lively, but at times wanders into objectionable and biased political correctness. For example, Schauer channels Naomi Oreskes and her critique of manufacturing industry in his own discussion of “manufactured evidence,”[6] but studiously avoids any number of examples of explicit manufacturing of fraudulent evidence in litigation by the lawsuit industry.[7] Perhaps the most serious omission in this book on evidence is its failure to discuss the relative quality and hierarchy of evidence in science, medicine, and in policy.  Readers will not find any mention of the methodology of systematic reviews or meta-analyses in Schauer’s work.

At the end of his chapter on burdens of proof, Schauer adds “A Long Footnote on Statistical Significance,” in which he expresses surprise that the subject of statistical significance is controversial. Schauer might well have brushed up on the statistical concepts he wanted to discuss.

Schauer’s treatment of statistical significance is both distinctly unbalanced, as well as misstated. In an endnote,[8] Schauer cites some of the controversialists who have criticized significance tests, but none of the statisticians who have defended their use.[9]

As for conceptual accuracy, after giving a serviceable definition of the p-value, Schauer immediately goes astray:

“And this likelihood is conventionally described in terms of a p-value, where the p-value is the probability that positive results—rejection of the “null hypothesis” that there is no connection between the examined variables—were produced by chance.”[10]

And again, for emphasis, Schauer tells us:

“A p-value of greater than .05 – a greater than 5 percent probability that the same results would have been the result of chance – has been understood to mean that the results are not statistically significant.”[11]

And then once more for emphasis, in the context of an emotionally laden hypothetical about an experimental drug “cures” a dread, incurable disease, p = 0.20, Schauer tells us that he suspects most people would want to take the medication:

“recognizing that an 80 percent likelihood that the rejection of ineffectiveness was still good enough, at least if there were no other alternatives.”

Schauer wants to connect his discussion of statistical significance to degrees or varying strengths of evidence, but his discursion into statistical significance largely conflates precision with strength. Evidence can be statistically robust but not be very strong. If we imagine a very large randomized clinical trial that found that a medication lowered systolic blood pressure by 1mm of mercury, p < 0.05, we would not consider that finding to constitute strong evidence for therapeutic benefit. If the observation of lowering blood pressure by 1mm came from an observational study, p < 0.05, the finding might not even qualify as evidence in the views of sophisticated cardiovascular physicians and researchers.

Earlier in the chapter, Schauer points to instances in which substantial evidence for a conclusion is downplayed because it is not “conclusive,” or “definitive.” He is obviously keen to emphasize that evidence that is not “conclusive” may still be useful in some circumstances. In this context, Schauer yet again misstates the meaning of significance probability, when he tells us that:

“[j]ust as inconclusive or even weak evidence may still be evidence, and may still be useful evidence for some purposes, so too might conclusions – rejections of the null hypothesis – that are more than 5 percent likely to have been produced by chance still be valuable, depending on what follows from those conclusions.”[12]

And while Schauer is right that weak evidence may still be evidence, he seems loathe to admit that weak evidence may be pretty crummy support for a conclusion. Take, for instance, a fair coin.  We have an expected value on ten flips of five heads and five tails.  We flip the coin ten times, but we observe six heads and four tails.  Do we now have “evidence” that the expected value and the expected outcome are wrong?  Not really. The probability of observing the expected outcome on the binomial model that most people would endorse for the thought experiment is 24.6%. The probability of not observing the expected value in ten flips is three times greater. If we look at an epidemiologic study, with a sizable number of participants, the “expected value” of 1.0, embodied in the null hypothesis, is an outcome that we would rarely expect to see, even if the null hypothesis is correct.  Schauer seems to have missed this basic lesson of probability and statistics.

Perhaps even more disturbing is that Schauer fails to distinguish the other determinants of study validity and the warrants for inferring a conclusion at any level of certainty. There is a distinct danger that his comments about p-values will be taken to apply to various study designs, descriptive, observational, and experimental. And there is a further danger that incorrect definitions of the p-value and statistical significance probabilities will be used to misrepresent p-values as relating to posterior probabilities. Surely, a distinguished professor of law, at a top law school, in a book published by a prestigious  publisher (Belknap Press) can do better. The message for legal practitioners is clear. If you need to define or discuss statistical concepts in a brief, seek out a good textbook on statistics. Do not rely upon other lawyers, even distinguished law professors, or judges, for accurate working definitions.

[1] Ronald L. Wasserstein & Nicole A. Lazar, “The ASA’s Statement on p-Values: Context, Process, and Purpose,” 70 The Am. Statistician 129, 131 (2016).

[2] Sander Greenland, Stephen J. Senn, Kenneth J. Rothman, John B. Carlin, Charles Poole, Steven N. Goodman, and Douglas G. Altman, “Statistical tests, P values, confidence intervals, and power: a guide to misinterpretations,” 31 European J. Epidemiol. 337 (2016).[cited as “Seven Sachems”]

[3] Martin T. Wells.

[4] Seven Sachems at 340 (emphasis added).

[5] Frederick Schauer, The Proof: Uses of Evidence in Law, Politics, and Everything Else (2022). [Schauer] One nit: Schauer cites a paper by A. Philip Dawid, “Statistical Risk,” 194 Synthese 3445 (2017). The title of the paper is “On individual risk.”

[6] Naomi Oreskes & Erik M. Conway, Merchants of Doubt: How a Handful of Scientists Obscured the Truth on Issues from Tobacco Smoke to Climate Change (2010).

[7] See, e.g., In re Silica Prods. Liab. Litig., 398 F.Supp. 2d 563 (S.D.Tex. 2005); Transcript of Daubert Hearing at 23 (Feb. 17, 2005) (“great red flags of fraud”).

[8] See Schauer endnote 44 to Chapter 3, “The Burden of Proof,” citing Valentin Amrhein, Sander Greenland, and Blake McShane, “Scientists Rise Up against Statistical Significance,” www .nature .com (March 20, 2019), which in turn commented upon Blakey B. McShane, David Gal, Andrew Gelman, Christian Robert, and Jennifer L. Tackett, “Abandon Statistical Significance,” 73 American Statistician 235 (2019).

[9] Yoav Benjamini, Richard D. DeVeaux, Bradly Efron, Scott Evans, Mark Glickman, Barry Braubard, Xuming He, Xiao Li Meng, Nancy Reid, Stephen M. Stigler, Stephen B. Vardeman, Christopher K. Wikle, Tommy Wright, Linda J. Young, and Karen Kafadar, “The ASA President’s Task Force Statement on Statistical Significance and Replicability,” 15 Annals of Applied Statistics 1084 (2021); see also “A Proclamation from the Task Force on Statistical Significance” (June 21, 2021).

[10] Schauer at 55. To be sure, Schauer, in endnote 43 to Chapter 3, disclaims any identification of p-values or measures of statistical significance with posterior probabilities or probabilistic measures of the burden of proof. Nonetheless, in the text, he proceeds to do exactly what he disclaimed in the endnote.

[11] Schauer at 55.

[12] Schauer at 56.

Posted in Evidence, Expert Witnesses, Historian Testimony, statistical evidence | No Comments »

The Rise of Agnothology as Conspiracy Theory

July 19th, 2022

A few egregious articles in the biomedical literature have begun to endorse explicitly asymmetrical standards for inferring causation in the context of environmental or occupational exposures. Very little if anything is needed for inferring causation, and nothing counts against causation.  If authors refuse to infer causation, then they are agents of “industry,” epidemiologic malfeasors, and doubt mongers.

For an example of this genre, take the recent article, entitled “Toolkit for detecting misused epidemiological methods.”[1] [Toolkit] Please.

The asymmetry begins with Trump-like projection of the authors’ own foibles. The principal hammer in the authors’ toolkit for detecting misused epidemiologic methods is personal, financial bias. And yet, somehow, in an article that calls out other scientists for having received money from “industry,” the authors overlooked the business of disclosing their receipt of monies from one of the biggest industries around – the lawsuit industry.

Under the heading “competing interests,” the authors state that “they have no competing interests.”[2]  Lead author, Colin L. Soskolne, was, however, an active, partisan expert witness for plaintiffs’ counsel in diacetyl litigation.[3] In an asbestos case before the Pennsylvania Supreme Court, Rost v. Ford Motor Co., Soskolne signed on to an amicus brief, supporting the plaintiff, using his science credentials, without disclosing his expert witness work for plaintiffs, or his long-standing anti-asbestos advocacy.[4]

Author Shira Kramer signed on to Toolkit, without disclosing any conflicts, but with an even more impressive résumé of pro-plaintiff litigation experience.[5] Kramer is the owner of Epidemiology International, in Cockeysville, Maryland, where she services the lawsuit industry. She too was an “amicus” in Rost, without disclosing her extensive plaintiff-side litigation consulting and testifying.

Carl Cranor, another author of Toolkit, takes first place for hypocrisy on conflicts of interest. As a founder of Council for Education and Research on Toxics (CERT), he has sterling credentials for monetizing the bounty hunt against “carcinogens,” most recently against coffee.[6] He has testified in denture cream and benzene litigation, for plaintiffs. When he was excluded under Rule 702 from the Milward case, CERT filed an amicus brief on his behalf, without disclosing that Cranor was a founder of that organization.[7], [8]

The title seems reasonably fair-minded but the virulent bias of the authors is soon revealed. The Toolkit is presented as a Table in the middle of the article, but the actual “tools” are for the most part not seriously discussed, other than advice to “follow the money” to identify financial conflicts of interest.

The authors acknowledge that epidemiology provides critical knowledge of risk factors and causation of disease, but they quickly transition to an effort to silence any industry commentator on any specific epidemiologic issue. As we will see, the lawsuit industry is given a complete pass. Not surprisingly, several of the authors (Kramer, Cranor, Soskolne) have worked closely in tandem with the lawsuit industry, and have derived financial rewards for their efforts.

Repeatedly, the authors tell us that epidemiologic methods and language are misused by “powerful interests,” which have financial stakes in the outcome of research. Agents of these interests foment uncertainty and doubt about causal relationships through “disinformation,” “malfeasance,” and “doubt mongering.” There is no correlative concern about false claiming or claim mongering..

Who are these agents who plot to sabotage “social justice” and “truth”? Clearly, they are scientists with whom the Toolkit authors disagree. The Toolkit gang cites several papers as exemplifying “malfeasance,”[9] but they never explain what was wrong with them, or how the malfeasors went astray.  The Toolkit tactics seem worthy of Twitter smear and run.

The Toolkit

The authors’ chart of “tools” used by industry might have been an interesting taxonomy of error, but mostly they are ad hominem attack on scientists with whom they disagree. Channeling Putin on Ukraine, those scientists who would impose discipline and rigor on epidemiologic science are derided as not “real epidemiologists,” and, to boot, they are guilty of ethical lapses in failing to advance “social justice.”

Mostly the authors give us a toolkit for silencing those who would get in the way of the situational science deployed at the beck and call of the lawsuit industry.[10] Indeed, the Toolkit authors are not shy about identifying their litigation goals; they tell us that the toolkit can be deployed in depositions and in cross-examinations to pursue “social justice.” These authors also outline a social agenda that greatly resembles the goals of cancel culture: expose the perpetrators who stand in the way of the authors’preferred policy choices, diminish their adversaries’ their influence on journals, and galvanize peer reviewers to reject their adversaries’ scientific publications. The Toolkit authors tell us that “[t] he scientific community should engage by recognizing and professionally calling out common practices used to distort and misapply epidemiological and other health-related sciences.”[11] What this advice translates into are covert and open ad hominem campaigns as peer reviewers to block publications, to deny adversaries tenure and promotions, and to use social and other media outlets to attack adversaries’ motives, good faith, and competence.

None of this is really new. Twenty-five years ago, the late F. Douglas K. Liddell railed at the Mt. Sinai mob, and the phenomenon was hardly new then.[12] The Toolkit’s call to arms is, however, quite open, and raises the question whether its authors and adherents can be fair journal editors and peer reviewers of journal submissions.

Much of the Toolkit is the implementation of a strategy developed by lawsuit industry expert witnesses to demonize their adversaries by accusing them of manufacturing doubt or ignorance or uncertainty. This strategy has gained a label used to deride those who disagree with litigation overclaiming: agnotology or the creation of ignorance. According to Professor Robert Proctor, a regular testifying historian for tobacco plaintiffs, a linguist, Iain Boal, coined the term agnotology, in 1992, to describe the study of the production of ignorance.[13]

The Rise of “Agnotology” in Ngram

Agnotology has become a cottage sub-industry of the lawsuit industry, although lawsuits (or claim mongering if you like), of course, remain their main product. Naomi Oreskes[14] and David Michaels[15] gave the agnotology field greater visibility with their publications, using the less erudite but catchier phrase “manufacturing doubt.” Although the study of ignorance and uncertainty has a legitimate role in epistemology[16] and sociology,[17] much of the current literature is dominated by those who use agnotology as propaganda in support of their own litigation and regulatory agendas.[18] One lone author, however, appears to have taken agnotology study seriously enough to see that it is largely a conspiracy theory that reduces complex historical or scientific theory, evidence, opinion, and conclusions to a clash between truth and a demonic ideology.[19]

Is there any substance to the Toolkit?

The Toolkit is not entirely empty of substantive issues. The authors note that “statistical methods are a critical component of the epidemiologist’s toolkit,”[20] and they cite some articles about common statistical mistakes missed by peer reviewers. Curiously, the Toolkit omits any meaningful discussion of statistical mistakes that increase the risk of false positive results, such as multiple comparisons or dichotomizing continuous confounder variables. As for the Toolkit’s number one identified “inappropriate” technique used by its authors’ adversaries, we have:

“A1. Relying on statistical hypothesis testing; Using ‘statistical significance’ at the 0.05 level of probability as a strict decision criterion to determine the interpretation of statistical results and drawing conclusions.”

Peer into the hearings of any federal court so-called Daubert motion, and you will see the lawsuit industry, and its hired expert witnesses, rail at statistical significance, unless of course, there is some subgroup that has nominal significance, in which case, they are all in for endorsing the finding as “conclusive.” 

Welcome to asymmetric, situational science.

[1] Colin L. Soskolne, Shira Kramer, Juan Pablo Ramos-Bonilla, Daniele Mandrioli, Jennifer Sass, Michael Gochfeld, Carl F. Cranor, Shailesh Advani & Lisa A. Bero, “Toolkit for detecting misused epidemiological methods,” 20(90) Envt’l Health (2021) [Toolkit].

[2] Toolkit at 12.

[3] Watson v. Dillon Co., 797 F.Supp. 2d 1138 (D. Colo. 2011).

[4] Rost v. Ford Motor Co., 151 A.3d 1032 (Pa. 2016). See “The Amicus Curious Brief” (Jan. 4, 2018).

[5] See, e.g., Sean v. BMW of North Am., LLC, 26 N.Y.3d 801, 48 N.E.3d 937, 28 N.Y.S.3d 656 (2016) (affirming exclusion of Kramer); The Little Hocking Water Ass’n v. E.I. Du Pont De Nemours & Co., 90 F.Supp.3d 746 (S.D. Ohio 2015) (excluding Kramer); Luther v. John W. Stone Oil Distributor, LLC, No. 14-30891 (5th Cir. April 30, 2015) (mentioning Kramer as litigation consultant); Clair v. Monsanto Co., 412 S.W.3d 295 (Mo. Ct. App. 2013 (mentioning Kramer as plaintiffs’ expert witness); In re Chantix (Varenicline) Prods. Liab. Litig., No. 2:09-CV-2039-IPJ, MDL No. 2092, 2012 WL 3871562 (N.D.Ala. 2012) (excluding Kramer’s opinions in part); Frischhertz v. SmithKline Beecham Corp., 2012 U.S. Dist. LEXIS 181507, Civ. No. 10-2125 (E.D. La. Dec. 21, 2012) (excluding Kramer); Donaldson v. Central Illinois Public Service Co., 199 Ill. 2d 63, 767 N.E.2d 314 (2002) (affirming admissibility of Kramer’s opinions in absence of Rule 702 standards).

[6]  “The Council for Education & Research on Toxics” (July 9, 2013) (CERT amicus brief filed without any disclosure of conflict of interest). Among the fellow travelers who wittingly or unwittingly supported CERT’s scheme to pervert the course of justice were lawsuit industry stalwarts, Arthur L. Frank, Peter F. Infante, Philip J. Landrigan, Barry S. Levy, Ronald L. Melnick, David Ozonoff, and David Rosner. See also NAS, “Carl Cranor’s Conflicted Jeremiad Against Daubert” (Sept. 23, 2018); Carl Cranor, “Milward v. Acuity Specialty Products: How the First Circuit Opened Courthouse Doors for Wronged Parties to Present Wider Range of Scientific Evidence” (July 25, 2011).

[7] Milward v. Acuity Specialty Products Group, Inc., 664 F. Supp. 2d 137, 148 (D. Mass. 2009), rev’d, 639 F.3d 11 (1st Cir. 2011), cert. den. sub nom. U.S. Steel Corp. v. Milward, 565 U.S. 1111 (2012), on remand, Milward v. Acuity Specialty Products Group, Inc., 969 F.Supp. 2d 101 (D. Mass. 2013) (excluding specific causation opinions as invalid; granting summary judgment), aff’d, 820 F.3d 469 (1st Cir. 2016).

[8] To put this effort into a sociology of science perspective, the Toolkit article is published in a journal, Environmental Health, an Editor in Chief of which is David Ozonoff, a long-time pro-plaintiff partisan in the asbestos litigation. The journal has an “ombudsman,”Anthony Robbins, who was one of the movers-and-shakers in forming SKAPP, The Project on Scientific Knowledge and Public Policy, a group that plotted to undermine the application of federal evidence law of expert witness opinion testimony. SKAPP itself now defunct, but its spirit of subverting law lives on with efforts such as the Toolkit. “More Antic Proposals for Expert Witness Testimony – Including My Own Antic Proposals” (Dec. 30, 2014). Robbins is also affiliated with an effort, led by historian and plaintiffs’ expert witness David Rosner, to perpetuate misleading historical narratives of environmental and occupational health. “ToxicHistorians Sponsor ToxicDocs” (Feb. 1, 2018); “Creators of ToxicDocs Show Off Their Biases” (June 7, 2019); Anthony Robbins & Phyllis Freeman, “ToxicDocs (www.ToxicDocs.org) goes live: A giant step toward leveling the playing field for efforts to combat toxic exposures,” 39 J. Public Health Pol’y 1 (2018).

[9] The exemplars cited were Paolo Boffetta, MD, MPH; Hans Olov Adami, Philip Cole, Dimitrios Trichopoulos, Jack Mandel, “Epidemiologic studies of styrene and cancer: a review of the literature,” 51 J. Occup. & Envt’l Med. 1275 (2009); Carlo LaVecchia & Paolo Boffetta, “Role of stopping exposure and recent exposure to asbestos in the risk of mesothelioma,” 21 Eur. J. Cancer Prev. 227 (2012); John Acquavella, David Garabrant, Gary Marsh G, Thomas Sorahan and Douglas L. Weed, “Glyphosate epidemiology expert panel review: a weight of evidence systematic review of the relationship between glyphosate exposure and non-Hodgkin’s lymphoma or multiple myeloma,” 46 Crit. Rev. Toxicol. S28 (2016); Catalina Ciocan, Nicolò Franco, Enrico Pira, Ihab Mansour, Alessandro Godono, and Paolo Boffetta, “Methodological issues in descriptive environmental epidemiology. The example of study Sentieri,” 112 La Medicina del Lavoro 15 (2021).

[10] The Toolkit authors acknowledge that their identification of “tools” was drawn from previous publications of the same ilk, in the same journal. Rebecca F. Goldberg & Laura N. Vandenberg, “The science of spin: targeted strategies to manufacture doubt with detrimental effects on environmental and public health,” 20:33 Envt’l Health (2021).

[11] Toolkit at 11.

[12] F.D.K. Liddell, “Magic, Menace, Myth and Malice,” 41 Ann. Occup. Hyg. 3, 3 (1997). See “The Lobby – Cut on the Bias” (July 6, 2020).

[13] Robert N. Proctor & Londa Schiebinger, Agnotology: The Making and Unmaking of Ignorance (2008).

[14] Naomi Oreskes & Erik M. Conway, Merchants of Doubt: How a Handful of Scientists Obscured the Truth on Issues from Tobacco Smoke to Global Warming (2010); Naomi Oreskes & Erik M. Conway, “Defeating the merchants of doubt,” 465 Nature 686 (2010).

[15] David Michaels, The Triumph of Doubt: Dark Money and the Science of Deception (2020); David Michaels, Doubt is Their Product: How Industry’s Assault on Science Threatens Your Health (2008); David Michaels, “Science for Sale,” Boston Rev. 2020; David Michaels, “Corporate Campaigns Manufacture Scientific Doubt,” 174 Science News 32 (2008); David Michaels, “Manufactured Uncertainty: Protecting Public Health in the Age of Contested Science and Product Defense,” 1076 Ann. N.Y. Acad. Sci. 149 (2006); David Michaels, “Scientific Evidence and Public Policy,” 95 Am. J. Public Health s1 (2005); David Michaels & Celeste Monforton, “Manufacturing Uncertainty: Contested Science and the Protection of the Public’s Health and Environment,” 95 Am. J. Pub. Health S39 (2005); David Michaels & Celeste Monforton, “Scientific Evidence in the Regulatory System: Manufacturing Uncertainty and the Demise of the Formal Regulatory Ssytem,” 13 J. L. & Policy 17 (2005); David Michaels, “Doubt is Their Product,” Sci. Am. 96 (June 2005); David Michaels, “The Art of ‘Manufacturing Uncertainty’,” L.A. Times (June 24, 2005).

[16] See, e.g., Sibilla Cantarini, Werner Abraham, and Elisabeth Leiss, eds., Certainty-uncertainty – and the Attitudinal Space in Between (2014); Roger M. Cooke, Experts in Uncertainty: Opinion and Subjective Probability in Science (1991).

[17] See, e.g., Ralph Hertwig & Christoph Engel, eds., Deliberate Ignorance: Choosing Not to Know (2021); Linsey McGoey, The Unknowers: How Strategic Ignorance Rules the World (2019); Michael Smithson, “Toward a Social Theory of Ignorance,” 15 J. Theory Social Behavior 151 (1985).

[18] See Janet Kourany & Martin Carrier, eds., Science and the Production of Ignorance: When the Quest for Knowledge Is Thwarted (2020); John Launer, “The production of ignorance,” 96 Postgraduate Med. J. 179 (2020); David S. Egilman, “The Production of Corporate Research to Manufacture Doubt About the Health Hazards of Products: An Overview of the Exponent BakeliteVR Simulation Study,” 28 New Solutions 179 (2018); Larry Dossey, “Agnotology: on the varieties of ignorance, criminal negligence, and crimes against humanity,” 10 Explore 331 (2014); Gerald Markowitz & David Rosner, Deceit and Denial: The Deadly Politics of Industrial Revolution (2002).

[19] See Enea Bianchi, “Agnotology: a Conspiracy Theory of Ignorance?” Ágalma: Rivista di studi culturali e di estetica 41 (2021).

[20] Toolkit at 4.

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