The most recent edition of the Reference Manual on epidemiology distinguishes more carefully between Bayesian and frequentist approaches to statistical analyses than did its previous iterations. In past editions, the authors conflated confidence and credible intervals, an error that is studiously avoided in the text of the chapter on epidemiology, in the fourth edition.[1]
The chapter acknowledges that “most published research does not” use Bayesian credible intervals of posterior probabilities. The authors then offer a largely unsupported conclusion about a “toehold”:
“Epidemiologic studies assessed by Bayesian statistical analyses have begun to gain a toehold in litigation, although court opinions are still dominated by discussion of traditional significance testing.”[2]
The authors do not define what a toehold is; nor do they specify whether it is a big toe or pinky toe. The new chapter cites three cases, which out of the universe of cases, seems like a tiny toe. The three cases cited by the Reference Manual as a toehold raise serious questions about the legitimacy of using Bayesian analyses, at least to date.
- Langrell.
In Langrell,[3] one of the three cases cited by the Manual, an expert witness claimed to have used a “Bayesian approach,” but in reality no Bayesian statistics were involved. The Manual describes the result in Langrell as admitting the testimony of a specific causation expert witness who had used a Bayesian approach for specific causation of a cancer “so rare that it was “unlikely or impossible for epidemiological studies to be performed.”[4]
Citing Langrell for the stated proposition was questionable scholarship at best. The case was one of several cancer claims against railroad employers, in which Robert Peter Gale served as an expert witness. Dr. Robert Peter Gale is a well-credentialed clinician whose career has focused on lymphopoietic cancers.[5] He has no apparent expertise in statistics or epidemiology.
In one reported decision, Byrd, Dr. Gale attempted to offer a “Bayesian” opinion that railroad yard exposures caused a worker’s lung cancer. The claimant had also been a two-pack per day smoker for many years.[6] The published opinion refers to Dr. Gale’s having used Bayesian methods, but there is nothing in the published opinion to suggest that such methods had been used.[7] Gale appeared to equate Bayesian analysis with a non-quantitative differential etiology. Given the claimant’s extensive smoking history, the trial court excluded Dr. Gale’s proffered opinion on the cause of the claimant’s lung cancer, as unreliable.
In another railroad case brought by Saul Hernandez, Gale also claimed to use Bayesian methods to assess the causation of the claimant’s stomach cancer. There is only one mention, however, of Bayes in Gale’s report:
“My opinion is based in Bayesian probabilities which consider the interdependence of individual probabilities. This process is sometimes referred to as differential diagnosis or differential causation determination or differential etiology. Differential diagnosis is a method of reasoning widely-accepted in medicine.”[8]
To be explicit, there was no discussion of prior or posterior probabilities or odds, no discussion of likelihood ratios, or Bayes factors. There was absolutely nothing in Dr. Gale’s report that would warrant his claim that he had done a Bayesian analysis of specific causation or of the “interdependence of individual probabilities” of putative specific causes. The court excluded Dr. Gale’s proffered opinion in Hernandez, with its scant reference to a Bayesian analysis.[9]
The third instance of Gale’s purported use of a Bayesian analysis occurred in the Langrell case, cited by the Manual. The authors of the new Manual do not specify what kind of rare cancer was involved in the Langrell case. For the record, Mr. Langrell developed squamous cell carcinoma of the tonsils, which is the most common type of oropharyngeal cancer, which has been studied for many decades. Alcohol, tobacco, and human papillomavirus (HPV), have long been associated with the occurrence of such cancers. Mr. Langrell had a history of exposure to all three risk factors. Contrary to Gale’s poor-mouthing about lack of data, there are many large cohort studies of railroad yard workers with diesel fume exposure.[10]
The full extent of the district court’s exposition about Gale’s “Bayesian” method was to state that:
“He testified he used a Bayesian approach, allowing him to ‘consider interdependence of individual probabilities’ and to render an opinion as to ‘whether the weight of the evidence indicates it is more likely than not to a reasonable degree of medical probability that exposure to the carcinogens discussed was a cause of tonsil cancer in Mr. Langrell’.”[11]
There is no evidence that Dr. Gale had the competence to conduct a Bayesian analysis, or that he actually did one. Dr. Gale’s participation in the Langrell, Byrd, and Hernandez cases seems like poor evidence of a toehold for Bayesian methods. Not even a pinky toe.
We might forgive the credulity of the judicial officers in these cases, but why would Dr. Gale state that he had done a Bayesian analysis? The only reason that suggests itself is that Dr. Gale was bloviating in order to give his specific causation opinions an aura of scientific and mathematical respectability. Falsus in uno, falsus in omnibus.[12] In two of the three related cases, his opinion was rejected. The Manual cites only the case in which Gale’s opinion was admitted. The cited opinion offers no support for Gale’s having actually conducted a Bayesian analysis of any sort.
- In re Abilify.
The second cited example of toe holds was the use of a Bayesian analysis by a statistician, David Madigan, in the Abilify litigation. Madigan has published on Bayesian statistics, but his litigation activities have repeatedly raised issues whether Madigan’s Bayesian analyses are reliable.
The Abilify litigation involved claims that the anti-psychotic medication caused impulsive gambling, eating, shopping, and sex. Of course, psychotic behavior itself involves those impulsive behaviors and many others. The Manual cited a decision of the multi-district litigation court that noted that “[n]umerous federal courts have found Dr. Madigan’s methodology of detecting safety signals using a combination of frequentist and Bayesian algorithms to be reliable under Rule 702 and Daubert.”[13]
The “signals” to which the Manual citation refers are suggestions of possible causal associations; they are hypotheses generated from pharmacovigilance studies of adverse event reports, not tests of those hypotheses. Signals are not causes; they may not rise even to the level of associations. The particular analyses proffered by Madigan in Abilify, and in many other litigations, for plaintiffs, involves comparing the rate of reporting specific adverse events for the drug with the reporting rate for all drugs, or for comparator drugs. The outcome of these analyses is a reporting rate ratio, not an incidence ratio.
The following 2 x 2 table illustrates how adverse event data are using to create “signals” of disproportional reporting.
The FDA provides very clear guidance on the meaning and use of such signal-finding algorithms or disproportionality analyses (DPAs):
“In the context of spontaneous report systems, some authors use the term “signal of disproportionate reporting” (SDR) when discussing associations highlighted by DPA methods. In reality, most SDRs that emerge from spontaneous report databases represent non-causal effects because the reports are associated with treatment indications (i.e., confounding by indication), co-prescribing patterns, co-morbid illnesses, protopathic bias, channeling bias, or other reporting artifacts, or, the reported adverse events are already labeled or are medically trivial.”[14]
Disproportionality analyses are not part of analytical epidemiology, but Madigan has tried to pass them off as such in any number of litigations. More discerning courts have excluded his attempts. In the Accutane litigation in Atlantic County, New Jersey, Judge Johnson conducted an extensive pre-trial hearing on challenges to Madigan’s causation opinions, and found them wanting under the New Jersey analogue of Federal Rule of Evidence 702.[15] On appeal, the New Jersey Supreme Court reviewed and affirmed the exclusion of Madigan’s litigation opinions that isotretinoin causes Crohn’s disease.[16]
The pattern of adverse event report filing in connection with isotretinoin has been carefully studied; it illustrates the FDA’s point about artifacts. One such study of isotretinoin adverse event reporting showed that attorneys reported 87.8% cases, while physicians reported 6.0%, and consumers reported only 5.1% cases. For the entire FAERS database, only 3.6% reports for all drug reactions during the same time period were reported by attorneys (p value < .01).[17]
In other areas less affected by litigation-created reporting bias, the results of DPAs have been compared with analytical epidemiology. A DPA of statin use and bladder cancer suggested a reporting odds ratio of 1.48, 95% CI; 1.36-1.61. The authors, in a peer-reviewed publication, reported the result with clearly inappropriate causal language: “Multi-methodological approaches suggest that statins are associated with an increased risk for bladder cancer.”[18] An appropriate meta-analysis of analytical epidemiologic studies reported an actual odds ratio of 1.07, 95 % CI (0.95, 1.21), which finding was interpreted as suggesting “that there was no association between statin use and risk of bladder cancer.”[19]
Dr. Madigan’s use of Bayesian methods to analyze reporting ratios and his passing them off as evidence that can support causal inference is a paradigmatic instance of an inappropriate methodology. Dr. Madigan’s use of Bayesian methods to analyze reporting rates seems like poor evidence of a toehold.
- In re Testosterone.
The third case cited by the Manual for the toehold proposition arose in the multi-district litigation created for claims against manufacturers of testosterone. This MDL aggregated cases based upon a speculative Public Citizen petition that transdermal testosterone used by men who have low testosterone levels causes heart attacks and strokes. The plaintiffs adopted what appeared to be a strategy of deploying complex arguments and analyses to obfuscate and defeat Rule 702 gatekeeping. As part of this strategy, two of the plaintiffs’ expert witness conducted a Bayesian “hypothesis test,” by which they took an out-of-date meta-analysis,[20] removed some of the studies that they incorrectly decided were duplicative, and recalculated a credible interval instead of a confidence interval.
This Bayesian hypothesis test came up in several decisions of the MDL court. The Manual cited only to a decision dated August 23, 2018, which it characterized as denying a motion to exclude expert witness testimony that advanced a Bayesian critique of epidemiologic studies.[21]
Looking at the cited decision of August 23, 2018, we see a reference to a previous ruling in May 2017, when the court held that an expert witness’s failure and inability to “quantify the cardiovascular risk he finds in his Bayesian analysis … is an issue affecting the weight to be accorded to his analysis, not its admissibility.”[22] On its face, this opinion does not quite make sense given that a Bayesian analysis would necessarily involve a quantification of posterior probability. The referenced May 2017 opinion also demonstrates the court’s failure to understand basic frequentist concepts, when it recited incorrect definitions of p-value and confidence intervals:
“According to conventional statistical practice, such a result—that is, a finding of a positive association between smoking and development of the disease—would be considered statistically significant if there is a 95% probability, also expressed as a “p-value” of <0.05, that the observed association is not the product of chance. If, however, the p-value were greater than 0.05, the observed association would not be regarded as statistically significant, according to prevailing conventions, because there is a greater than 5% probability that the association observed was the result of chance.
* * *
Statistical significance can also be expressed equivalently in terms of a confidence interval. A confidence interval consists of a range of values. For a 95% confidence interval, one would expect future studies sampling the same population to produce values within the range 95% of the time.”[23]
There is, however, also a discussion in the May 2017 decision to the Bayesian hypothesis test, which had been developed by plaintiffs’ expert witnesses,
Burt Gerstman and Martin Wells.[24] The new Manual’s citation to the testosterone MDL case seems to be to this Bayesian analysis.
While the testosterone MDL case cited by the Manual refers only obliquely to a putative Bayesian analysis that had no quantification, the May 2017 decision, not cited by the Manual, actually involved a Bayesian analysis that supposedly yielded a posterior probability of 85% that there was some increased risk for a composite of heart attack and stroke outcomes from use of testosterone therapies.
In the May 2017 decision, the MDL court rejected AbbVie’s Rule 702 motion to exclude Gerstman’s opinion based upon the Bayesian hypothesis test. AbbVie’s approach to the challenge to the Gerstman-Wells’ Bayesian analysis seemed to avoid the complexity inherent in the analysis. The AbbVie motion included several grounds, not all discussed in the court’s decision of May 2017, for excluding the Bayesian analysis, including:
“1) the plaintiffs’ witnesses’ failure to publish their analysis;
2) the challenged witness’s having never published a significant Bayesian analysis previously;
3) the absence of Bayesian analyses in the relevant studies on testosterone;
4) the rarity of Bayesian analyses in product liability cases;
5) the witnesses’ failure to state what the actual risk was, as opposed to the probability that it exceeded 1.0; and
6) the defense expert witness’s calculation that the “Increased [cardiovascular] risk meets only a 70% level of evidence, which is far below the 95% level required.”[25]
Grounds one through four were extremely weak as stated, and ground five did not affect the relevancy of the analysis to general causation. Ground six was the shot in the foot, with the defense’s falling into the trap of conflating the coefficient of confidence (95%) with the posterior probability of a Bayesian analysis.
According to the district court’s opinion, AbbVie challenged Gerstman’s Bayesian analysis because Gerstman never used or published on Bayesian statistics, and thus he lacked expertise in Bayesian analysis. This part of the challenge was readily dismissed because the level of qualifications for an expert witness is very low. A somewhat more substantive objection complained that the Bayesian analysis was “inappropriately based on subjective assumptions.”
The MDL court refused to exclude Gerstman’s Bayesian analysis, relying in part upon the suggestion in the statistics chapter of the Reference Manual third edition that Bayesians constitute a “a well-established minority” in the field of statistics.[26]
On AbbVie’s claim that Bayesian methods are excessively “subjective,” the court declared that AbbVie had failed to explain how the subjective aspect of Bayesian analysis made the proffered Bayesian analysis “any less reliable than frequentist approaches to statistics, which also involve subjective judgments in interpretation of study results.”
Unfortunately, important issues raised by the plaintiffs’ Bayesian meta-analysis were not raised by counsel or addressed by the MDL court’s initial gatekeeping opinion of May 2017. The court briefly revisited the Bayesian analysis as proffered by Martin Wells, with the same lack of specificity, in August 2018.[27] The Bayesian analysis had been prepared jointly by Gerstman and Wells, and the August 2018 decision followed the earlier decision from 2017, without adding any analysis or explanation.
A third challenge to Wells’ Bayesian analysis was filed in 2019, by a different defendant in the testosterone MDL. This challenge was supported by an expert witness report that carefully identified the invalidity of the proffered Bayesian analysis.
Bayes’ Rule is a theorem that provides a posterior probability for a claim or proposition based upon a prior probability and the strength of the evidence at hand. Unlike frequentist statistics, which treat the population value (mean or risk ratio) as having a fixed, but unknown value, Bayesian analyses treat both prior and posterior probabilities as probability distributions. Every Bayesian analysis must start with a prior probability, and therein lies a serious methodological problem, not addressed by the MDL testosterone court in May 2017.
In the Bayesian hypothesis test advanced by the plaintiffs’ expert witnesses in the testosterone cases was based on a method described by John Carlin.[28] The analysis invokes a prior risk ratio of 1.0, which standing alone might seem like a perfectly fair and disinterested prior. The chosen variance around 1.0, which makes up the prior probability distribution, however, was extremely wide and flat, essentially encompassing no risk at the low end, and absolute risk, at the high end. A flat distribution implies that the priors of testosterone causing all heart attacks and strokes, preventing all such outcomes, and having no effect at all, were roughly equally likely as a starting point. Given that we start with a very good understanding that testosterone does not prevent all heart attacks and strokes; nor does it cause all such events, we know that these starting points are unrealistic. The starting assumptions of the plaintiffs’ meta-analysis were, therefore, completely unrealistic and counterfactual.
Carlin’s method used in the proffered Bayesian meta-analysis in the testosterone cases further assumed a “hierarchical normal model.” Carlin described his assumption as reasonable “as long as the studies are large and observed counts are not too small.”[29] In the dataset used by plaintiffs’ expert witnesses, however, virtually all the studies had very low event counts, often zero or one, in either the TRT or placebo arm, or both. Carlin acknowledged that it was difficult to assess the validity of the normal model, and emphasized that
“[a] study of the sensitivity of conclusions to the choice of prior would be important.”[30]
Subsequent simulation studies of Carlin’s approach have shown that so-called “vague” or “non-informative” priors, such as were used by plaintiffs’ expert witnesses, can exercise an “unintentionally large degree of influence on any inferences.”[31]
AbbVie’s earlier challenges to Gerstman and Wells failed to note that they had offered no tests of the validity of Carlin’s method in the context of meta-analyzing clinical trials for sparse safety outcomes. The challenge filed in the Martin case, in 2019, challenged the unsupported assumptions of the proffered Bayesian hypothesis test. This Rule 702 challenge pointed out not only the subjectivity of the assumed prior probability distribution, but its counter-factual nature, and the failure of the proffered Bayesian analysis to comply with the methodological requirements of Carlin’s method.
There were additional problems with the Bayesian hypothesis test as put forward by plaintiffs’ expert witnesses. First, advancing of a causal claim with an 85% posterior probability was bound to be confused with the plaintiffs’ burden of proof of greater than 50%, notwithstanding that the calculated posterior probability did not take into account uncertainty from bias and other non-random errors in the aggregated clinical trial data, which were out-of-date and which had questionable inclusionary and exclusionary criteria. Second, the posterior probability was based upon a composite end point that combined heart attack and stroke. As a later deposition of one of the Bayesian analysts, Martin Wells, showed, had the Carlin method been applied to just the heart attack summary point estimate, then the posterior probability that TRT causes heart attack would have been less than 50%, and thus greater than 50% that testosterone does not cause heart attack.[32]
Notwithstanding the plaintiffs’ failure to rebut the very specific methodological challenges to their witnesses’ Bayesian analysis, the MDL court denied the third Rule 702 motion to exclude, without meaningful analysis.[33] The case (Martin) was later tried to a jury that returned a verdict for the defense. Neither in Martin nor in any other testosterone case that was tried did plaintiffs actually present their Bayesian analysis to the trier of fact. The likely interpretation of this failure is that the Bayesian analysis was always meant to obfuscate the weaknesses of their causation case and to help deflect Rule 702 challenges.
The ultimate verdict on the plaintiffs’ case and the Bayesian hypothesis test with its ill-informed non-inormative priors was returned only after most of the MDL cases were tried or had settled. In 2023, a “mega-trial,” a large, well-conducted randomized controlled trial was concluded and published with findings of no increased risk of heart or stroke after long-term use of TRT in men who resembled the TRT plaintiffs. The trial enrolled over 5,000 men, about whom the researchers reported that a primary composite cardiovascular end-point event occurred in 182 men (7.0%) on testosterone therapy, and in 190 men (7.3%) receiving placebo, with a hazard ratio below one (HR = 0.96, 95% C.I., 0.78 – 1.17). None of the components of the composite (heart attack, stroke) showed an increased risk.[34]
“Falshood flies, and Truth comes limping after it; so that when Men come to be undeceived, it is too late, the Jest is over, and the Tale has had its Effect: Like a Man who has thought of a good Repartee, when the Discourse is changed, or the Company parted: Or, like a Physician who hath found out an infallible Medicine after the Patient is dead.”[35]
CONCLUSION
The Reference Manual’s chapter on epidemiology claims that Bayesian analyses have gained a toehold in litigation. The authors cited three cases, all involving the evaluation of health effects. One of the cases (Langrell) cited a claim of specific causation, and the case cited showed no evidence of an actual Bayesian analysis. The cited case was one of three in which the same expert witness, Dr. Gale, claimed to use Bayesian analysis. The other two cases, not cited, rejected the admissibility of Dr. Gale’s proffered testimony.
The second case cited (In re Ability) actually involved a Bayesian analysis, but for a so-called disproportionality analysis, which is a technique for interpreting a signal of possible health effect. The misuse of the analysis by the Bayesian analyst (David Madigan) was overlooked by the court, and by the Reference Manual.
The third case cited by the Manual also involved an actual Bayesian analysis, In re Testosterone, in the form of a Bayesian hypothesis test. The proffered analysis actually did, in theory, speak to a material issue of general causation. The Manual’s credulous citation, and the MDL court’s gatekeeper, however, overlooked that the methodology was misspecified and misapplied in multiple ways.
If these three citations are a toehold, then we need a tow-truck for these wrecks!
[1] Steve C. Gold, Michael D. Green, Jonathan Chevrier, & Brenda Eskenazi, Reference Guide on Epidemiology, in National Academies of Sciences, Engineering, and Medicine & Federal Judicial Center, REFERENCE MANUAL ON SCIENTIFIC EVIDENCE 939 (4th ed. 2025) [cited as GGCE]
[2] GGCE at 963 n.178.
[3] Langrell v. Union Pac. Ry. Co., No. 8:18CV57, 2020 WL 3037271, at *3 (D. Neb. June 5, 2020).
[4] Id.
[5] See, e.g., Robert Peter Gale, et al., Fetal Liver Transplantation (1987); Robert Peter Gale & Thomas Hauser, CHERNOBYL: THE FINAL WARNING (1988); Kenneth A. Foon, Robert Peter Gale, et al., IMMUNOLOGIC APPROACHES TO THE CLASSIFICATION AND MANAGEMENT OF LYMPHOMAS AND LEUKEMIAS (1988); Eric Lax & Robert Peter Gale, RADIATION: WHAT IT IS, WHAT YOU NEED TO KNOW (2013).
[6] Byrd v. Union Pacific RR, 453 F. Supp. 3d 1260 (D. Neb. 2020).
[7] Id. at 1270 (“Dr. Gale states that his opinion is based on Bayesian probabilities which consider the interdependence ofindividual probabilities. This process is sometimes referred to as differential diagnosis or differential etiology.”).
[8] Report of Robert Peter Gale in Saul Hernandez at 13 (July 23, 2019)[on file with author]. There was no evidence that Mr. Hernandez was tested for infection by helicobacter pylori.
[9] Hernandez v. Union Pacific RR, No. 8: 18CV62 (D. Neb. Aug. 14, 2020).
[10] See, e.g., Monireh Sadat Seyyedsalehi, Giulia Collatuzzo, Federica Teglia & Paolo Boffetta, Occupational exposure to diesel exhaust and head and neck cancer: a systematic review and meta-analysis of cohort studies, 33 EUR. J. CANCER PREV. 435 (2024).
[11] Langrell v. Union Pac. Ry. Co., No. 8:18CV57, 2020 WL 3037271, at *3-4 (D. Neb. June 5, 2020).
[12] Dr. Gale’s testimony has not fared well elsewhere. See, e.g., In re Incretin-Based Therapies Prods. Liab. Litig., 524 F.Supp.3d 1007 (S.D. Cal. 2021) (excluding Gale); Wilcox v. Homestake Mining Co., 619 F. 3d 1165 (10th Cir. 2010); June v. Union Carbide Corp., 577 F. 3d 1234 (10th Cir. 2009) (affirming exclusion of Dr. Gale and entry of summary judgment); Finestone v. Florida Power & Light Co., 272 F. App’x 761 (11th Cir. 2008); In re Rezulin Prods. Liab. Litig., 309 F.Supp.2d 531 (S.D.N.Y. 2004) (excluding Dr. Gale from offering ethical opinions); Cundy v. BNSF Ry, No. 40095-6-III. Wash. Ct. App. (Mar. 5, 2026) (affirming dismissal of case; Gale was one of plaintiffs expert witnesses); Russo v. Metro-North RR., Index No. 159201/2019, 2025 NY Slip Op 34659(U), N.Y.S.Ct., N.Y. Cty. (Dec. 5, 2025); Saverino v. Metro-North RR, 2024 NY Slip Op 31326(U), Index No. 161353/2019, N.Y. S. Ct., N.Y. Cty. (Apr. 8, 2024).
[13] In re Abilify (Arpiprazole) Prods. Liab. Litig., No. 3:16MD2734, 2021 WL 4951944, at *5 (N.D. Fla. July 15, 2021).
[14] FDA Adverse Event Reporting System (FAERS) (Last updated Sept. 8, 2014), available at <http://www.fda.gov/Drugs/GuidanceComplianceRegulatoryInformation/Surveillance/AdverseDrugEffects/default.htm>.
[15] In re Accutane Litig., No. 271(MCL), 2015 WL 753674, at *15 (N.J. Super. Law Div., Feb. 20, 2015) (Hon. Nelson C. Johnson, also known as the author of Boardwalk Empire).
[16] In re Accutane, 234 N.J. 340 (2018) (affirming exclusion of David Madigan).
[17] Derrick J. Stobaugh, et al., Alleged isotretinoin-associated inflammatory bowel disease: Disproportionate reporting by attorneys to the Food and Drug Administration Adverse Event Reporting System, 69 J. AM. ACAD. DERMATOL. 393 (2013).
[18] Mai Fujimoto, et al., Association between Statin Use and Bladder Cancer: Data Mining of a Spontaneous Reporting Database and a Claim Database, 1 J. PHARMACOL. & PHARMACOVIGILANCE 1 (2015).
[19] Xiao-long Zhang, et al., Statin use and risk of bladder cancer: a meta-analysis, 24 CANCER CAUSES & CONTROL 769 (2013).
[20] S. Albert & J. Morley, Testosterone therapy, association with age, initiation and mode of therapy with cardiovascular events: a systematic review, 95 CLIN. ENDOCRINOL. 436 (2016).
[21] GGCE at 963 n.178 (citing In re Testosterone Replacement Therapy Prods. Liab. Litig., No. 14 C 1748, 2018 WL 4030585, at *8 (N.D. Ill. Aug. 23, 2018), and explaining that the court had denied a “motion to exclude testimony of expert ‘whose Bayesian critiques of epidemiological studies’ were similar to those of another expert whose testimony ‘the Court has previously found admissible’.”).
[22] In re Testosterone Replacement Therapy Prods. Liab. Litig., No. 14 C 1748, 2017 WL 1833173, at *4 (N.D. Ill. May 8, 2017).
[23] Id.
[24] This is the same Martin Wells found to be a methodological shapeshifter in the paraquat parkinsonism litigagion. In re Paraquat Prods. Prods. Liab. Litig., Case No. 3:21-md-3004-NJR, MDL No. 3004, 730 F.Supp.3d 793, 838 (2024) (S.D. Ill. 2024). See also Schachtman, Paraquat Shape-Shifting Expert Witness Quashed, TORTINI (Apr. 24, 2024).
[25] Defendants’ Motion to Exclude Plaintiffs’ Expert Testimony on the Issue of Causation, and for Summary Judgment, and Mem. of Law in Support, No. 1:14-CV-01748, MDL 2545, 2017 WL 1104501, at *69–70 (N.D. Ill. Feb. 20, 2017) (citing Reference Manual 259 (3rd ed. 2011), for the proposition that “‘subjective Bayesians are a well-established minority’ of scientists whose methods ‘have rarely been used in court.’”). See also Plaintiffs’ Mem. of Law in Opp. to Motion of AbbVie Defendants to Exclude Plaintiffs’ Expert Testimony on Causation, and for Summary Judgment, MDL No. 2545, Dkt. No. 1753 (N.D. Ill. Mar. 23, 2017).
[26] See David H. Kaye & David Freedman, Reference Guide on Statistics, in National Academies of Sciences, Engineering, and Medicine & Federal Judicial Center, REFERENCE MANUAL ON SCIENTIFIC EVIDENCE 529 (3rd ed. 2011).
[27] In re Testosterone Replacement Therapy Prods. Liab. Litig., MDL No. 2545, MDL No. 2545, 2018 WL 4030585, at *8 (N.D. Ill. Aug. 23, 2018).
[28] John Carlin, Meta-analysis for 2 x 2 tables: a Bayesian approach, 11 STAT. MED. 141 (1992) [Carlin]
[29] Carlin at 157.
[30] Id.
[31] See P. Lambert et al., How vague is vague? A simulation study of the impact of the use of vague prior distributions in MCMC using WinBUGS, 24 STATS. MED. 2401, 2402 (2005). See also Andrew Gelman, Prior distributions for variance parameters in hierarchical models, 1 BAYESIAN ANALYSIS 515
(2006); E. Pullenayegum, An informed reference prior for between-study heterogeneity in meta-analyses of binary outcomes, 30 STATS. MED. 3082 (2010).
[32] Deposition of Martin Wells, in Martin v. Actavis, Inc., No. 15-cv-4292, 2018 WL 7350886 (N.D. Ill. Apr. 2, 2018).
[33] Martin v. Actavis, Inc., Case No. 15 C 4292, MDL No. 2545, 430 F. Supp.3d 516, 534 (2019).
[34] A. Lincoff et al., Cardiovascular Safety of Testosterone-Replacement Therapy, 389 NEW ENGL. J. MED. 107, 114 (2023).
[35] Jonathan Swift, The Examiner No. 14 (Nov. 9, 1710), in THE EXAMINER & OTHER PIECES WRITTEN IN 1710-11 at 8, 11-12 (Herbert Davis, ed. 1966).
