I have posted before about the curious saga of two university professors of economics who curiously tried to befriend the United States Supreme Court.  Professors Ziliak and McCloskey submitted an amicus brief to the Court, in connection with Matrixx Initiativives, Inc. v. Siracusano, ___ U.S. ___, 131 S.Ct. 1309 (2011).  Nothing unusual there, other than the Professors’ labeling themselves “Statistics Experts,” and then proceeding to commit a statistical howler of deriving a posterior probability from only a p-value.  See “The Matrixx Oversold” (April 4, 2011).

I seemed to be alone in my dismay over this situation, but recently Professor David Kaye, an author of the chapter on statistics in the Reference Manual on Scientific Evidence, weighed in with his rebuttal to Ziliak and McCloskey’s erroneous statistical contentions.  See “The Transposition Fallacy in Matrixx Initiatives, Inc. v. Siracusano: Part I” (August 19, 2011), and “The Transposition Fallacy in Matrixx Initiatives, Inc. v. Siracusano: Part II” (August 26, 2011).  Kaye’s analysis is well worth reading.

Having attempted to bamboozle the Justices on statistics, Stephen Ziliak has now turned his attention to an audience of statisicians and students of statistical science, with a short article in Significance on the Court’s decision in Matrixx.  Stephen Ziliak, “Matrixx v. Siracusano and Student v. Fisher:  Statistical Significance on Trial,”  Significance 131 (September 2011).  Tellingly, Ziliak did not advance his novel, erroneous views of how to derive posterior odds or probabilities from p-values in the pages of a magazine published by the Royal Statistical Society.  Such gems were reserved for the audience of Justices and law clerks in Washington, D.C.  Instead of holding forth on statistical issues, Ziliak has used the pages of a statistical journal to advance equally bizarre, inexpert views about the legal meaning of a Supreme Court case.

The Matrixx decision involved the appeal from a dismissal of a complaint for failure to plead sufficient allegations in a securities fraud action.  No evidence was ever offered or refused; no expert witness opinion was held reliable or unreliable.  The defendant, Matrixx Initiatives, Inc., won the dismissal at the district court, only to have the complaint reinstated by the Court of Appeals for the Ninth Circuit.  The Supreme Court affirmed the reinstatement, and in doing so, did not, and could not, have created a holding about the sufficiency of evidence to show causation in a legal proceeding.  Indeed, Justice Sotomayor, in writing for a unanimous Court, specifically stated that causation was not at issue, especially given that evidentiary displays far below what is necessary to show causation between a medication and an adverse event might come to the attention of the FDA, which agency in turn might find the evidence sufficient to order a withdrawal of the medication.

Ziliak, having given dubious statistical advice to the U.S. Supreme Court, now sets himself up to give equally questionable legal advice to the statistical community.  He asserts that Matrixx claimed that anosmia (the loss of the sense of smell) was unimportant because not “statistically significant.”  Id. at 132.  Matrixx Initiatives no doubt made several errors, but it never made this erroneous claim.  Ziliak gives no citation to the parties’ briefs; nor could one be given.  Matrixx never contended that anosmia was unimportant; its claim was that the plaintiffs had not sufficiently alleged facts that Matrixx had knowledge of a causal relationship such that its failure to disclose adverse event reports became a “material” omission under the securities laws.  The word “unimportant” does not occur in the Matrixx’s briefs; nor was it uttered at oral argument.

Ziliak’s suggestion that “[t]he district court dismissed the case on the basis that investors did not prove ‘materiality’, by which that court meant ‘statistical significance’,” is nonsense.  Id. at 132.  The issue was never the sufficiency of evidence.  Matrixx did attempt to equate materiality with causation, and then argued that allegations of causation required, in turn, allegations of statistical significance.  In arguing the necessity of statistical significance, Matrixx was implicitly suggesting that an evidentiary display that fell short of supporting causation could not be material, when withheld from investors.  The Supreme Court had an easy time of disposing of Matrixx’s argument because causation was never at issue.  Everything that the Court did say about causation is readily discernible as dictum.

Ziliak erroneously reads into the Court’s opinion a requirement that a pharmaceutical company, reporting to the Securities and Exchange Commission “can no longer hide adverse effect [sic] reports from investors on the basis that reports are not statistically significant.”   Id. at 133.  Ziliak incorrectly refers to adverse event reports as “adverse effect reports,” which is a petitio principii.  Furthermore, this was not the holding of the Court.  The potentially fraudulent aspect of Matrixx’s conduct was not that it had “hidden” adverse event reports, but rather that it had adverse event reports and a good deal of additional information, none of which it had disclosed to investors, when at the same time, the company chose to give the investment community particularly bullish projections of future sales.  The medication involved, Zicam, was an over-the-counter formulation that never had the rigorous testing required for a prescription medication’s new drug application.

Curiously, Ziliak, the self-described statistics expert fails to point out that adverse event reports could not achieve, or fail to achieve, statistical significance on the basis of the facts alleged in the plaintiffs’ complaint.  Matrixx, and its legal counsel, might be forgiven this oversight, but surely Ziliak the statistical expert should have noted this.  Indeed, if the parties and the courts had recognized that there never was an issue of statistical significance involved in the case, the entire premiss of Matrixx’s appeal would have been taken away.

To be a little fair to Ziliak, the Supreme Court, having disclaimed any effort to require proof of causation or to define that requisites of reliable evidence of causation, went ahead and offered its own dubious dictum on how statistical significance might not be necessary for causation:

“Matrixx’s argument rests on the premise that statistical significance is the only reliable indication of causation. This premise is flawed: As the SEC points out, “medical researchers … consider multiple factors in assessing causation.” Brief for United States as Amicus Curiae 12. Statistically significant data are not always available. For example, when an adverse event is subtle or rare, “an inability to obtain a data set of appropriate quality or quantity may preclude a finding of statistical significance.” Id., at 15; see also Brief for Medical Researchers as Amici Curiae 11. Moreover, ethical considerations may prohibit researchers from conducting randomized clinical trials to confirm a suspected causal link for the purpose of obtaining statistically significant data. See id., at 10-11.

A lack of statistically significant data does not mean that medical experts have no reliable basis for inferring a causal link between a drug and adverse events. As Matrixx itself concedes, medical experts rely on other evidence to establish an inference of causation. See Brief for Petitioners 44-45, n. 22. We note that courts frequently permit expert testimony on causation based on evidence other than statistical significance. See, e.g., Best v. Lowe’s Home Centers, Inc., 563 F.3d 171, 178 (C.A.6 2009); Westberry v. Gislaved Gummi AB, 178 F.3d 257, 263-264 (C.A.4 1999) (citing cases); Wells v. Ortho Pharmaceutical Corp., 788 F.2d 741, 744-745 (C.A.11 1986). We need not consider whether the expert testimony was properly admitted in those cases, and we do not attempt to define here what constitutes reliable evidence of causation.”

What is problematic about this passage is that Justice Sotomayor was addressing situations that were not before the Court, and about which she had no appropriate briefing.  Her suggestion that randomized clinical trials are not always ethically appropriate is, of course, true, but that does not prevent an expert witness from relying upon observational epidemiologic studies – with statistically significant results – to support their causal claims.  Justice Sotomayor’s citation to the Best and the Westberry cases, again in dictum, is equally off the mark.  Both cases involve the application of differential etiological reasoning about specific causation, which presupposes that  general causation has been previously, sufficiently shown.  Finally, Justice Sotomayor’s citation to the Wells case, which involved both general and specific causation issues, was inapposite because plaintiff’s expert witness in Wells did rely upon at least one study with a statistically significant result.  As I have pointed out before, the Wells case went on to become an example of one trial judge’s abject failure to understand and evaluate scientific evidence.

Postscript:

The Supreme Court’s statistical acumen may have been lacking, but the Justices seemed to have a good sense of what was really going on in the case.  In December 2010, Matrixx settled over 2,000 Zicam injury claims. On February 24, 2011, a month before the Supreme Court decided the Matrixx case, the federal district judge responsible for the Zicam multi-district litigation refused Matrixx’ motion to exclude plaintiffs’ expert witnesses’ causation opinions.  “First Zicam Experts Admitted by MDL Judge for Causation, Labeling Opinions” 15 Mealey’s Daubert Reporter (February 2011); In re Zicam Cold Remedy Marketing, Sales Practices and Products Liab. Litig., MDL Docket No. 2:09-md-02096, Document 1360 (D. Ariz. 2011).

After the Supreme Court affirmed the reinstatement of the securities fraud complaint, Charles Hensley, the inventor of Zicam, was arrested on federal charges of illegally marketing another drug, Vira 38, which he claimed was therapeutic and preventive for bird flu.  Stuart Pfeifer, “Zicam inventor arrested, accused of illegal marketing of flu drug,” Los Angeles Times (June 2, 2011).  Earlier this month, Mr. Hensley pleaded guilty to the charges of unlawful distribution.

As I have previously discussed, a risk ratio (RR) ≤ 2 is a strong practical argument against specific causation. See Courts and Commentators on Relative Risks to Infer Specific Causation;  Relative Risks and Individual Causal Attribution; and  Risk and Causation in the Law.   But a relative risk greater than 2 threshold has little to do with general causation.  There are any number of well-established causal relationships, where the magnitude of the ex ante risk in an exposed population is > 1, but ≤ 2.  The magnitude of risk for cardiovascular disease and smoking is one such well-known example.

When assessing general causation from only observational epidemiologic studies, where residual confounding and bias may be lurking, it is prudent to require a RR > 2, as a measure of strength of the association that can help us rule out the role of systemic error.  As the cardiovascular disease/smoking example illustrates, however, there is clearly no scientific requirement that the RR be greater than 2 to establish general causation.  Much will depend upon the entire body of evidence.  If the other important Bradford Hill factors are present – dose-response, consistent, coherence, etc. – then risk ratios ≤ 2, from observational studies, may suffice to show general causation.  So the requirement of a RR > 2, for the showing of general causation, is a much weaker consideration than it is for specific causation.

Randomization and double blinding are major steps in controlling confounding and bias, but they are not complete guarantees that systematic bias has been eliminated.  A double-blinded, placebo-controlled, randomized clinical trial (RCT) will usually have less opportunity for bias and confounding to play a role.  Imposing a RR > 2 requirement for general causation thus makes less sense in the context of trying to infer general causation from the results of RCTs.

Somehow the Texas Supreme Court managed to confuse these concepts in an important decision this week, Merck & Co. v. Garza (August 26, 2011).

Mr. Garza had a long history of heart disease, at least two decades long, including a heart attack, and quadruple bypass and stent surgeries.  Garza’s physician prescribed 25 mg Vioxx for pain relief.  Garza died less than a month later, at the age of 71, of an acute myocardial infarction.  The plaintiffs (Mr. Garza’s survivors) were thus faced with a problem of showing the magnitude of the risk experienced by Mr. Garza, which risk would allow them to infer that his fatal heart attack was caused by his having taken Vioxx.  The studies relied upon by plaintiffs did show increased risk, consistently, for larger doses (50 mg.) taken over longer periods of time.  The trial court entered judgment upon a jury verdict in favor of the plaintiffs.

The Texas Supreme Court reversed, and rendered the judgment for Merck.  The Court’s judgment was based largely upon its view that the studies relied upon did not apply to the plaintiff.  Here the Court was on pretty solid ground.  The plaintiffs also argued that Mr. Garza had a higher pre-medication, baseline risk, and that he therefore would have sustained a greater increased risk from short-term, low-dose use of Vioxx.  The Court saw through this speculative argument, and cautioned that the “absence of evidence cannot substitute for evidence.” Slip op. at 17.  The greater baseline does not mean that the medication imposed a greater relative risk on people like Mr. Garza, although it would mean that we would expect to see more cases from any subgroup that looked like him.  The attributable fraction and the difficulty in using risk to infer individual attribution, however, would remain the same.

The problematic aspect of the Garza case arises from the Texas Supreme Court’s conflating and confusing general with specific causation.  There was no real doubt that Vioxx at high-doses, for prolonged use, can cause heart attacks.  General causation was not at issue.  The attribution of Mr. Garza’s heart attack to his short-term, low-dose use of Vioxx, however, was at issue, and was a rather dubious claim.

The Texas Supreme Court proceeded to rely heavily upon its holding and language in Merrell Dow Pharmaceuticals, Inc. v. Havner, 953 S.W.2d 706 (Tex. 1997).  Havner was a Bendectin case, in which plaintiffs claimed that the medication caused specific birth defects.  Both general and specific causation were contested by the parties. The epidemiologic evidence in Havner came from observational studies, either case-control or cohort studies, and not RCTs.

The Havner decision insightfully recognized that risk does not equal causation, but RR > 2 is a practical compromise for allowing courts and juries to make the plaintiff-specific attribution in the face of uncertainty.  Havner, 953 S.W.2d at 717 .  Merck latched on to this and other language, arguing that “Havner requires a plaintiff who claims injury from taking a drug to produce two independent epidemiological studies showing a statistically significant doubling of the relative risk of the injury for patients taking the drug under conditions substantially similar to the plaintiff’s (dose and duration, for example) as compared to patients taking a placebo.” Slip op. at 7.

The plaintiffs in Garza responded by arguing that their reliance upon RCTs relieved them of Havner‘s requirement of showing a RR > 2.

The Texas Supreme Court correctly rejected the plaintiffs’ argument and followed its earlier decision in Havner on specific causation:

“But while the controlled, experimental, and prospective nature of clinical trials undoubtedly make them more reliable than retroactive, observational studies, both must show a statistically significant doubling of the risk in order to be some evidence that a drug more likely than not caused a particular injury.”

Slip op. at 10.

The Garza Court, however, went a dictum too far by expressing some of the Havner requirements as applying to general causation:

“Havner holds, and we reiterate, that when parties attempt to prove general causation using epidemiological evidence, a threshold requirement of reliability is that the evidence demonstrate a statistically significant doubling of the risk. In addition, Havner requires that a plaintiff show ‘that he or she is similar to [the subjects] in the studies’ and that ‘other plausible causes of the injury or condition that could be negated [are excluded] with reasonable certainty’.⁴⁰“

Slip op. at 13-14 (quoting from Havner at 953 S.W.2d at 720).

General causation was not the dispositive issue in Garza, and so this language must be treated as dictum.  The sloppiness in confusing the requisites of general and specific causation is regrettable.

The plaintiffs also advanced another argument, which is becoming a commonplace in health-effects litigation.  They threw all their evidence into a pile, and claimed that the “totality of the evidence” supported their claims.  This argument is somehow supposed to supplant a reasoned approach to the issue of what specific inferences can be drawn from what kind of evidence.  The Texas Supreme Court saw through the pile, and dismissed the hand waving:

“The totality of the evidence cannot prove general causation if it does not meet the standards for scientific reliability established by Havner. A plaintiff cannot prove causation by presenting different types of unreliable evidence.”

Slip op. at 17.

All in all, the Garza Court did better than many federal courts that have consistently confused risk with cause, as well as general with specific causation.