EPA Post Hoc Statistical Tests – One Tail vs Two

EPA 1992 Meta-Analysis of ETA & Lung Cancer – Part 2

In 1992, the U.S. Environmental Protection Agency (EPA) published a risk assessment of lung cancer (and other) risks from environmental tobacco smoke (ETS).  See Respiratory Health Effects of Passive Smoking: Lung Cancer and Other Disorders EPA/600/6-90/006F (1992).  The agency concluded that ETS causes about 3,000 lung cancer deaths each year among non-smoking adults.  See also EPA “Fact Sheet: Respiratory Health Effects of Passive Smoking,” Office of Research and Development, and Office of Air and Radiation, EPA Document Number 43-F-93-003 (Jan. 1993).

In my last post, I discussed  how various plaintiffs, including tobacco companies, challenged the EPA’s conclusions as agency action that violated administrative and statutory procedures. “EPA Cherry Picking (WOE) – EPA 1992 Meta-Analysis of ETA & Lung Cancer – Part 1” (Dec. 2. 2012). The plaintiffs further claimed that the EPA had manufactured its methods to achieve the result it desired in advance of the analyses. A federal district court agreed with the methodological challenges to the EPA’s report, but the Court of Appeals reversed on grounds that the agency’s report was not reviewable agency action.  Flue-Cured Tobacco Cooperative Stabilization Corp. v. EPA, 4 F. Supp. 2d 435 (M.D.N.C. 1998), rev’d 313 F.3d 852, 862 (4th Cir. 2002) (Widener, J.) (holding that the issuance of the report was not “final agency action”).

One of the grounds of the plaintiffs’ challenge was that the EPA had changed, without explanation, from a 95% to a 90% confidence interval.  The change in the specification of the coefficient of confidence was equivalent to a shift from a two-tailed to a one-tailed test of confidence, with alpha set at 5%.  This change, along with gerrymandering or “cherry picking” of studies, allowed the EPA to claim a statistically significant association between ETS and lung cancer. 4 F. Supp. 2d at 461.  The plaintiffs pointed to EPA’s own previous risk assessments, as well as statistical analyses by the World Health Organization (International Agency for Research on Cancer), the National Research Council, and the Surgeon General, all of which routinely use 95% intervals, and two-tailed tests of significance.  Id.

In its 1990 Draft ETS Risk Assessment, the EPA had used a 95% confidence interval, but in later drafts, changed to a 90% interval.  One of the epidemiologists on the EPA’s Scientific Advisory Board, Geoffrey Kabat, criticized this post hoc change, noting that the use of 90% intervals are disfavored and that the post hoc change in statistical methodology created the appearance of an intent to influence the outcome of the analysis. Id. (citing Geoffrey Kabat, “Comments on EPA’s Draft Report: Respiratory Health Effects of Passive Smoking: Lung Cancer and Other Disorders,” II.SAB.9.15 at 6 (July 28, 1992) (JA 12,185).

The EPA argued that its adoption of a one-tailed test of significance was justified on the basis of an a priori hypothesis that ETS is associated with lung cancer.  Id. at 451-52, 461 (citing to ETS Risk Assessment at 5–2). The court found this EPA argument hopelessly circular.  The agency postulated its a priori hypothesis, which it then took as license to dilute the statistical test for assessing the evidence.  The agency, therefore, had assumed what it wished to show, in order to achieve the result it sought.  Id. at 456.  The EPA claimed that the one-tailed test had more power, but with dozens of studies aggregated into a summary result, the court recognized that Type I error was a larger threat to the validity of the agency’s conclusions.

The EPA also advanced a muddled defense of its use of 90% confidence intervals by arguing that if it used a 95% interval, the results would have been incongruent with the one-tailed p-values.  The court recognized that this was really no discrepancy at all, but only a corollary of using either one-tailed 5% tests or 90% confidence intervals.  Id. at 461.

If the EPA had adhered to its normal methodology, there would have been no statistically significant association between ETS and lung cancer. With its post hoc methodological choice, and highly selective approach to study inclusions in its meta-analysis, the EPA was able to claim a weak statistically significant association between ETS and lung cancer.  Id. at 463.  The court found this to be a deviation from the legally required use of “best judgment possible based upon the available evidence.”  Id.

Of course, the EPA could have announced its one-tailed test from the inception of the risk assessment, and justified its use on grounds that it was attempting to reach only a precautionary judgment for purposes of regulation.  Instead, the agency tried to showcase its finding as a scientific conclusion, which only further supported the tobacco companies’ challenge to the post hoc change in plan for statistical analysis.

Although the validity issues in the EPA’s 1992 meta-analysis should have been superseded by later studies, and later meta-analyses, the government’s fraud case, before Judge Kessler, resurrected the issue:

“3344. Defendants criticized EPA’s meta-analysis of U.S. epidemiological studies, particularly its use of an ‘unconventional 90 percent confidence interval’. However, Dr. [David] Burns, who participated in the EPA Risk Assessment, testified that the EPA used a one-tailed 95% confidence interval, not a two-tailed 90% confidence interval. He also explained in detail why a one-tailed test was proper: The EPA did not use a 90% confidence interval. They used a traditional 95% confidence interval, but they tested for that interval only in one direction. That is, rather than testing for both the possibility that exposure to ETS increased risk and the possibility that it decreased risk, the EPA only tested for the possibility that it increased the risk. It tested for that possibility using the traditional 5% chance or a P value of 0.05. It did not test for the possibility that ETS protected those exposed from developing lung cancer at the direction of the advisory panel which made that decision based on its prior decision that the evidence established that ETS was a carcinogen. What was being tested was whether the exposure was sufficient to increase lung cancer risk, not whether the agent itself, that is cigarette smoke, had the capacity to cause lung cancer with sufficient exposure. The statement that a 90% confidence interval was used comes from the observation that if you test for a 5% probability in one direction the boundary is the same as testing for a 10% probability in two directions. Burns WD, 67:5-15. In fact, the EPA Risk Assessment stated, ‘Throughout this chapter, one-tailed tests of significance (p = 0.05) are used …’ .”

U.S. v. Philip Morris USA, Inc., 449 F. Supp. 2d 1, 702-03 (D.D.C., 2006) (Kessler, J.) (internal citations omitted).

Judge Kessler was misled by Dr. Burns, a frequent testifier for plaintiffs’ counsel in tobacco cases.  Burns should have known that with respect to the lower bound of the confidence interval, which is what matters for determining whether the meta-analysis excludes a risk ratio of 1.0, there is no difference between a one-tailed 95% confidence interval and a two-tailed 90% interval.  Burns’ sophistry hardly saves the EPA’s error in changing its pre-specified end point and statistical analysis, or the danger of unduly increasing the risk of Type I error in the EPA meta-analysis. SeePin the Tail on the Significance Test” (July 14th, 2012)


Judge Widener wrote the opinion for a panel of the United States Court of Appeals, for the Fourth Circuit, which reversed the district court’s judgment, enjoining the EPA’s report.  The Circuit’s decision did not address the scientific issues, but by holding that the agency action was not reviewable, the basis for the district court’ review of the scientific and statistical issues was removed.  For those pundits who see only self-interested behavior in judging, the author of the Circuit’s decision was a life-time smoker, who grew Burley tobacco on his farm, outside Abingdon, Virginia.  Judge Widener died on September 19, 2007, of lung cancer.

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