Statistical Significance at the New England Journal of Medicine

Some wild stuff has been going on in the world of statistics, at the American Statistical Association, and elsewhere. A very few obscure journals have declared p-values to be verboten, and presumably confidence intervals as well. The world of biomedical research has generally reacted more sanely, with authors defending the existing frequentist approaches and standards.[1]

This week, the editors of the New England Journal of Medicine have issued new statistical guidelines for authors. The Journal’s approach seems appropriately careful and conservative for the world of biomedical research. In an editorial introducing the new guidelines,[2] the Journal editors remind their potential authors that statistical significance and p-values are here to stay:

“Despite the difficulties they pose, P values continue to have an important role in medical research, and we do not believe that P values and significance tests should be eliminated altogether. A well-designed randomized or observational study will have a primary hypothesis and a prespecified method of analysis, and the significance level from that analysis is a reliable indicator of the extent to which the observed data contradict a null hypothesis of no association between an intervention or an exposure and a response. Clinicians and regulatory agencies must make decisions about which treatment to use or to allow to be marketed, and P values interpreted by reliably calculated thresholds subjected to appropriate adjustments have a role in those decisions.”[3]

The Journal’s editors described their revamped statistical policy as being based upon three premises:

(1) adhering to prespecified analysis plans if they exist;

(2) declaring associations or effects only for statistical analyses that have pre-specified “a method for controlling type I error”; and

(3) presenting evidence about clinical benefits or harms requires “both point estimates and their margins of error.”

With a hat tip to the ASA’s recent pronouncements on statistical significance,[4] the editors suggest that their new guidelines have moved away from bright-line applications of statistical significance “as a bright-line marker for a conclusion or a claim”[5]:

“[T]he notion that a treatment is effective for a particular outcome if P < 0.05 and ineffective if that threshold is not reached is a reductionist view of medicine that does not always reflect reality.”[6]

The editors’ language intimates greater latitude for authors in claiming associations or effects from their studies, but this latitude may well be circumscribed by tighter control over such claims in the inevitable context of multiple testing within a dataset.

The editors’ introduction of the new guidelines is not entirely coherent. The introductory editorial notes that the use of p-values for reporting multiple outcomes, without adjustments for multiplicity, inflates the number of findings with p-values less than 5%. The editors thus caution against “uncritical interpretation of multiple inferences,” which can be particularly threatening to valid inference when not all the comparisons conducted by the study investigators have been reported in their manuscript.[7] They reassuringly tell prospective authors that many methods are available to adjust for multiple comparisons, and can be used to control Type I error probability “when specified in the design of a study.”[8]

But what happens when such adjustment methods are not pre-specified in the study design? Failure to to do so do not appear to be disqualifying factors for publication in the Journal. For one thing, when the statistical analysis plan of the study has not specified adjustment methods for controlling type I error probabilities, then authors must replace p-values with “estimates of effects or association and 95% confidence intervals.”[9] It is hard to understand how this edict helps when the specified coefficient of 95% is a continuation of the 5% alpha, which would have been used in any event. The editors seem to be saying that if authors fail to pre-specify or even post-specify methods for controlling error probabilities, then they cannot declare statistical significance, or use p-values, but they can use confidence intervals in the same way they have been using them, and with the same misleading interpretations supplied by their readers.

More important, another price authors will have to pay for multiple testing without pre-specified methods of adjustment is that they will affirmatively have to announce their failure to adjust for multiplicity and that their putative associations “may not be reproducible.” Tepid as this concession is, it is better than previous practice, and perhaps it will become a badge of shame. The crucial question is whether judges, in exercising their gatekeeping responsibilities, will see these acknowledgements as disabling valid inferences from studies that carry this mandatory warning label.

The editors have not issued guidelines for the use of Bayesian statistical analyses, because “the large majority” of author manuscripts use only frequentist analyses.[10] The editors inform us that “[w]hen appropriate,” they will expand their guidelines to address Bayesian and other designs. Perhaps this expansion will be appropriate when Bayesian analysts establish a track record of abuse in their claiming of associations and effects.

The new guidelines themselves are not easy to find. The Journal has not published these guidelines as an article in their published issues, but has relegated them to a subsection of their website’s instructions to authors for new manuscripts:

Presumably, the actual author instructions control in any perceived discrepancy between this week’s editorial and the guidelines themselves. Authors are told that p-values generally should be two-sided. Authors’ use of:

“Significance tests should be accompanied by confidence intervals for estimated effect sizes, measures of association, or other parameters of interest. The confidence intervals should be adjusted to match any adjustment made to significance levels in the corresponding test.”

Similarly, the guidelines call for, but do not require, pre-specified methods of controlling family-wide error rates for multiple comparisons. For observational studies submitted without pre-specified methods of error control, the guidelines recommend the use of point estimates and 95% confidence intervals, with an explanation that the interval widths have not been adjusted for multiplicity, and a caveat that the inferences from these findings may not be reproducible. The guidelines recommend against using p-values for such results, but again, it is difficult to see why reporting the 95% confidence intervals is recommended when p-values are not recommended.

[1]  Jonathan A. Cook, Dean A. Fergusson, Ian Ford, Mithat Gonen, Jonathan Kimmelman, Edward L. Korn, and Colin B. Begg, “There is still a place for significance testing in clinical trials,” 16 Clin. Trials 223 (2019).

[2]  David Harrington, Ralph B. D’Agostino, Sr., Constantine Gatsonis, Joseph W. Hogan, David J. Hunter, Sharon-Lise T. Normand, Jeffrey M. Drazen, and Mary Beth Hamel, “New Guidelines for Statistical Reporting in the Journal,” 381 New Engl. J. Med. 285 (2019).

[3]  Id. at 286.

[4]  See id. (“Journal editors and statistical consultants have become increasingly concerned about the overuse and misinterpretation of significance testing and P values in the medical literature. Along with their strengths, P values are subject to inherent weaknesses, as summarized in recent publications from the American Statistical Association.”) (citing Ronald L. Wasserstein & Nicole A. Lazar, “The ASA’s statement on p-values: context, process, and purpose,” 70 Am. Stat. 129 (2016); Ronald L. Wasserstein, Allen L. Schirm, and Nicole A. Lazar, “Moving to a world beyond ‘p < 0.05’,” 73 Am. Stat. s1 (2019)).

[5]  Id. at 285.

[6]  Id. at 285-86.

[7]  Id. at 285.

[8]  Id., citing Alex Dmitrienko, Frank Bretz, Ajit C. Tamhane, Multiple testing problems in pharmaceutical statistics (2009); Alex Dmitrienko & Ralph B. D’Agostino, Sr., “Multiplicity considerations in clinical trials,” 378 New Engl. J. Med. 2115 (2018).

[9]  Id.

[10]  Id. at 286.

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