The New England Journal of Medicine NEJM announced new guidelines for authors for statistical reporting yesterday*. The ASA describes the change as “in response to the ASA Statement on P-values and Statistical Significance and subsequent The American Statistician special issue on statistical inference” (ASA I and II,(note) in my abbreviation). If so, it seems to have backfired. I don’t know all the differences in the new guidelines, but those explicitly noted appear to me to move in the reverse direction from where the ASA I and II(note) guidelines were heading.
The most notable point is that the NEJM highlights the need for error control, especially for constraining the Type I error probability, and pays a lot of attention to adjusting P-values for multiple testing and post hoc subgroups. ASA I included an important principle (#4) that P-values are altered and may be invalidated by multiple testing, but they do not call for adjustments for multiplicity, nor do I find a discussion of Type I or II error probabilities in the ASA documents. NEJM gives strict requirements for controlling family-wise error rate or false discovery rates (understood as the Benjamini and Hochberg frequentist adjustments).
They do not go along with the ASA II(note) call for ousting thresholds, ending the use of the words “significance/significant”, or banning “p ≤ 0.05”. In the associated article, we read:
“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”.
When it comes to confidence intervals, the recommendations of ASA II(note), to the extent they were influential on the NEJM, seem to have had the opposite effect to what was intended–or is this really what they wanted?
- When no method to adjust for multiplicity of inferences or controlling false discovery rate was specified in the protocol or SAP of a clinical trial, the report of all secondary and exploratory endpoints should be limited to point estimates of treatment effects with 95% confidence intervals. In such cases, the Methods section should note that the widths of the intervals have not been adjusted for multiplicity and that the inferences drawn may not be reproducible. No P values should be reported for these analyses.
Significance levels and P-values, in other words, are terms to be reserved for contexts in which their error statistical meaning is legitimate. This is a key strong point of the NEJM guidelines. Confidence levels, for the NEJM, lose their error statistical or “coverage probability” meaning, unless they follow the adjustments that legitimate P-values call for. But they must be accompanied by a sign that warns the reader the intervals were not adjusted for multiple testing and thus “the inferences drawn may not be reproducible.” The P-value, but not the confidence interval, remains an inferential tool with control of error probabilities. Now CIs are inversions of tests, and strictly speaking should also have error control. Authors may be allowed to forfeit this, but then CIs can’t replace significance tests and their use may even (inadvertently, perhaps) signal lack of error control. (In my view, that is not a good thing.) Here are some excerpts:
For all studies:
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.
For clinical trials:
Original and final protocols and statistical analysis plans (SAPs) should be submitted along with the manuscript, as well as a table of amendments made to the protocol and SAP indicating the date of the change and its content.
The analyses of the primary outcome in manuscripts reporting results of clinical trials should match the analyses prespecified in the original protocol, except in unusual circumstances. Analyses that do not conform to the protocol should be justified in the Methods section of the manuscript. …
When comparing outcomes in two or more groups in confirmatory analyses, investigators should use the testing procedures specified in the protocol and SAP to control overall type I error — for example, Bonferroni adjustments or prespecified hierarchical procedures. P values adjusted for multiplicity should be reported when appropriate and labeled as such in the manuscript. In hierarchical testing procedures, P values should be reported only until the last comparison for which the P value was statistically significant. P values for the first nonsignificant comparison and for all comparisons thereafter should not be reported. For prespecified exploratory analyses, investigators should use methods for controlling false discovery rate described in the SAP — for example, Benjamini–Hochberg procedures.
When no method to adjust for multiplicity of inferences or controlling false discovery rate was specified in the protocol or SAP of a clinical trial, the report of all secondary and exploratory endpoints should be limited to point estimates of treatment effects with 95% confidence intervals. In such cases, the Methods section should note that the widths of the intervals have not been adjusted for multiplicity and that the inferences drawn may not be reproducible. No P values should be reported for these analyses.
As noted earlier, since P-values would be invalidated in such cases, it’s entirely right not to give them. CIs are permitted, yes, but are required to sport an alert warning that, even though multiple testing was done, the intervals were not adjusted for this and therefore “the inferences drawn may not be reproducible.” In short their coverage probability justification goes by the board.
I wonder if practitioners can opt out of this weakening of CIs, and declare in advance that they are members of a subset of CI users who will only report confidence levels with a valid error statistical meaning, dual to statistical hypothesis tests.
The NEJM guidelines continue:
…When the SAP prespecifies an analysis of certain subgroups, that analysis should conform to the method described in the SAP. If the study team believes a post hoc analysis of subgroups is important, the rationale for conducting that analysis should be stated. Post hoc analyses should be clearly labeled as post hoc in the manuscript.
Forest plots are often used to present results from an analysis of the consistency of a treatment effect across subgroups of factors of interest. …A list of P values for treatment by subgroup interactions is subject to the problems of multiplicity and has limited value for inference. Therefore, in most cases, no P values for interaction should be provided in the forest plots.
If significance tests of safety outcomes (when not primary outcomes) are reported along with the treatment-specific estimates, no adjustment for multiplicity is necessary. Because information contained in the safety endpoints may signal problems within specific organ classes, the editors believe that the type I error rates larger than 0.05 are acceptable. Editors may request that P values be reported for comparisons of the frequency of adverse events among treatment groups, regardless of whether such comparisons were prespecified in the SAP.
When possible, the editors prefer that absolute event counts or rates be reported before relative risks or hazard ratios. The goal is to provide the reader with both the actual event frequency and the relative frequency. Odds ratios should be avoided, as they may overestimate the relative risks in many settings and be misinterpreted.
Authors should provide a flow diagram in CONSORT format. The editors also encourage authors to submit all the relevant information included in the CONSORT checklist. …The CONSORT statement, checklist, and flow diagram are available on the CONSORT
Detailed instructions to ensure that observational studies retain control of error rates are given.
In the associated article:
P values indicate how incompatible the observed data may be with a null hypothesis; “P<0.05” implies that a treatment effect or exposure association larger than that observed would occur less than 5% of the time under a null hypothesis of no effect or association and assuming no confounding. Concluding that the null hypothesis is false when in fact it is true (a type I error in statistical terms) has a likelihood of less than 5%. [i]…
The use of P values to summarize evidence in a study requires, on the one hand, thresholds that have a strong theoretical and empirical justification and, on the other hand, proper attention to the error that can result from uncritical interpretation of multiple inferences.5 This inflation due to multiple comparisons can also occur when comparisons have been conducted by investigators but are not reported in a manuscript. A large array of methods to adjust for multiple comparisons is available and can be used to control the type I error probability in an analysis when specified in the design of a study.6,7 Finally, the 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. [ii]
… 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.
Finally, the current guidelines are limited to studies with a traditional frequentist design and analysis, since that matches the large majority of manuscripts submitted to the Journal. We do not mean to imply that these are the only acceptable designs and analyses. The Journal has published many studies with Bayesian designs and analyses8-10 and expects to see more such trials in the future. When appropriate, our guidelines will be expanded to include best practices for reporting trials with Bayesian and other designs.
What do you think?
I will update this with corrections and thoughts using (i), (ii), etc.
The author guidelines:
The associated article:
*I meant to thank Nathan Schachtman for notifying me and sending links; also Stuart Hurlbert.
[i] It would be better, it seems to me, if the term “likelihood” was used only for its technical meaning in a document like this.
[ii] I don’t see it as a matter of “reductionism” but simply a matter of the properties of the test and the discrepancies of interest in the context at hand.
Nathan Schachtman has blogged on this today I see. He write:
“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.”
Mayo, I’ll opt out of this one. There are so many things wrong or poorly stated in the NEJM documents that dealing with them here would be awkward and unproductive. The core error underlying all the problems is their preoccupation with trying to control or correct for multiplicities, which cannot be done in any logical, objective way and which is, in fact, unneccessary. This is a fetish largely restricted to statisticians working for clinical trials, and not one affecting most other disciplines. And of course, they are half a century out of date in insisting on dichotomizing the P scale.
Justification for those opinions may be found in, inter alia: Hurlbert, S.H. and C.M. Lombardi. 2012. Lopsided reasoning on lopsided tests and multiple comparisons. Australian and New Zealand Journal of Statistics 54:23-42.