Author + information
- Jeehyoung Kim, MD,
- Jay S. Kaufman, PhD and
- Heejung Bang, PhD∗ ()
- ↵∗Department of Public Health Sciences, University of California, Davis, One Shield Avenue, Med-Sci 1C, Davis, California 95616
We read the recent paper by Echouffo-Tcheugui et al. (1) with great interest. There is, however, an important statistical problem in the Central Illustration in the paper. The choice of scale for the x-axis is inappropriate. The effect parameter (which is in fact a hazard ratio but is labeled “RR”) is not symmetrical around the null value of 1. The authors start the x-axis with a value of 0, which corresponds to an infinitely protective effect. Along the current axis, values of 0 and 2 lie equidistant from the null, and yet RR = 0 is infinitely larger than RR = 2. Indeed, if a binary exposure yielding RR = 2 were recoded, it would produce an RR = 0.5, demonstrating that these 2 numbers actually have the same magnitude (2,3).
Statisticians recommend 1 of the following 2 options to better communicate estimated effects: either plot the log of the RR so that the plotted values are symmetrical around the null of 0 or plot the untransformed RR but on a logarithmic scale so that the numbers will be arrayed asymmetrically around the null value of 1 (e.g., 2 and 0.5 = 1/2 would be equidistant from 1). These options are readily managed in most statistical software programs, and the second option seems the most common in biomedical statistical reporting. A comparison of these representations can be seen in Figure 1 in the study by Echouffo-Tcheugui et al. (1).
Our recommendation applies equally to all popular ratio scale measurements, including the odds ratio, risk ratio, rate ratio, and hazard ratio. Additive contrasts such as the risk difference should remain on the linear scale (2,3). Although this may seem a minor issue in this specific example, it is important for making the graphed results independent of arbitrary coding decisions. For example, there is no objective reason why women should be coded 1 and men 0, or vice versa, yet on the additive scale, the effect of sex could appear dramatically larger or smaller based on this arbitrary choice. The logarithmic scale resolves this problem, which is exactly why it is the standard approach in many biomedical publications.
Please note: Dr. Bang was partly supported by the National Institutes of Health through grant UL1 TR001860. The funders had no role in the design and conduct of the study; collection, management, analysis, and interpretation of the data; preparation, review, or approval of the manuscript; and decision to submit the manuscript for publication. The interpretation and reporting of the data are the responsibility of the authors and in no way should be seen as an official policy or interpretation of the U.S. government. The authors have reported that they have no relationships relevant to the contents of this paper to disclose.
- 2018 American College of Cardiology Foundation