# Forest Plots: The Basics

When I was recently asked to give a presentation on forest plots at work, I was less than enthused. Figures are my least favorite part of a manuscript to edit because they usually require a lot of tedious work, and determining how to best visually present statistics makes my brain hurt. Forest plots in particular had become the subject of my nightmares leading up to the time of preparation of my presentation after a few experiences with editing unwieldy ones. However, thanks to being subjected to presenting on forest plots, I’ve gained some basic knowledge that I thought I would share.

There are a few types of forest plots, namely those presenting the results of meta-analyses and those presenting subgroup analyses. Here, I will focus on a forest plot for a meta-analysis. In a meta-analysis, a forest plot acts as a visual representation of the results of the individual studies and the overall result of the analysis. It also shows overall effect estimates and study heterogeneity (ie, variation in results in the individual studies). A forest plot for ratio data should include the following data:

1. The sources included in the meta-analysis, with citations. If the source author or study name is listed more than once, query the author to ensure that the study samples are unique; overlapping samples would lead to inaccurate estimates. Also, remember to renumber the references if you have renumbered them in the body of the article.
2. The number of events and total number of participants in each group of the study and in the combined studies.
3. Risk ratio and 95% CI for each study and overall.
4. Graphed relative risk and 95% CI, with top labels describing what data markers on either side of the null line mean. The squares represent the results of each study and are centered on the point estimate, with the horizontal line in the center representing the 95% CI. The diamond shows the overall meta-analysis estimate, with the center representing the pooled estimate and the horizontal tips indicating the confidence limits.
5. Log scale for the x axis with a label indicating the measure.
6. Percentage of weight given to the study. Weights are given when pooled results are presented. Studies with narrower confidence intervals are weighted more heavily.
7. Heterogeneity and data on overall effect.

(Open image in a new tab to see more detail.)

The caption should indicate the test and model (fixed or random effects) used in the evaluation and may include an explanation of the meaning of the different marker sizes.

If you follow these basic rules, forest plots are a breeze. If you would like an example of a forest plot for a subgroup analysis, let us know in the Comments.—Sara M. Billings

# Putting P Values in Their Place

Although I am not a statistician, I find something very appealing about mathematics and statistics and am pleased when I find a source to help me understand some of the concepts involved. One of these sources intersects with my obsession with politics: Nate Silver’s website fivethirtyeight.com. Yesterday, during a scan of fivethirtyeight’s recent posts, this one by Christie Ashwanden caught my eye: “Statisticians Found One Thing They Can Agree On: It’s Time to Stop Misusing P-Values.”

P values and data in general are frequently on the minds of manuscript editors at the JAMA Network. Instead of just making sure that statistical significance is defined and P values provided, we always ask for odds ratios or 95% confidence intervals to go with them. P values are just not enough anymore, and Ashwanden’s article was really useful in helping me understand why these additional data are needed (as well as making me feel better about not fully understanding the definition of a P value—it turns out I’m not alone. According to another fivethirtyeight article, “Not Even Scientists Can Easily Explain P-Values”). One of the bad things about relying on P values alone is that they are used as a “litmus test” for publication. Findings with low P values but not contextual data are published, yet important studies with high P values are not—and this has real scientific and medical consequences. These articles explain why P values only can  be a cause for concern.

And then there was even more information about statistical significance to think about. A colleague shared a link to a story on vox.com by Julia Belluz: “An Unhealthy Obsession With P-Values Is Ruining Science.” This article a discussed a recent report in JAMA  by Chavalarias et al “that should make any nerd think twice about p-values.” The recent “epidemic” of statistical significance means that “as p-values have become more popular, they’ve also become more meaningless.” Belluz also provides a useful example of what a P value will and will not tell researchers in, say, a drug study, and wraps up with highlights of the American Statistical Association’s guide to using P values.—Karen Boyd

# Ch-ch-ch-changes

To pass the time between stylebook editions, the JAMA Network staff keep an in-house file of little tips, tricks, guidelines, and style changes that have occurred since the last time the manual was published. Here is a small peek inside that file—2 things from this past summer.

The terms multivariable and multivariate are not synonymous, as the entries in the Glossary of Statistical Terms suggest (Chapter 20.9, page 881 in the print). To be accurate, multivariable refers to multiple predictors (independent variables) for a single outcome (dependent variable). Multivariate refers to 1 or more independent variables for multiple outcomes. (This update was implemented June 1, 2014.)

Cross-section, as a verb or adjective should be capped in titles as Cross-section; cross section as a noun should be capped in titles as Cross Section. (This update was implemented August 4, 2014).—Brenda Gregoline, with help from John McFadden

# Lies and Statistics

Check out this post from Skeptical Scalpel about uncool tricks with statistical graphs. Editors beware!—Brenda Gregoline, ELS

# Bucking the “Trend” and Approaching “Approaching Significance”

I believe we are on an irreversible trend toward more freedom and democracy – but that could change.

—Dan Quayle

In general usage, the concept of trend implies movement. Not only is this implied in its definitions, but the word can be traced to its Middle High German root of trendel, which is a disk or spinning top.1

In scientific writing, when is a trend not a trend? When it is not referring to comparisons of findings across an ordered series of categories or across periods of time. However, this and related terms are often misused in manuscripts and articles.

Most studies are constructed as hypothesis testing. Because an individual study only provides a point estimate of the truth, the researchers must determine before conducting the study an acceptable cutoff for the probability that a finding of an association is due to chance (the α value, most commonly but not universally set at .05 in clinical studies). This creates a dichotomous situation in interpreting the result: the study either does or does not meet this criterion. If the criterion is met, the finding is described as “statistically significant”; if it is not met, the finding is described as “not statistically significant.”

There are many limitations to this approach. Where the α level is set is arbitrary; therefore, in general all findings should be expressed as the study’s point estimate and confidence interval, rather than just the study estimate and the P value. Despite the limitations, if a researcher designs a study on the basis of hypothesis testing, it is not appropriate to change the rules after the results are available, and the results should be interpreted accordingly. The entire study design (such as calculation of the sample size and study power – the ability of a study to detect an actual difference or effect, if one truly exists) is dependent on setting the rules in advance and adhering to them.

If a study does not meet the significance criterion (for example, if the α level was set as < .05, and the P value for the finding was .08), authors sometimes describe the findings as “trending toward significance,” “having a trend toward significance,” “approaching significance,” “borderline significant,” or “nearly significant.” None of these terms is correct. Results do not trend toward significant—they either are or are not statistically significant based on the prespecified study assumptions. Similarly, the results do not include any movement and so cannot “approach” significance; and because of the dichotomous definition, “nearly significant” is no more meaningful than “nearly pregnant.”

When a finding does not meet statistical significance, there are generally 2 possible explanations: (1) There is no real association. (2) There might be an association, but the study was underpowered to detect it, usually because there were not enough participants or outcome events. A finding that does not meet statistical significance may still be clinically important and warrant further consideration.

However, when authors use terms such as trend or approaching significance, they are hedging the interpretation. In effect, they are treating the findings as if the association were statistically significant, or as if it might have been if the study had just gone a little differently. This is not justified. (Lang and Secic2 make the fascinating observation that “Curiously, P values never seem to ‘trend’ away from significance.”)

A proper use of the term trend refers to the results of one of the specific statistical tests for trend, the purpose of which is to estimate the likelihood that differences across 3 or more groups move (increase or decrease) in a meaningful direction more than would be expected by chance. For example, if a population of persons is ranked by evenly divided quintiles based on serum cholesterol level (from lowest to highest), and the risk of subsequent myocardial infarction is measured in each group, the researcher may want to determine whether risk increases in a linear way across the groups. Statistical tests that might be used for analyzing trends include the χ2 test for trend and the Cochran-Armitage test.

Similarly, a researcher may want to test for a directional movement in the values of data over time, such as a month-to-month decrease in prescriptions of a medication following publication of an article describing major adverse effects. A number of analytic approaches can be used for this, including time series and other regression models.

Instead of using these terms, the options are:

1. Delete the reported finding if it is not clinically important or a primary outcome. OR

2. Report the finding with its P value. Describe the result as “not statistically significant,” or “a statistically nonsignificant reduction/increase,” and provide the confidence interval so that the reader can judge whether insufficient power is a likely reason for the lack of statistical significance.

If the finding is considered clinically important, authors should discuss why they believe the results did not achieve statistical significance and provide support for this argument (for example, explaining how the study was underpowered). However, this type of discussion is an interpretation of the finding and should take place in the “Discussion” (or “Comment”) section, not in the “Results” section.

Bottom line:

1. The term trend should only be used when reporting the results of statistical tests for trend.

2. Other uses of trend or approaching significance should be removed and replaced with a simple statement of the findings and the phrase not statistically significant (or the equivalent). Confidence intervals, along with point estimates, should be provided whenever possible.—Robert M. Golub, MD

1. Mish FC, ed in chief. Merriam-Webster’s Collegiate Dictionary. 11th ed. Springfield, MA: Merriam-Webster Inc; 2003.

2. Lang TA, Secic M. How to Report Statistics in Medicine: Annotated Guidelines for Authors, Editors, and Publishers. 2nd ed. Philadelphia, PA: American College of Physicans; 2006:56, 58.

# Incidence

In medical contexts, incidence is most often used in its epidemiologic sense, ie, the number of new cases of a disease occurring over a defined period among persons at risk for that disease. When thus used, incidence may be expressed as a percentage (new cases divided by number of persons at risk during the period) or as a rate (number of new cases divided by number of person-years at risk).

Reporting several incidence values in the same sentence can nearly always be accomplished using the singular form (eg, “the incidence of nonfatal myocardial infarction during follow-up was 10% at 6 months, 19% at 12 months, and 26% at 18 months” or “the incidence of clinical stroke decreased significantly, from 7.6 to 5.3 per 1000 person-years in men and from 6.2 to 5.1 per 1000 person-years in women). However, in rare instances, sentence construction may necessitate the use of the plural, which of course is… what, exactly? The understandable urge to simply add an “s” at the end of the word to form the plural results in incidences — a form not found in most dictionaries and a clunker of a word if ever there was one. Writers wishing for a more mellifluous plural sometimes use incidence rates, a valid term but one perhaps best reserved for reporting incidence values expressed as actual rates rather than simple percentages. Moreover, incidences is sometimes used when reporting values either as percentages or as rates, in the latter case missing a valuable opportunity to emphasize that rates rather than percentages are being reported.

Thus, it is perhaps best to use incidences, awkward as it may be, when reporting multiple incidence values as percentages and incidence rates when reporting such values as rates, eg, “at first follow-up, the incidences of falls resulting from frailty, neuromuscular disorders, or improper use of mobility devices were 15% (95% CI, 10%-20%), 12% (95% CI, 7%-17%), and 12% (5%-19%), respectively” or “the incidence rates for falls resulting from frailty, neuromuscular disorders, or improper use of mobility devices were 5.1, 6.3, and 4.6 per person-year, respectively.” Incidentally, these 2 examples report occurrences (falls) rather than diseases or conditions, and so represent 2 instances reporting the incidence of incidents.

To further muddy the waters, incidence is sometimes confused with prevalence, defined as the proportion of persons with a disease at any given time (ie, total number of cases divided by total population). Thus, whereas incidence describes how commonly cases are diagnosed, prevalence describes how widespread the disease already is; on a more personal level, incidence describes one’s risk of developing the disease, whereas prevalence describes the likelihood that one already has it. The confusion between the terms is perhaps attributable to the occasional use of prevalence in place of incidence in the study of rare, chronic diseases for which few newly diagnosed cases are available; however, this circumstance is unusual, and incidence and prevalence should always be distinguished from one another and used appropriately. (See also §20.9, Glossary of Statistical Terms, in the AMA Manual of Style, p 872 in print.)

Whereas prevalence is often used in general contexts to indicate predominance or general acceptance, the circumstances calling for the use of incidence in general contexts are quite few and become fewer still when one takes into account that incidence is often used when incidents (the simple plural of incident) or instance (again denoting an occurrence) would be the better choice. Perhaps incidents or instances was intended but never made it to the page — as is so often the case with homophones and near-homophones, even the careful writer who usually would not confuse incidence, incidents, and instance might one day look back over a hastily typed passage only to see that a wayward incidence has crept in; if the passage is hastily edited to boot, the error might well go unnoticed until the passage is in print and a discerning reader takes pains to point it out in a letter or e-mail. The plural form, incidences, has virtually no use outside of the epidemiologic discussed above, although it has been used to subtly disorienting effect by translators rendering the Kafkaesque works of Russian writer Daniil Kharms (1904-1942) into English, most notably when rendering the 1-word title of Incidences, Kharms’ 1934 collection of absurdist critiques on life in the Soviet Union under Stalin. However, writers who are not political dissidents aiming for absurdist effect — presumably all medical writers — would do well to proofread carefully and often. — Phil Sefton, ELS

# Statistical Rounding and the (Mis)Leading Zero

Sometimes editors (not you or I, of course) obey the rules of their institution’s preferred style manual without fully understanding, or really thinking about, why some of these rules exist. For example, some editors (not you or I, of course) automatically delete (or, if they’re lucky, their editing program deletes for them) the leading zero in a few statistics, but not all. They know exactly when and where to delete the leading zero, but not why. Or they round some statistics, but not all, assuming that all of this has something to do with saving space. It does, of course,1(p830) but this isn’t the only reason we do it.

The AMA Manual of Style defines a P value as “The probability of obtaining the observed data (or data that are more extreme) if the null hypothesis were exactly true.”1(p888) Per AMA style, P values greater than .01 are expressed to a maximum of 2 decimal places and those less than .01 are expressed to a maximum of 3 decimal places. I set out in search of the complicated statistical reason why we use this specific number of decimal places and found that, in addition to saving space, we do it for one simple reason: it’s all we need. Yep, that’s it. It’s all we need to know. P < .00000001 doesn’t tell us any more of value than P < .001. Both tell us that the probability is very low, and that’s good enough. Of course, if the author protests or rounding will make P appear nonsignificant, an exception is made (for example, if P = .046 and significance is set at P = .05).1(pp851-852) Also, studies such as genome-wide association studies report P values of P < .00001 or smaller, often in scientific notation, to address the issue of multiple comparisons; it is essential not to round these. So every rule has exceptions, I guess (remember Spanish class, anyone?).

Why then, you ask, do we not save ourselves the confusion and simply round P < .001 to P = .00? There’s a reason for that, too, and it’s the same reason we don’t use leading zeros with certain probability statistics (ah, you say, it all comes together). If probability is the chance that a given event will occur,2 and we have only surveyed a sample of a given population, probability cannot equal 1.0 or 0 because we can’t say absolutely that a null hypothesis will definitely or definitely not happen in that population.1(p889) And if P can’t equal 1.0 or 0, why include a zero that doesn’t tell us anything new? For this reason, we use P > .99 and P < .001 as the highest and lowest P values. For the same reason, and because they are used often, the leading zero rule applies to α and β probabilities as well. Why? To save space, of course.–Roya Khatiblou, MA

1. Iverson C, Christiansen S, Flanagin A, et al. AMA Manual of Style: A Guide for Authors and Editors. 10th ed. New York, NY: Oxford University Press; 2007.

2. Merriam-Webster’s Collegiate Dictionary. 10th ed. Springfield, MA: Merriam-Webster Inc; 1997.

# Quiz Bowl: Statistical Terms

What’s the difference between an α level and a β level? Do you know your y-axis from your x-axis from your z-axis? What term means the spread or dispersion of data? This month’s quiz, which subscribers can find at http://www.amamanualofstyle.com/, can help you learn the answers to these and other questions on statistical terms. On the basis of your understanding of section 20.9 of the AMA Manual of Style, select the correct answer from the choices listed in the following sample quiz question.

Which of the following terms means the correlation coefficient for bivariate analysis?
r
R
r2
R2

So, how did you do? Here’s the answer (use your mouse to highlight the blank line):

Which of the following terms means the correlation coefficient for bivariate analysis?
r

R is the correlation coefficient for multivariate analysis. r2 is the coefficient of determination for bivariate analysis. R2 is the coefficient to determination for multivariate analysis.

If you want to further test your knowledge of statistical terms, subscribe to the AMA Manual of Style online and take the full quiz. Stay tuned next month for another edition of Quiz Bowl.—Laura King, MA, ELS