# The forest plot and the box-and-whisker plot

To quote the college, "candidates either knew this topic or knew nothing about it". We have all seen these graphs before, but when pushed to give specific definitions people tend to do poorly. Fortunately, there is not much to know.

The forest plot has appeared in many past paper questions:

Primary Exam:

Fellowship Exam:

The box-and-whisker plot has never appeared in any Part II papers, but made frequent appearances in Part I:

In brief summary, this is all the exam candidate is expected to know to satisfy the college demands:

Now, to revel in apocryphal detail:

## The box and whisker plot

The box and whisker plot is a way of graphically representing the "five number summary", or four parameters which demonstrate the central tendency of the data set.

• Range (the minimum and maximum values)
• First quartile (25%)
• Third quartile (75%)
• Median, represented by the vertical bar in the centre

Uses of this graph:

• Good for comparing distributions (the centre, spread and overall range are immediately apparent)
• Useful for indicating whether a distribution is skewed
• Detects outliers
• Useful for summarising a set of data measured on an interval scale

This thing was invented by John W. Tukey, the man also responsible for introducing the term "bit" to computers. He introduced the world to this concept in 1977, in his book "Exploratory Data Analysis." Tukey's original drawings had slightly different conventions (for instance, he extended the whiskers all the way to the extreme data points whereas modern box-and-whisker plots tend to extend the "whiskers" to the farthest points that are not outliers (i.e, that are within 3/2 times the interquartile range of the first and third quartiles). Other weird conventions exist, for instance whether to add dots or circles for every outlier data point, etc.

Judging by the college answer to Question 14 from the second paper of 2014, the examiners either don't know or don't care about such nonsense. Myles and Gin are the reference text, and offer only a bare minimum. On page 17 (Ch. 2, Descriptive statistics) they offer an unlabelled box and whisker plot of creatinine clearance as an example, and spend literally three lines on it (listing the five data points it represents). The rest of the brief section is wasted on highly specific and useful statements like "tables and diagrams are a convenient way of summarisizing data". One supposes we must be grateful for even these scraps; the forest plot is completely ignored by that entire textbook and the trainee who used textbooks exclusively will find themselves ill-prepared for the forest plot questions (of which there have now been four).

## Anatomy of the Forest Plot

This thing is also more properly referred to as a "conﬁdence interval plot", or - if Wikipedia is to be believed - a blobbogram. It is in essence a series of severely mutated box-and-whisker plots, stacked together and summarised in a manner which favours rapid assessment by persons well instructed in the interpretation of such graphics.

In summary, its properties are as follows:

• The x-axis: odds ratio
• The y-axis: a list of studies. How you list them is a lawless free-for-all; Anzures-Cabrera reports that "no general recommendation is appropriate for the order in which the studies should be presented in a forest plot. Many authors default to an alphabetical ordering for ease of cross-referencing with tables and reference lists"
• The vertical line: line of "no effect", OR=1.0
• The horizontal lines: the confidence interval of the individual study
• The position of the square: a point estimate of the odds ratio (OR)
• The size of the square: the weight of the study according to the weighing rules of the meta-analysis, likely representing the sample size and statistical power. This is a powerful tool of psychological manipulation. A paper by a couple of psychiatrists dissected this practice, and suggested that a failure to use square size to identify study weight "may result in unnecessary attention being attracted to those smaller studies with wider confidence intervals that put more ink on the page (or more pixels on the screen)".
• The diamond at the bottom: the combined result of the trial
• Results can be considered statistically significant if the confidence intervals of the combined result do not cross the line of no effect

From the college's lazy answer to Question 14 from the first paper of 2017, some candidates might get the impresison that occasionally it is ok to refer to this representation as a "Forrest plot". That would be an incorrect impression. It's a forest plot. Because it looks like a forest of lines. Forrest is the surname of Pat Forrest, a medical oncologist. A fellow medical oncologist joked about the plot being named after Forrest at some sort of provincial breast cancer meeting in 1990 (Lewis & Clarke; 2001). Idiotic terminological laxity had ensued from this. Let us maintain high standards in medical literature by eradicating it.

## References

Methodological Expectations of Cochrane Intervention Reviews

Schriger, David L., et al. "Forest plots in reports of systematic reviews: a cross-sectional study reviewing current practice." International journal of epidemiology39.2 (2010): 421-429.

Lewis, Steff, and Mike Clarke. "Forest plots: trying to see the wood and the trees." Bmj 322.7300 (2001): 1479-1480.

Anzures‐Cabrera, Judith, and Julian Higgins. "Graphical displays for meta‐analysis: An overview with suggestions for practice." Research Synthesis Methods 1.1 (2010): 66-80.

Cochrane: "Considerations and recommendations for
figures in Cochrane reviews: graphs of statistical data"
4 December 2003 (updated 27 February 2008)

Reade, Michael C., et al. "Bench-to-bedside review: Avoiding pitfalls in critical care meta-analysis–funnel plots, risk estimates, types of heterogeneity, baseline risk and the ecologic fallacy." Critical Care 12.4 (2008): 220.

DerSimonian, Rebecca, and Nan Laird. "Meta-analysis in clinical trials."Controlled clinical trials 7.3 (1986): 177-188.

Biggerstaff, B. J., and R. L. Tweedie. "Incorporating variability in estimates of heterogeneity in the random effects model in meta-analysis." Statistics in medicine 16.7 (1997): 753-768.

The Cochrane Handbook: 9.5.4 "Incorporating heterogeneity into random-effects model"

Larsen, Russell D. "Box-and-whisker plots." J. Chem. Educ 62.4 (1985): 302.

Weisstein, Eric W. "Box-and-whisker plot.From MathWorld–A Wolfram Web Resource.[Cited 2006 June 7]. Available from: URL: http://mathwold. wolfram. com/Box-and-Whiskerplot (1999).

Tukey, J. W. "Box-and-Whisker plots, in: Exploratory Data Analysis." (1977).