Forest Plots: Trying to See the Wood and the Trees
Total Page:16
File Type:pdf, Size:1020Kb
Downloaded from bmj.com on 10 September 2007 Forest plots: trying to see the wood and the trees Steff Lewis and Mike Clarke BMJ 2001;322;1479-1480 doi:10.1136/bmj.322.7300.1479 Updated information and services can be found at: http://bmj.com/cgi/content/full/322/7300/1479 These include: References This article cites 6 articles, 1 of which can be accessed free at: http://bmj.com/cgi/content/full/322/7300/1479#BIBL 12 online articles that cite this article can be accessed at: http://bmj.com/cgi/content/full/322/7300/1479#otherarticles Rapid responses 7 rapid responses have been posted to this article, which you can access for free at: http://bmj.com/cgi/content/full/322/7300/1479#responses You can respond to this article at: http://bmj.com/cgi/eletter-submit/322/7300/1479 Email alerting Receive free email alerts when new articles cite this article - sign up in the box at service the top left of the article Topic collections Articles on similar topics can be found in the following collections Systematic reviews (incl meta-analyses): descriptions (135 articles) Other Statistics and Research Methods: descriptions (600 articles) Notes To order reprints follow the "Request Permissions" link in the navigation box To subscribe to BMJ go to: http://resources.bmj.com/bmj/subscribers Downloaded from bmj.com on 10 September 2007 Education and debate Forest plots: trying to see the wood and the trees Steff Lewis, Mike Clarke Few systematic reviews containing meta-analyses are Neurosciences complete without a forest plot. But what are forest Trials Unit, Summary points Department of plots, and where did they come from? Clinical Neurosciences, Forest plots show the information from the University of individual studies that went into the meta-analysis Edinburgh, Western What is a forest plot? General Hospital, at a glance Edinburgh In a typical forest plot, the results of component stud- EH4 2XU ies are shown as squares centred on the point estimate They show the amount of variation between the Steff Lewis of the result of each study. A horizontal line runs studies and an estimate of the overall result medical statistician through the square to show its confidence interval— UK Cochrane Forest plots, in various forms, have been Centre, NHS usually, but not always, a 95% confidence interval. The Research and overall estimate from the meta-analysis and its published for about 20 years Development confidence interval are put at the bottom, represented Programme, Oxford OX2 7LG as a diamond. The centre of the diamond represents During this time, they have been improved, but it is still not easy to draw them in most standard Mike Clarke the pooled point estimate, and its horizontal tips associate director represent the confidence interval. Significance is computer packages (research) achieved at the set level if the diamond is clear of the Correspondence to: line of no effect. S Lewis [email protected] The plot allows readers to see the information from nication). He based the idea on modified box plots.4 the individual studies that went into the meta-analysis Ideas such as radial plots were also proposed.56 BMJ 2001;322:1479–80 at a glance. It provides a simple visual representation of The first meta-analyses to include squares of differ- the amount of variation between the results of the ent sizes to show the positions of the point estimates studies, as well as an estimate of the overall result of all were probably those produced by the Clinical Trial the studies together. Forest plots increasingly feature in Service Unit in Oxford in the 1998 overview of the medical journals, and the growth of the Cochrane Col- prevention of vascular disease by antiplatelet therapy.7 laboration has seen the publication of thousands in 1 The area of each square was proportional to the weight recent years. that the individual study contributed to the meta- analysis. History The origin of forest plots goes back at least to the 1970s. Freiman et al displayed the results of several Oxprenolol Wilcox Propranolol Norris studies with horizontal lines showing the confidence Propranolol Multicentre interval for each study and a mark to show the point Propranolol Baber estimate. This study was not a meta-analysis, and the Atenolol Wilcox Alprenolol Andersen results of the individual studies were therefore not Propranolol Balcon 2 combined into an overall result. In 1982, Lewis and Propranolol Wilcox Ellis produced a similar plot but this time for a Practolol Barber Oxprenolol CPRG meta-analysis, and they put the overall effect on the Narrow Practolol Multicentre bottom of the plot (fig 1 ).3 However, smaller studies, confidence limits Propranolol Barber with less precise estimates of effect, had larger Propranolol BHAT Timolol Multicentre confidence intervals and, perversely, were the most Metoprolol Hjalmarson noticeable on the plots. Alprenolol Wilhelmsson Means of focusing attention on the larger, more All β blockers Pooled precise, studies were sought. Replacement of the mark with a square whose size was proportional to the preci- -300 -250 -200 -150 -100 -50 0 50 100% sion of the estimate may have been first suggested by Increase in mortality on treatment Reduction in mortality on treatment Stephen Evans at a Royal Statistical Society medical Fig 1 First use of forest plot for meta-analysis of effect of â blockers on mortality3 section meeting at the London School of Hygiene and (reproduced with permission from Physicians World/Thomson Healthcare, Secaucus, NJ) Tropical Medicine in 1983 (S Evans, personal commu- BMJ VOLUME 322 16 JUNE 2001 bmj.com 1479 Education and debate Downloaded from bmj.com on 10 September 2007 ß blocker deaths and they came from specially produced computer No (%) of deaths patients Logrank Variance Ratio of crude death rates (99% CI) programs. Even now, most standard statistical packages observed of observed Study ß blocker Control – expected – expected ß blocker: control cannot easily produce such a plot. Wilcox 14/157 10/158 2.0 5.6 (oxprenolol) (8.9) (8.9) Why a forest plot? Norris 21/226 24/228 -1.4 10.2 (propranolol) (9.3) (9.3) The plot was not called a “forest plot” in print for some Multicentre 15/100 12/95 1.2 5.8 time, and the origins of this title are obscured by (15.0) (12.6) (propranolol) history and myth. At the September 1990 meeting of Baber 28/355 27/365 0.9 12.7 (propranolol) (7.9) (7.4) the breast cancer overview, Richard Peto jokingly men- Andersen 61/238 64/242 -1.0 23.2 tioned that the plot was named after the breast cancer (alprenolol) (25.6) (26.4) researcher Pat Forrest, and, at times, the name has been Balcon 14/56 15/58 -0.2 5.5 (propranolol) (25.0) (25.9) spelt “forrest plot.” However, the phrase actually origi- Barber 47/221 53/228 -2.2 19.5 nates from the idea that the typical plot appears as a (practolol) (21.3) (23.2) forest of lines. A contender for the first use of the name Wilcox 36/259 19/129 -0.7 10.5 (propranolol) (13.9) (14.7) “forest plot” in print is a review of nursing 9 CPRG 9/177 5/136 1.1 3.3 interventions for pain that was published in 1996. An (oxprenolol) (5.1) (3.6) abstract at the Cochrane colloquium later that year Multicentre 102/1533 127/1520 -13.0 53.0 also used this name.10 We would welcome suggestions (practolol) (6.7) (8.4) of precedents to these uses or any other versions of this Barber 10/52 12/47 -1.6 4.3 (propranolol) (19.2) (25.5) brief history of the plot. BHAT 138/1916 188/1921 -24.8 74.6 (propranolol) (7.2) (9.8) We thank Jon Godwin for preparing figure 2. Multicentre 98/945 152/939 -27.4 54.2 Funding: None. (timolol) (10.4) (16.2) Competing interests: None declared. Hjalmarson 40/698 62/697 -11.0 23.7 (5.7) (8.9) (metoprolol) 1 Cochrane Collaboration. Cochrane Library. Issue 1. Oxford: Update Soft- Wilhelmsson 7/114 14/116 -3.4 4.8 ware, 2001. (alprenolol) (6.1) (12.1) 2 Freiman JA, Chalmers TC, Smith H, Kuebler RR. The importance of beta, the type II error and sample size in the design and interpretation of the randomized control trial: survey of 71 “negative trials”. N Engl J Med Total* 640/7047 784/6879 -81.6 310.7 1978;299:690-4. (9.1) (11.4) 3 Lewis JA, Ellis SH. A statistical appraisal of post-infarction beta-blocker 0 0.5 1.0 1.5 2.0 trials. Prim Cardiol 1982;suppl 1:31-7. Reduction 23.1% (SE5.0) P<0.0001 ß blocker better ß blocker worse 4 McGill R, Tukey JW, Larsen WA. Variations of box plots. Am Stat 1978;32:12-6. Heterogeneity between 15 trials: χ2 = 13.9; df = 14; P > 0.1 Treatment effect P < 0.0001 5 DeMets DL. Methods for combining randomized clinical trials: strengths and weaknesses. Stat Med 1987;6:341-50. * 95% confidence interval as shown for the odds ratio 6 Galbraith RL. A note on graphical presentation of estimated odds ratios Fig 2 Updated version of Lewis and Ellis’s original plot (fig 1 ) showing effect of â blockers from several clinical trials. Stat Med 1988;7:889-94. on mortality 7 Antiplatelet Trialists’ Collaboration. Secondary prevention of vascular disease by prolonged antiplatelet treatment. BMJ 1988;296:320-31. 8 Yusuf S, Peto R, Lewis J, Collins R, Sleight P.