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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

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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 . 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 through the square to show its — UK 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 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 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 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 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. Beta blockade during and after myocardial infarction: an overview of the randomized trials. Prog Cardiovasc Dis 1985;275:335-71. We have updated the original Lewis and Ellis plot3 9 Sindhu F. Are non-pharmacological nursing interventions for the manage- ment of pain effective? A meta-analysis. J Adv Nurs 1996;24:1152-9. to show how it might look in the modern style (fig 2 ). 10 Bijnens L, Collette L, Ivanov A, Hoctin Boes G, Sylvester R. Optimal We obtained for most of the component studies graphical display of the results of meta-analyses of individual patient 8 data. In: Proceedings of the 4th Cochrane colloquium, Adelaide, Australia, 1996. from a subsequent paper. In the 1980s, no standard Oxford: Cochrane Collaboration, 1996. computer packages could easily produce these plots, (Accepted 20 February 2001)

A memorable patient A chandelier and a vat of custard

It was a busy Friday night in casualty. We were one senior house It took a second or two for me to realise what he’d said. I officer down and there had been a major accident on a nearby looked up at him in disbelief. “Really?” I asked. “No,” he said, “but main road. All of us had been looking after seriously injured I’ve been sitting in the waiting room for two hours trying to pluck patients for the preceding couple of hours—not all of them had up the courage to say that.” survived, and emotions were running high. During that time, the As a grin broke over my face, I asked what had really backlog of minor injuries had built up to a six hour wait, and happened, and he told me what he had done. As I treated him, I tempers were fraying in the waiting room. The nurses were relaxed and chatted to him as a real person, not a patient. fielding angry patients, often with trivial injuries, and were I spent the rest of the shift smiling. It inspired me to think that desperate for one of us to come and help. someone faced with a long wait had thought up something like I returned to the minor side to start clearing the backlog as that, and kept it in his mind, without getting annoyed or soon as possible. I was in a superefficient and slightly impatient. He changed my perspective, brightened up my short-tempered mood—didn’t they realise that we had to deal evening, and reminded me of the fact that people, not patients, with far more important things than cut fingers or drunks? I were in the waiting room. picked the next card out of the box and went to the cubicle. I have long since forgotten his name, but I still think about him With barely a glance at the patient I said brusquely, “Well, what’s the matter then?” A middle aged man looked back at me when I’m having a bad day. and said, in a nonchalant tone, “I was preparing for my usual Friday night sexual activity when the chandelier broke, and I fell Katherine Whybrew GP registrar, 19 Beaumont Street Surgery, into the vat of custard.” Oxford

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