Knowledge of regression to the mean can help with everything from interpreting test results to improving your career prospects. All healthcare professionals should be aware of its implication

Morton, V

Torgerson, D J

English

PubMed

White Rose Research Online

This is a repository copy of Effect of regression to the mean on decision making in health care.White Rose Research Online URL for this paper:https://eprints.whiterose.ac.uk/42/Article:Morton, V orcid.org/0000-0003-3783-2030 and Torgerson, D J orcid.org/0000-0002-1667-4275 (2003) Effect of regression to the mean on decision making in health care. British medical journal. pp. 1083-1084. ISSN 0959-535X https://doi.org/10.1136/bmj.326.7398.1083eprints@whiterose.ac.ukhttps://eprints.whiterose.ac.uk/Reuse Items deposited in White Rose Research Online are protected by copyright, with all rights reserved unless indicated otherwise. They may be downloaded and/or printed for private study, or other acts as permitted by national copyright laws. The publisher or other rights holders may allow further reproduction and re-use of the full text version. This is indicated by the licence information on the White Rose Research Online record for the item. Takedown If you consider content in White Rose Research Online to be in breach of UK law, please notify us by emailing eprints@whiterose.ac.uk including the URL of the record and the reason for the withdrawal request. Education and debateEffect of regression to the mean on decision making inhealth careVeronica Morton, David J TorgersonKnowledge of regression to the mean can help with everything from interpreting test results toimproving your career prospects. All healthcare professionals should be aware of its implicationsRegression to the mean is a widespread statistical phe-nomenon with potentially serious implications forhealth care. It can result in wrongly concluding that aneffect is due to treatment when it is due to chance.Ignorance of the problem will lead to errors in decisionmaking. We discuss the importance of the issue and itseffects on many common clinical, public health, andmanagerial decisions.What is regression to the mean?Regression to the mean occurs whenever a non-random sample is selected from a population and twoimperfectly correlated variables are measured, such astwo consecutive blood pressure measurements. Theless correlated the two variables, the larger the effect ofregression to the mean. Also, the more extreme thevalue from the population mean, the more room thereis to regress to the mean. It occurs whenever a group isselected with extreme values for one variable andanother variable is then measured.1 2Francis Galton documented the phenomenon in1886. Galton measured the height of 930 adultchildren and their parents and calculated the averageheight of the parents. He noted that when the averageheight of the parents was greater than the mean of thepopulation, the children tended to be shorter then theparents. Likewise, when the average height of the par-ents was shorter than the population mean, thechildren tended to be taller than their parents. Galtoncalled this phenomenon regression towards medioc-rity, and it is now known as regression to the mean.3Ignorance of this phenomenon is widespread. Pilotinstructors noted that when a trainee pilot was praisedfor a good landing they invariably made a subsequentpoor landing. This was misinterpreted as praise lullingpilots into complacency when the real explanation wasregression towards the mean.4 All healthcare profes-sionals need to be aware of regression to the mean as ithas wide ranging effects.Diagnostic testsClinicians use diagnostic tests to target and monitortreatment. Regression to the mean can confound thisstrategy. The preliminary test has a high probability ofgiving an abnormal result through chance, and initialtreatment may be unnecessary. Because of this chanceeffect, there is a high probability that subsequent meas-urements will spontaneously regress towards the meanvalue. This misleads clinicians and patients into think-ing that treatment has been effective when thetreatment was either not required or ineffective.The figure shows the effect of regression to the meanin women treated for osteoporosis. Some womencontinue to lose bone at the first follow up measure-ment despite effective treatment.5 It is tempting toassume that treatment is ineffective in those women whoare losing bone. However, because of regression to themean, most patients ( > 80%) who lost bone in the firstyear of treatment went on to gain bone in the secondyear despite no change in treatment.The solution to this problem depends on the costand complexity of the test. Firstly, monitoring may beunnecessary. In the case of bone density measurements,one solution is to forego monitoring and change apatient’s treatment only on clinical grounds, such asintolerance. When monitoring of treatment is lessexpensive, such as measuring blood pressure, the effectof regression to the mean can be reduced by takingserial measurements and calculating the averagechange.A further figureis available onbmj.comSummary pointsRegression to the mean affects all aspects ofhealth careAny intervention aimed at a group or characteristicthat is very different from the average will appearto be successful because of regression to the meanIn clinical practice, the phenomenon can lead tomisinterpretation of results of tests, newtreatments, and the placebo effectPublic health interventions are often aimed atsudden increases in disease and thus vulnerableto the effects of regression to the meanYork Trials Unit,Department ofHealth Sciences,University of York,York YO10 5DDVeronica Mortonresearch fellowDavid J TorgersondirectorCorrespondence to:Dr Torgersondjt6@york.ac.ukBMJ 2003;326:1083–41083BMJ VOLUME 326 17 MAY 2003 bmj.comNew treatmentsWhen new treatments become available, someclinicians may yield to the temptation of trying out thetreatment on the patients who are most ill. This under-standable desire to treat clinical outliers will usuallyproduce a gratifying and sharp response to treatmentbecause of regression to the mean. Furthermore, if therelevant clinical trials excluded patients who wereresistant to treatment and clinicians use the treatmentoutside the licensed conditions, they may get themistaken impression that the new treatment is evenbetter among such patients.Placebo effectTrials of hormone replacement therapy show a strongplacebo effect on menopausal symptoms.6 This impliesthat menopausal symptoms are susceptible to placebotreatment. However, a recent systematic review ofplacebo versus “open” no treatment found littleevidence for the placebo effect.7 A more likely explana-tion is that the placebo effect is simply regression to themean. Women recruited to trials of hormonereplacement therapy typically score highly on a symp-tom index. Because the trialists are identifying womenwith relatively extreme menopausal symptoms, oncetreatment starts, improvement will occur in both theplacebo and active treatment groups because ofregression to the mean. An indication that regressionto the mean is occurring is that patients with the worstclinical scores have the biggest placebo effect.Public healthPublic health interventions are often driven byunexpected increases in incidence of disease. A classicexample is the response to a sudden rise in traffic inci-dents. Because a sudden peak in road crashes is oftendue to chance, changes in policy, such as morerigorous enforcement of speed laws, will reducecrashes because of regression to the mean. The policyof vaccinating children against meningitis was intro-duced at a time of heightened incidence (see bmj.com).The headline benefit of a 75%-90% reduction in cases8is an overestimate as most of the reduction would havebeen due to regression to the mean.If public health physicians wish to prove theirworth, our advice is that they focus their efforts on agroup of problems that are much worse than thenational average or have shown an unexpectedincrease as there will usually be an improvement. It isimportant, however, to focus on a group of outliers toguarantee an effect because there is a chance thatregression to the mean will not affect the results of asingle outlier as it is a group phenomenon.Healthcare managementRegression to the mean can justify league tableinitiatives for improving poorly performing hospitals.When poor hospitals are helped by allocating themmore resources, regression to the mean will ensure thatmost will suddenly climb the league table. In contrast,hospitals at the top of the league table who arerewarded with increased resources for their efforts willfall in the table. If governments want to justify any ini-tiative, it is better to target those at the bottom of theleague than those at the top. For the individual hospi-tal manager, the problem is more complex. Those whomanage the worst hospitals are likely to see animprovement and thus enhance their careers. How-ever, because regression to the mean is a groupphenomenon, the improvement is not certain, andsome hospitals will move in the opposite direction.Clinical auditAn audit might identify patients that were operated onby a particular surgical team and had unexpectedlypoor results, such as increased postoperative infec-tions. Implementation of a policy of aggressiveprocedures to control infection will again often seemto work because of regression to the mean.What are the solutions?Understanding the phenomenon is a first step toovercoming the problems caused by regression to themean. Whenever possible, policy should be based onevidence from trials. The effectiveness of managementleague tables, for example, could be tested by randomis-ing poorly performing hospitals to new management orextra resources. This would tell us which interventionwas most effective. In clinical practice, sequential testingto get an average value, which most doctors would do forblood pressure, is a solution for some tests.We thank Ian Watt for his suggestions on the manuscript andEric Faragher, the referee, for helpful comments.Competing interests: None declared.1 Bland JM, Altman DG. Regression towards the mean BMJ 1994;308:1499.2 Bland JM, Altman DG. Some examples of regression towards the mean.BMJ 1994;309:780.3 Galton F. Regression towards mediocrity in hereditary stature. Journal ofthe Anthropological Institute 1886;15:246-63.4 Tversky A, Kahneman D. Judgement under uncertainty: heuristics andbiases. Science 1974:185:1124-31.5 Cummings SR, Palermo L, Browner W, Marcus R, Wallace R, Pearson J, etal. Monitoring osteoporosis therapy with bone densitormetry: misleadingchanges and regression to the mean. JAMA 2000;283:1318-21.6 Pearce J, Hawton K, Blake F. Psychological and sexual symptoms associ-ated with the menopause and the effects of hormone replacementtherapy. Br J Psych 1995;167:163-73.7 Hrobjartsson A, Gotzsche PC. Is the placebo powerless? An analysis ofclinical trials comparing placebo with no treatment. N Engl J Med2001;344:1594-602.8 Wise J. News roundup: meningitis C rates show steep fall. BMJ2001;322:70.(Accepted 5 March 2003)-10Months% change0 12 24-5051015Raloxifene% change-10-5051015Alendronate<-4<-200 to <22 to <44 to <66 to <8>8Percentage changes in bone mineral density among women treated with alendronate orraloxifene after 12 and 24 months, showing regression to the mean at 24 months. Womenare grouped according to the percentage change at 12 months, and values for 24 months arepercentage change from value at 12 monthsEducation and debate1084 BMJ VOLUME 326 17 MAY 2003 bmj.com

Effect of regression to the mean on decision making in health care

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Effect of regression to the mean on decision making in health care

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