Regression to the mean: what it is and how to deal with it
Abstract
BACKGROUND: Regression to the mean (RTM) is a statistical phenomenon that can make natural variation in repeated data look like real change. It happens when unusually large or small measurements tend to be followed by measurements that are closer to the mean. METHODS: We give some examples of the phenomenon, and discuss methods to overcome it at the design and analysis stages of a study. RESULTS: The effect of RTM in a sample becomes more noticeable with increasing measurement error and when follow-up measurements are only examined on a sub-sample selected using a baseline value. CONCLUSIONS: RTM is a ubiquitous phenomenon in repeated data and should always be considered as a possible cause of an observed change. Its effect can be alleviated through better study design and use of suitable statistical methods.
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By taking several years as baseline, the study limits concerns associated with regression to the mean.
“By taking several years as baseline, we limit concerns associated with regression to the mean (Barnett et al., 2005).”
From The joint impact of the European Union emissions trading system on carbon emissions and economic performance (2023) · cites this paper as Barnett et al., 2005
Duplicate baseline assessments mitigate the influence of regression to the mean and elevation bias that may confound clinical trials.
“Duplicate baseline assessments will be performed to mitigate the influence of certain non-specific effects (i.e. regression to the mean [179] and elevation bias [180]) that may confound clinical trials.”
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Cites
Blood pressure, stroke, and coronary heart disease
Collins, R., Peto, R., MacMahon, S., Godwin, J., Qizilbash, N., Collins, R., MacMahon, S., Hebert, P., Eberlein, K. A., Taylor, J. O., et al. (1990) · The Lancet · doi:10.1016/0140-6736(90)90944-z · Cited by 4,491 · see citing works
Applied Longitudinal Data Analysis for Epidemiology: A Practical Guide
Twisk, J. W. R. (2003) · Cited by 1,248 · see citing works
Green, A., Williams, G., Nèale, R., Hart, V., Leslie, D., Parsons, P., Marks, G. C., Gaffney, P., Battistutta, D., Frost, C., et al. (1999) · The Lancet · doi:10.1016/s0140-6736(98)12168-2 · Cited by 976 · see citing works
THE EFFECT OF REGRESSION TO THE MEAN IN EPIDEMIOLOGIC AND CLINICAL STUDIES
DAVIS, C. E. (1976) · American Journal of Epidemiology · doi:10.1093/oxfordjournals.aje.a112321 · Cited by 393 · see citing works
Statistics Notes: Some examples of regression towards the mean
Bland, J. M., & Altman, D. G. (1994) · BMJ · doi:10.1136/bmj.309.6957.780 · Cited by 381 · see citing works
Regression towards the mean, historically considered
Stigler, S. M. (1997) · Statistical Methods in Medical Research · doi:10.1177/096228029700600202 · Cited by 253 · see citing works
Some effects of within-person variability in epidemiological studies
Gardner, M. J., & Heady, J. A. (1973) · Journal of Chronic Diseases · doi:10.1016/0021-9681(73)90013-1 · Cited by 207 · see citing works
How to deal with regression to the mean in intervention studies
Yudkin, P. L., & STRATTON, I. M. (1996) · The Lancet · doi:10.1016/s0140-6736(96)90410-9 · Cited by 196 · see citing works
Kario, K., Schwartz, J. E., & Pickering, T. G. (2000) · Hypertension · doi:10.1161/01.hyp.35.3.787 · Cited by 164 · see citing works
Shephard, R. J. (2003) · Sports Medicine · doi:10.2165/00007256-200333080-00003 · Cited by 126 · see citing works
Marcovina, S. M., Gaur, V. P., & Albers, J. J. (1994) · Clinical Chemistry · doi:10.1093/clinchem/40.4.574 · Cited by 102 · see citing works
The effects of parity on birthweight using successive pregnancies
Wilcox, M. A., Chang, A. M. Z., & Johnson, I. R. (1996) · Acta Obstetricia Et Gynecologica Scandinavica · doi:10.3109/00016349609033354 · Cited by 100 · see citing works
Bays, H. E., McKenney, J. M., Dujovne, C. A., et al. (2003) · The American Journal of Cardiology · doi:10.1016/s0002-9149(03)00721-5 · Cited by 45 · see citing works
Effect of regression to the mean in the presence of within‐subject variability
Johnson, W. D., & George, V. T. (1991) · Statistics in Medicine · doi:10.1002/sim.4780100812 · Cited by 43 · see citing works
Non-normal variation and regression to the mean
Chesher, A. (1997) · Statistical Methods in Medical Research · doi:10.1177/096228029700600205 · Cited by 20 · see citing works
SOME FURTHER RESULTS CONCERNING REGRESSION TO THE MEAN1
Chinn, S., & Heller, R. F. (1981) · American Journal of Epidemiology · doi:10.1093/oxfordjournals.aje.a113260 · Cited by 20 · see citing works
Chapurlat, R. D., BLACKWELL, T. L., Bauer, D. C., et al. (2001) · Osteoporosis International · doi:10.1007/s001980170009 · Cited by 13 · see citing works
A history of hypercholesterolemia influences cholesterol measurements.
Schectman, G., & Hoffmann, R. G. (1988) · PubMed · Cited by 8 · see citing works
Meningitis C rates show steep fall
Wise, J. (2001) · BMJ · doi:10.1136/bmj.322.7278.70/d · Cited by 2 · see citing works
Flagged first, then by citations
Research works printed but not linked: 2
- 20 Laird N. Further comparative analysis of pre-test post-test research designs. Am Statistician 1983; 37: 329-30.
- 21 Senn S. Regression to the mean. Statist Meth Med Res 1997; 6: 99-102.
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A Controlled Trial of Renal Denervation for Resistant Hypertension
Bhatt, D. L., Kandzari, D. E., O'Neill, W. W., D'Agostino, R., Flack, J. M., Katzen, B. T., Leon, M. B., Liu, M., Mauri, L., Negoita, M., et al. (2014) · New England Journal of Medicine · doi:10.1056/nejmoa1402670 · Cited by 2,186 · see citing works
Inkster, B., Sarda, S., & Subramanian, V. (2018) · doi:10.2196/preprints.12106 · Cited by 1,063 · see citing works
Translating the Diabetes Prevention Program into the Community
Ackermann, R. T., Finch, E. A., Brizendine, E., Zhou, H., & Marrero, D. G. (2008) · American Journal of Preventive Medicine · doi:10.1016/j.amepre.2008.06.035 · Cited by 622 · see citing works
Different ways to estimate treatment effects in randomised controlled trials
J, T., L, B., T, H., J, R., M, W., & M, H. (2018) · Contemporary Clinical Trials Communications · doi:10.1016/j.conctc.2018.03.008 · Cited by 532 · see citing works
Detecting and avoiding likely false‐positive findings – a practical guide
Forstmeier, W., Wagenmakers, E., & Parker, T. H. (2017) · Biological Reviews · doi:10.1111/brv.12315 · Cited by 436 · see citing works
Vaiserman, A., & Krasnienkov, D. (2021) · Frontiers in Genetics · doi:10.3389/fgene.2020.630186 · Cited by 454 · see citing works
Effectiveness of manual therapies: the UK evidence report
Bronfort, G., Haas, M., Evans, R., Leininger, B., & Triano, J. (2010) · Chiropractic & Osteopathy · doi:10.1186/1746-1340-18-3 · Cited by 434 · see citing works
Dechezleprêtre, A., Nachtigall, D., & Venmans, F. (2023) · Journal of Environmental Economics and Management · doi:10.1016/j.jeem.2022.102758 · Cited by 416 · see citing works
Treatment of internet addiction: a meta-analysis
Winkler, A., Dörsing, B., Rief, W., Shen, Y., & Glombiewski, J. A. (2013) · Clinical Psychology Review · doi:10.1016/j.cpr.2012.12.005 · Cited by 404 · see citing works
Fried, E. I., van Borkulo, C. D., Epskamp, S., Schoevers, R. A., Tuerlinckx, F., & Borsboom, D. (2016) · Psychological Assessment · doi:10.1037/pas0000275 · Cited by 314 · see citing works
Matching and Regression to the Mean in Difference‐in‐Differences Analysis
Daw, J. R., & Hatfield, L. A. (2018) · Health Services Research · doi:10.1111/1475-6773.12993 · Cited by 270 · see citing works
A Model of Placebo Response in Antidepressant Clinical Trials
Rutherford, B. R., & Roose, S. P. (2013) · American Journal of Psychiatry · doi:10.1176/appi.ajp.2012.12040474 · Cited by 268 · see citing works
Engvig, A., Fjell, A. M., Westlye, L. T., Moberget, T., Sundseth, Ø., Larsen, V. A., & Walhovd, K. B. (2012) · Human Brain Mapping · doi:10.1002/hbm.21370 · Cited by 250 · see citing works
Bambs, C., Kip, K. E., Dinga, A., Mulukutla, S. R., Aiyer, A. N., & Reis, S. E. (2011) · Circulation · doi:10.1161/circulationaha.110.980151 · Cited by 235 · see citing works
Aday, J. S., Heifets, B. D., Pratscher, S. D., Bradley, E., Rosen, R., & Woolley, J. D. (2022) · Psychopharmacology · doi:10.1007/s00213-022-06123-7 · Cited by 237 · see citing works
Araghi, M. H., Chen, Y.-F., Jagielski, A., Choudhury, S., Banerjee, D., Hussain, S., Thomas, G. N., & Taheri, S. (2013) · Sleep · doi:10.5665/sleep.3056 · Cited by 214 · see citing works
Qouta, S. R., Palosaari, E., Diab, M., & Punamäki, R. (2012) · Journal of Traumatic Stress · doi:10.1002/jts.21707 · Cited by 197 · see citing works
Haun, C. T., Vann, C. G., Roberts, B. M., Vigotsky, A. D., Schoenfeld, B. J., & Roberts, M. D. (2019) · Frontiers in Physiology · doi:10.3389/fphys.2019.00247 · Cited by 192 · see citing works
Having a creative day: understanding entrepreneurs' daily idea generation through a recovery lens
Weinberger, E., Wach, D., Stephan, U., & Wegge, J. (2018) · Journal of Business Venturing · doi:10.1016/j.jbusvent.2017.09.001 · Cited by 181 · see citing works
Clifton, L., & Clifton, D. A. (2019) · Trials · doi:10.1186/s13063-018-3108-3 · Cited by 178 · see citing works
Ezpeleta, M., Gabel, K., Cienfuegos, S., Kalam, F., Lin, S., Pavlou, V., Song, Z., Haus, J. M., Koppe, S., Alexandria, S. J., et al. (2023) · Cell Metabolism · doi:10.1016/j.cmet.2022.12.001 · Cited by 181 · see citing works
Correcting for Regression to the Mean in Behavior and Ecology
Kelly, C., & Price, T. D. (2005) · The American Naturalist · doi:10.1086/497402 · Cited by 163 · see citing works
Homeopathic medical practice: Long-term results of a cohort study with 3981 patients
Witt, C. M., Lüdtke, R., Baur, R., & Willich, S. N. (2005) · BMC Public Health · doi:10.1186/1471-2458-5-115 · Cited by 134 · see citing works
Crane, D., Garnett, C., Michie, S., West, R., & Brown, J. (2018) · Scientific Reports · doi:10.1038/s41598-018-22420-8 · Cited by 118 · see citing works
Raising early achievement in math with interactive apps: A randomized control trial.
Outhwaite, L. A., Faulder, M., Gulliford, A., & Pitchford, N. J. (2019) · Journal of Educational Psychology · doi:10.1037/edu0000286 · Cited by 124 · see citing works
Hengartner, M. P., & Plöderl, M. (2022) · BMJ Evidence-Based Medicine · doi:10.1136/bmjebm-2020-111600 · Cited by 114 · see citing works
Calcium and dairy intakes in relation to long-term weight gain in US men
Rajpathak, S. N., Rimm, E. B., Rosner, B., Willett, W. C., & Hu, F. B. (2006) · The American Journal of Clinical Nutrition · doi:10.1093/ajcn.83.3.559 · Cited by 116 · see citing works
Emotional support during times of stress: can text messaging compete with in-person interactions?
Holtzman, S., DeClerck, D., Turcotte, K., Lisi, D., & Woodworth, M. (2017) · Computers in Human Behavior · doi:10.1016/j.chb.2017.01.043 · Cited by 106 · see citing works
Kleindienst, N., Priebe, K., Görg, N., Dyer, A., Steil, R., Lyssenko, L., Winter, D., Schmahl, C., & Bohus, M. (2016) · European Journal of Psychotraumatology · doi:10.3402/ejpt.v7.30375 · Cited by 105 · see citing works
Schwarz, E., Guest, P. C., Steiner, J., Bogerts, B., & Bahn, S. (2012) · Translational Psychiatry · doi:10.1038/tp.2012.3 · Cited by 91 · see citing works
Sjöholm, K., Pajunen, P., Jacobson, P., Karason, K., Sjöström, C. D., Torgerson, J., Carlsson, L. M. S., Sjöström, L., & Peltonen, M. (2015) · Diabetologia · doi:10.1007/s00125-015-3591-y · Cited by 86 · see citing works
Antioxidants in Personalized Nutrition and Exercise
Margaritelis, N. V., Paschalis, V., Theodorou, A. A., Kyparos, A., & Nikolaidis, M. G. (2018) · Advances in Nutrition · doi:10.1093/advances/nmy052 · Cited by 84 · see citing works
Early enhanced processing and delayed habituation to deviance sounds in autism spectrum disorder
Hudac, C. M., DesChamps, T. D., Arnett, A. B., Cairney, B. E., Ma, R., Webb, S. J., & Bernier, R. A. (2018) · Brain and Cognition · doi:10.1016/j.bandc.2018.03.004 · Cited by 81 · see citing works
Levinson, C. A., Christian, C., Ram, S. S., Vanzhula, I., Brosof, L. C., Michelson, L. P., & Williams, B. M. (2020) · Journal of Affective Disorders · doi:10.1016/j.jad.2020.07.075 · Cited by 79 · see citing works
BERNSTEIN, J. A., BERNSTEIN, E., & HEEREN, T. C. (2010) · Drug and Alcohol Review · doi:10.1111/j.1465-3362.2010.00174.x · Cited by 68 · see citing works
What aspects of online peer feedback robustly predict growth in students' task performance?
Zong, Z., Schunn, C. D., & Wang, Y. (2021) · Computers in Human Behavior · doi:10.1016/j.chb.2021.106924 · Cited by 61 · see citing works
Ackermann, R. T., Finch, E. A., Caffrey, H. M., Lipscomb, E. R., Hays, L. M., & Saha, C. (2011) · Chronic Illness · doi:10.1177/1742395311407532 · Cited by 58 · see citing works
Herwanto, V., Shetty, A., Nalos, M., Chakraborty, M., McLean, A., Eslick, G. D., & Tang, B. (2019) · Critical Care Explorations · doi:10.1097/cce.0000000000000043 · Cited by 58 · see citing works
McCambridge, J., Kypri, K., & McElduff, P. (2014) · Drug and Alcohol Dependence · doi:10.1016/j.drugalcdep.2013.11.017 · Cited by 54 · see citing works
Cimino, S., Cerniglia, L., Almenara, C. A., Jezek, S., Erriu, M., & Tambelli, R. (2016) · Scientific Reports · doi:10.1038/srep20211 · Cited by 50 · see citing works
Ronk, F. R., Hooke, G. R., & Page, A. C. (2012) · Clinical Psychology Science and Practice · doi:10.1111/j.1468-2850.2012.01281.x · Cited by 47 · see citing works
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d’Huart, D., Steppan, M., Seker, S., Bürgin, D., Boonmann, C., Birkhölzer, M., Jenkel, N., Fegert, J. M., Schmid, M., & Schmeck, K. (2022) · Frontiers in Psychiatry · doi:10.3389/fpsyt.2022.840678 · Cited by 35 · see citing works
Schröder, J., Jelinek, L., & Moritz, S. (2017) · Journal of Behavior Therapy and Experimental Psychiatry · doi:10.1016/j.jbtep.2016.05.002 · Cited by 32 · see citing works
Daniel, K. E., Daros, A. R., Beltzer, M. L., Boukhechba, M., Barnes, L. E., & Teachman, B. A. (2020) · Cognitive Therapy and Research · doi:10.1007/s10608-020-10088-2 · Cited by 26 · see citing works
Worksite Health Promotion: The Value of the Tune Up Your Heart Program
Chung, M., Melnyk, P., Blue, D., Renaud, D., & Breton, M.-C. (2009) · Population Health Management · doi:10.1089/pop.2008.0044 · Cited by 25 · see citing works
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Salavati, B., Seeman, M. V., Agha, M., Atenafu, E., Chung, J., Nathan, P. C., & Barrera, M. (2014) · Children's Health Care · doi:10.1080/02739615.2013.837820 · Cited by 19 · see citing works
Sieder, K., Thiedmann, P., Voracek, M., & Tran, U. S. (2024) · Applied Psychology: Health and Well-Being · doi:10.1111/aphw.12550 · Cited by 16 · see citing works
Björnsdóttir, S. V., Triebel, J., Arnljótsdóttir, M., Tómasson, G., & Valdimarsdóttir, U. A. (2018) · Disability and Rehabilitation · doi:10.1080/09638288.2017.1312565 · Cited by 14 · see citing works
Browning, M. E., Morena, A., Gould, E. R., & Lloyd-Richardson, E. E. (2023) · Journal of College Student Psychotherapy · doi:10.1080/87568225.2022.2029659 · Cited by 12 · see citing works
Fragkos, K. C., Keetarut, K., Cox, A., Eady, J., Emmanuel, A. V., & Zarate-Lopez, N. (2019) · Gastroenterology Research · doi:10.14740/gr1133 · Cited by 11 · see citing works
de Viron, S., Trotta, L., Steijn, W., Young, S., & Buyse, M. (2024) · Therapeutic Innovation & Regulatory Science · doi:10.1007/s43441-024-00613-w · Cited by 9 · see citing works
“A theoretical concern exists that sites observed with a high DIS at one timepoint will naturally tend toward a lower DIS subsequently due to a regression-to-the-mean effect [21].”
BackgroundPerez, T. M., Glue, P., Adhia, D. B., Navid, M. S., Zeng, J., Dillingham, P., Smith, M., Niazi, I. K., Young, C. K., & De Ridder, D. (2022) · Trials · doi:10.1186/s13063-022-06863-z · Cited by 8 · see citing works
“regression to the mean [179] and elevation bias [180]) that may confound clinical trials.”
BackgroundBortoncello, C. F., Cardoso, N. D. O., Salvador, E. Z., de Avila, R. C., Machado, W. D. L., & Ferrão, Y. A. (2022) · Brazilian Journal of Psychiatry · doi:10.47626/1516-4446-2021-2264 · Cited by 8 · see citing works
Nilsen, R., Pripp, A. H., Høstmark, A. T., Haug, A., & Skeie, S. (2016) · Food & Nutrition Research · doi:10.3402/fnr.v60.32017 · Cited by 8 · see citing works
Bisby, M. A., Chandra, S. S., Scott, A. J., Dudeney, J., Titov, N., & Dear, B. F. (2023) · The Journal of Pain · doi:10.1016/j.jpain.2023.06.004 · Cited by 4 · see citing works
Reviewer2: Optimizing Review Generation Through Prompt Generation
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Zhong, L.-A., Chen, K.-Y., Hsieh, M.-J., & Ho, M.-C. (2025) · Acta Psychologica · doi:10.1016/j.actpsy.2025.105499 · Cited by 1 · see citing works
- Authors
- Barnett, A. G.
- Affiliations
- The University of Queensland (AU)
- Corresponding author
- Barnett, A. G
- ORCID
- Barnett, A. G
- Venue
- International Journal of Epidemiology
- Publisher
- Oxford University Press (OUP)
- Published
- 2004-08-27
- Volume
- 34
- Issue
- 1
- Pages
- 215-220
- ISSN
- 0300-5771 (ISSN-L)
- 1464-3685
- OpenAlex
- W2155188667
- Semantic Scholar
- afe8b4315341c30682d3cb34c9028add4471841c
- Cited by
- 1,988
- References
- 20
- Citations by year
- 2026: 199 · 2025: 147 · 2024: 163 · 2023: 131 · 2022: 145 · 2021: 140 · 2020: 115 · 2019: 97 · 2018: 106 · 2017: 89 · 2016: 92 · 2015: 108 · 2014: 88 · 2013: 80 · 2012: 60
- FWCI
- 17.89
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- International Journal of Epidemiology (publishedVersion)
- PubMed (publishedVersion)
- Funders
- National Health and Medical Research Council
- National Medical Research Council
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Epidemiology
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Clinical Trials
- Keywords
- regression to the mean, repeated measures, measurement error, research design, baseline selection, follow-up data, natural variation, statistical analysis
- MeSH terms
- Clinical Trials as Topic, Data Interpretation, Statistical, Humans, Cholesterol, HDL, Regression Analysis, Research Design, Skin Neoplasms
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