Regression to the mean: what it is and how to deal with it.

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.

[1]  Stephen M Stigler,et al.  Regression towards the mean, historically considered , 1997, Statistical methods in medical research.

[2]  J. Twisk,et al.  Applied Longitudinal Data Analysis for Epidemiology: A Practical Guide , 2003 .

[3]  A Chesher,et al.  Non-normal variation and regression to the mean , 1997, Statistical methods in medical research.

[4]  Nan M. Laird,et al.  Further Comparative Analyses of Pretest-Posttest Research Designs , 1983 .

[5]  S. Marcovina,et al.  Biological variability of cholesterol, triglyceride, low- and high-density lipoprotein cholesterol, lipoprotein(a), and apolipoproteins A-I and B. , 1994, Clinical chemistry.

[6]  D. Altman,et al.  Statistics Notes: Some examples of regression towards the mean , 1994 .

[7]  R. Hoffmann,et al.  A history of hypercholesterolemia influences cholesterol measurements. , 1988, Archives of internal medicine.

[8]  S. Senn.  Editorial: regression to the mean , 1997 .

[9]  S. Chinn,et al.  Some further results concerning regression to the mean. , 1981, American Journal of Epidemiology.

[10]  M. Gardner,et al.  Some effects of within-person variability in epidemiological studies , 1973 .

[11]  J. Mckenney,et al.  Effectiveness and tolerability of a new lipid-altering agent, gemcabene, in patients with low levels of high-density lipoprotein cholesterol. , 2003, The American journal of cardiology.

[12]  R. Collins,et al.  Blood pressure, stroke, and coronary heart disease Part 2, short-term reductions in blood pressure: overview of randomised drug trials in their epidemiological context , 1990, The Lancet.

[13]  Gail M. Williams,et al.  Daily sunscreen application and betacarotene supplementation in prevention of basal-cell and squamous-cell carcinomas of the skin: a randomised controlled trial , 1999, The Lancet.

[14]  I. Johnson,et al.  The effects of parity on birthweight using successive pregnancies , 1996, Acta obstetricia et gynecologica Scandinavica.

[15]  W. D. Johnson,et al.  Effect of regression to the mean in the presence of within-subject variability. , 1991, Statistics in medicine.

[16]  R. Collins,et al.  Blood pressure, stroke, and coronary heart disease Part 1, prolonged differences in blood pressure: prospective observational studies corrected for the regression dilution bias , 1990, The Lancet.

[17]  P. L. Yudkin,et al.  How to deal with regression to the mean in intervention studies , 1996, The Lancet.

[18]  D. C. Bauer,et al.  Changes in Biochemical Markers of Bone Turnover in Women Treated with Raloxifene: Influence of Regression to the Mean , 2001, Osteoporosis International.

[19]  C. E. Davis,et al.  The effect of regression to the mean in epidemiologic and clinical studies. , 1976, American journal of epidemiology.

[20]  J. Schwartz,et al.  Changes of nocturnal blood pressure dipping status in hypertensives by nighttime dosing of alpha-adrenergic blocker, doxazosin : results from the HALT study. , 2000, Hypertension.