This paper examines mathematically the origin of the regression toward the mean phenomenon. The magnitude of regression effect in terms of mean and mean percentage change for a selected target population was calculated under the assumption of a bivariate normal distribution. The impact of regression effect on the statistical estimation of a treatment effect was addressed. Methods to reduce and to adjust for regression effect were reviewed and discussed. Questions concerning the designs and the analyses of clinical trials in light of the presence of regression effect were posed.
McDonaldCJMazzucaSAMcCabeGPJr.How much of the placebo ‘effect’ is really statistical regression?Stat Med.1983;2:417–427.
2.
GaltonF. Regression towards mediocrity in hereditary stature. J Anthropological Institute. 1886;5: 246–263.
3.
JamesKE. Regression toward the mean in uncontrolled clinical trials. Biometrics. 1973;29: 121–130.
4.
FreedmanDPisaniRPurvesR. Statistics. New York: Norton & Company: 1978.
5.
EdererF. Serum cholesterol changes: effects of diet and regression toward the mean. J Chronic Diseases. 1972;25: 277–289.
6.
CotloveEHarrisEWilliamsG. Biological and analytic components of variation in long-term studies of serum constituents in normal subjects III. Physiological and medical implications. Clin Chem. 1970;16: 1028–1032.
7.
DavisCE. The effect of regression to the mean in epidemiologic and clinical studies. Am J Epidemiol. 1976;104: 493–498.
8.
GardnerMJHeadyJA. Some effects of within-person variability in epidemiological studies. J Chronic Diseases. 1973;26: 781–795.
9.
CurnowRN. Correcting for regression in assessing the response to treatment in a selected population. Stat Med.1987;6: 113–117.
10.
SennSJBrownRA. Estimating treatment effects in clinical trials subject to regression to the mean. Biometrics. 1985;41: 555–560.
11.
GrenderJMJohnsonWDElstonRC. Regression toward the mean in 2 × 2 cross-over designs with baseline measurements. Stat Med.1992;11: 727–741.
