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Another Example of Regression to the Mean (Not)

Peter Alston, R., MD, FRCA; Deary, Ian J., MB, ChB, PhD, MRCPsych, FRCP; Robson, Michael J., MB, ChB, FRCA; Andrews, Peter J., MD, FRCA; Souter, Michael J., MD, FRCA

doi: 10.1097/00000539-200212000-00079
LETTERS TO THE EDITOR: Letters & Announcements

Department of Anaesthesia, Critical Care and Pain Medicine, Royal Infirmary of EdinburghEdinburgh, UK

Department of Psychology

University of Edinburgh

Department of Anaesthesia, Western General Hospital, Edinburgh, UK

Departments of Anesthesiology and Neurointensive Care

University of Washington

Seattle, WA

To the Editor:

Landow in his letter in the June 2002 issue implies that our study of cognition following coronary artery bypass grafting surgery is flawed by regression to the mean (1,2).

Dichotomization of cognitive change into those who do/don’t decline results in people with high preoperative test scores appearing spuriously to have excess cognitive decline (3). However, we modeled postoperative cognitive scores as continuous variables to prevent this problem.

In regression to the mean, change scores show spurious correlation with baseline scores in instances where the baseline scores have themselves been used in computing change. We used postoperative cognitive scores as the dependent variable and preoperative cognitive scores as the first-entered independent variables in our models. Thus, “cognitive change” variance lay in the residuals that followed this procedure, and these are uncorrelated with the preoperative scores!

The extent of regression to the mean is a function of measurement error in the predictors. By using multiple cognitive indicators, which are individually reliable and highly correlated, we achieved highly reliable composite cognitive measures.

Our abjuring cognitive change thresholds, using a residualized approach to cognitive change, and multiple cognitive measures makes Landow’s comment on our study incomprehensible. Could he indicate specifically how its results might be affected by regression to the mean?

R. Peter Alston, MD, FRCA

Ian J. Deary, MB, ChB, PhD, MRCPsych, FRCP

Michael J. Robson, MB, ChB, FRCA

Peter J. Andrews, MD, FRCA

Michael J. Souter, MD, FRCA

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1. Landow L. Another example of regression to the mean. Anesth Analg 2002; 94: 1673.
2. Robson MJA, Alston RP, Deary IJ, et al. Jugular bulb oxyhaemoglobin desaturation, S100β and neurologic and cognitive outcome after coronary artery surgery. Anesth Analg 2001; 93: 839–45.
3. Browne SM, Halligan PW, Wade DT, Taggart DP. Cognitive performance after cardiac operation: implications of regression toward the mean. J Thorac Cardiovasc Surg 1999; 117: 481–5.
© 2002 International Anesthesia Research Society