Warning: your browser isn't supported. Please install a modern one, like Firefox, Opera, Safari, Chrome or the latest Internet Explorer. Thank you!

## Regression to the mean

Regression to the mean artifacts are present whenever repeated measures are employed. In simple English, regression to the mean refers to the fact that those with extreme scores on any measure at one point in time will probably have less extreme scores the next time they are tested for purely statistical reasons.

See Regression to the mean: wikipedia for an excellent description of the concept, with fascinating real world examples of consequences for failure to understand regression artifacts. If nothing else, the excerpt from psychologist Daniel Kahneman's acceptance speech when he won the 2002 Bank of Sweden prize for economics (also known as the Nobel prize for economics) is worth reading.

The best book I have found on the subject is A Primer on Regression Artifacts; Campbell & Kenny, 1999

Because scores on outcome measures are correlated over time, the change scores will also be correlated with the intake score. This means that patients with high levels of distress will average more change than patients with low levels of distress. Case mix adjustment through use of the Generalized Linear Model is necessary to account for these regression artifacts.

How do we know if the change we measure exceeds regression to the mean? One method that is strongly recommended by Campbell and Kenny is the use of a time reversed regression analysis.

While this may seem nonsensical, the principle is sound. Pure regression to the mean is based on random error, and is "time symmetrical". If the regression formula obtained by using the first score to predict the last score is essentially the same formula obtained by using the last score to predict the first score, then the change observed is probably simply regression to the mean even if scores trended downwards from the first to last administration. If the two regression lines are different,however, then the change exceeded regression to the mean.

The following graph shows the results of a time reversed regression using OQ-30 data from the PBH ALERT system. In this case, the effect size for the regression analysis going forward is much larger than the reverse analysis at every level of severity, demonstrating the measured pre-post change exceeded regression to the mean.

-- JebBrown - 27 Feb 2007

Primary topics:

You may also view all topics in alphabetical order in WebTopicList.
Copyright © by the contributing authors. All material on this collaboration platform is the property of the contributing authors.
Ideas, requests, problems regarding ACORN Wiki? Send feedback