Regression to the mean

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Regression toward the mean is a statistical concept that refers to the fact that if one sample of a random variable is more extreme, then the next sampling of that same random variable is likely to be closer to its mean. Subsequent measures of that variable will be less extreme and closer to the mean.

This was first described by Francis Galton in 1886 who that, on average, taller parents have children shorter than themselves and shorter parents have taller children than themselves.

Relevance of Regression to the Mean:
Regression to the mean is one reason why sham, alternative or pseudoscientific based treatments are claimed to work when they don’t. This concept is taken advantage of by those promoting such approaches. It also can be deceptive as to if a traditional treatment appearing to be effective when it may not be. Typically, people tend to seek care for their problem when their symptoms are at their worst, and any regression or improvement could falsely be attributed to a successful treatment when that may or may not be the case.

For example, a patient may be seen at a low point in their disease process or when they are just having a bad day, so any sort of intervention is going to appear to work because of the natural history of the disease. Alternative practitioners exploit this by making it appear that the therapy to be somewhat effective in enough patients.

In clinical practice an assumed response to a treatment could just be due to regression to the mean and it may take time before a clear pattern emerges in a patient’s status rather than the random ups and downs of regression to the mean. Clinical trails with adequately randomized and blinded control groups are needed to allow this regression to the mean concept to be ruled out for a particular intervention.

Linden (2013):

Interventions targeting individuals classified as “high-risk” have become common-place in the health care industry. High-risk may capture anything from high utilization or cost of health services, to outlier values on clinical measures (e.g., blood glucose, blood pressure, cholesterol). Typically, such individuals are invited to participate in an intervention intended to reduce their level of risk, and after a period of time, a follow-up measurement is taken. The pre-test to post-test change in the outcome is then generally presented as the impact of the intervention. This evaluation approach is problematic from a statistical standpoint because individuals initially identified by their high values will likely have lower values on re-measurement in the absence of an intervention. This statistical phenomenon is known as “regression to the mean” (RTM) and often leads to an inaccurate conclusion that the intervention resulted in a treatment effect.

Deep dive:

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