Regression toward the mean--a detection method for unknown population mean based on Mee and Chua's algorithm

Regression to the mean (RTM) occurs in situations of repeated measurements when extreme values are followed by measurements in the same subjects that are closer to the mean of the basic population. In uncontrolled studies such changes are likely to be interpreted as a real treatment effect.

Several statistical approaches have been developed to analyse such situations, including the algorithm of Mee and Chua which assumes a known population mean mu. We extend this approach to a situation where mu is unknown and suggest to vary it systematically over a range of reasonable values. Using differential calculus we provide formulas to estimate the range of mu where treatment effects are likely to occur when RTM is present.

We successfully applied our method to three real world examples denoting situations when (a) no treatment effect can be confirmed regardless which mu is true, (b) when a treatment effect must be assumed independent from the true mu and (c) in the appraisal of results of uncontrolled studies.

Our method can be used to separate the wheat from the chaff in situations, when one has to interpret the results of uncontrolled studies. In meta-analysis, health-technology reports or systematic reviews this approach may be helpful to clarify the evidence given from uncontrolled observational studies.