Regression toward the mean--a detection method for unknown population mean based on Mee and Chua's algorithm.
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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.Using differential calculus we provide formulas to estimate the range of mu where treatment effects are likely to occur when RTM is present.
Affiliation: Department of Medical Theory and Complementary Medicine, University of Witten/Herdecke, Gerhard-Kienle-Weg 4, 58313 Herdecke, Germany. thomaso@uni-wh.de
ABSTRACT
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Background: 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. Methods: 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. Results: 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. Conclusion: 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. Related in: MedlinePlus |
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Mentions: Fourth, our approach is restricted to treatment effects which work additive on the mean. In contrast to this assumption, several complementary and alternative therapies are based on the therapeutic principle of "functional normalisation", i.e. they claim to actively exploit the self regulative capacities of the organism. In this sense, these approaches are assumed to have the potential not to shift a mean but to decrease high values and to increase low values to "normal" values, e.g. of blood pressure [31] or cardio-respiratory coordination [32]. This corresponds to a multiplicatively working treatment effect, a model first proposed by James [33] and extensively discussed by Senn and Brown [26,34], Chen and Cox [35], and Naranjo and McKean [36]. Again, it is difficult to distinguish such a treatment effect from RTM especially when data is collected selectively, for examples from the tails of a given distribution. This dilemma is quite illustrative in the example of Gutenbruner and Ruppel [31], redrawn in Fig. 3. |
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Affiliation: Department of Medical Theory and Complementary Medicine, University of Witten/Herdecke, Gerhard-Kienle-Weg 4, 58313 Herdecke, Germany. thomaso@uni-wh.de
Background: 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.
Methods: 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.
Results: 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.
Conclusion: 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.