Regression toward the mean--a detection method for unknown population mean based on Mee and Chua's algorithm.
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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.
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: Following the approach we suggested here, one might wonder whether this result is sensitive to the assumption of μ = 75. In other words one should calculate if there would have been a chance of an intervention effect if another μ had been chosen. Fig. 1 shows the values for p(μ) based on the data given in table 1 within a range from 30 <μ < 80. From equation (4) and (5) the maximum value for t is given at μmax = 58.96, with a t-value of tmax = 1.938. This finally leads to a corresponding one sided p-value of pmin = p(μmax) = 0.0504. Hence, we can surprisingly conclude, that independent of any given μ no intervention-effect can be confirmed in this group of students. Thus, the data does not support the hypothesis, that the special course to refresh the language skills is not suitable for the given student profile that failed in the first exam. |
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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.