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

Ostermann T, Willich SN, Lüdtke R - BMC Med Res Methodol (2008)

Bottom Line: 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.

View Article: PubMed Central - HTML - PubMed

Affiliation: Department of Medical Theory and Complementary Medicine, University of Witten/Herdecke, Gerhard-Kienle-Weg 4, 58313 Herdecke, Germany. thomaso@uni-wh.de

ABSTRACT

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.

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Related in: MedlinePlus

Graphs for p(μ) and (μ) based on example 2 (Becker-Witt [16]).
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Figure 2: Graphs for p(μ) and (μ) based on example 2 (Becker-Witt [16]).

Mentions: Fig. 2 shows that the p-values drawn from the Mee-Chua-test are far below 0.025 when the true mean is below 55 score points. Thus, in these situations a significant intervention effect can be confirmed. Having in mind that the true (healthy) population in Germany has a mean SF-36 physical summary score of 50.24 [17] it seems very unlikely that the true mean in our (diseased) target population is bigger than 55 points. Consequently, our analyses show unambiguously, that the observed effect in this study cannot only attributed to RTM.


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

Ostermann T, Willich SN, Lüdtke R - BMC Med Res Methodol (2008)

Graphs for p(μ) and (μ) based on example 2 (Becker-Witt [16]).
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC2527023&req=5

Figure 2: Graphs for p(μ) and (μ) based on example 2 (Becker-Witt [16]).
Mentions: Fig. 2 shows that the p-values drawn from the Mee-Chua-test are far below 0.025 when the true mean is below 55 score points. Thus, in these situations a significant intervention effect can be confirmed. Having in mind that the true (healthy) population in Germany has a mean SF-36 physical summary score of 50.24 [17] it seems very unlikely that the true mean in our (diseased) target population is bigger than 55 points. Consequently, our analyses show unambiguously, that the observed effect in this study cannot only attributed to RTM.

Bottom Line: 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.

View Article: PubMed Central - HTML - PubMed

Affiliation: Department of Medical Theory and Complementary Medicine, University of Witten/Herdecke, Gerhard-Kienle-Weg 4, 58313 Herdecke, Germany. thomaso@uni-wh.de

ABSTRACT

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.

Show MeSH
Related in: MedlinePlus