In the case of no change in distributions between the two repeated measurements (i.e. We assume that both measurements follow a bivariate normal distribution with means μ 1 and μ 2, a common variance σ 1 2 = σ 2 2 = σ 2 and a correlation ρ. Realisations of Y 1 and Y 2 are denoted as y 1 and y 2. physiological parameters like blood pressure, or quality of life scores): The random variables Y 1 (Y 2) denote these values/scores before (after) an intervention. In the following we consider two measurements of one quality (e.g. In this paper, we therefore revisit the approach of Mee and Chua and extend it to a situation where no population mean is available but evidence for or against a treatment effect is needed when RTM is present. However, the basic necessity of a population mean is quite obstructive and often such a value can not be determined. If μ can be obtained, this approach has already been proven to distinguish between RTM-effects and treatment effects in clinical study reality. This method does not depend on truncated sampling but requires the knowledge of the true mean μ in the target population. The approach we focus on in this paper is a straightforward method developed by Mee and Chua based on classical t-test statistics and a linear regression model. only those members which have a first measurement beyond (or below) a predefined cut-point are sampled. Most of these methods deal with common situations of truncated sampling, i.e. In the last two decades several methods for detecting RTM have been developed both for the case of normal distributed data as well as for the non-parametric case. This is especially true for the results of complementary therapies, which are often claimed to be a mixture of RTM effects, non-specific (placebo) effects, the effects of a previous or concomitant conventional treatment and the actual effectiveness of the complementary treatment. The discussion about the development of methods to detect RTM in observational studies is still vital. Other examples include the evaluation of asthma disease management programmes or cholesterol screening. Unaware of RTM effects a patient's recovery typically is interpreted as a treatment effect. Medical rehabilitation programmes for example, often are evaluated for their ability to restore the patient's ability to work. RTM affects all fields of life science, when effects of an intervention have to be evaluated in an uncontrolled longitudinal setting. Such changes are likely to be interpreted as a real drift, although they just might be artificial coming from the fact that the sampling of values was not random but selected. It occurs in situations of repeated measurements when extremely large or small values are followed by measurements in the same subjects that on average are closer to the mean of the basic population. Regression to the mean (RTM) first described by Galton is a statistical phenomenon broadly discussed when it comes to measure changes in the course of time. In meta-analysis, health-technology reports or systematic reviews this approach may be helpful to clarify the evidence given from uncontrolled observational 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. We successfully applied our method to three real world examples denoting situations when (a) no treatment effect can be confirmed regardless which μ is true, (b) when a treatment effect must be assumed independent from the true μ and (c) in the appraisal of results of uncontrolled studies. Using differential calculus we provide formulas to estimate the range of μ where treatment effects are likely to occur when RTM is present. We extend this approach to a situation where μ is unknown and suggest to vary it systematically over a range of reasonable values. Several statistical approaches have been developed to analyse such situations, including the algorithm of Mee and Chua which assumes a known population mean μ. In uncontrolled studies such changes are likely to be interpreted as a real treatment effect. 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.
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