The impact and implication of regression to the mean on the design and analysis of medical investigations

We have examined the regression effect and its magnitude under the Gaussian distributional assumption. The impact and implication of regression to the mean on the analysis of medical investigations was discussed. For simplicity, we called the approach adjusting for the regression effect a two-stage procedure and noted its relationship to the analysis of covariance model for comparing treatment groups. We also proposed to examine the correlation structure among repeated measurements in the absence of any external interventions through a model more realistic than the one assuming equal correlations. The proposed structure led us to investigate ways to reduce or eliminate regression effect via study designs when patient selection is inevitable. Two examples were given to help illustrate the discussion in this paper.