Methods for assessing whether change depends on initial value

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Abstract
Statistical analysis of whether the change in a variable depends on its initial value, in clinical trials and other studies, is complicated by the phenomenon of regression to the mean. We review this problem and examine some approaches for handling it. MacGregor's log-log plot fails to correct for the regression effect, while Oldham's method of plotting the change against the average of initial and final values is shown to give misleading results when the effect of treatment varies between subjects, or when subjects are selected for study if their initial observations fall above or below a specified cut-off point. These results are illustrated by computer simulations. We prefer the use of Blomqvist's method of correcting the association between change and initial value to allow for the regression effect.