Revisiting the relation between change and initial value: a review and evaluation

The relation between initial disease status and subsequent change following treatment has attracted great interest in clinical research. However, statisticians have repeatedly warned against correlating/regressing change with baseline due to two methodological concerns known as mathematical coupling and regression to the mean. Oldham's method and Blomqvist's formula are the two most often adopted methods to rectify these problems. The aims of this article are to review briefly the proposed solutions in the statistical and psychological literature, and to clarify the popular misconception that Blomqvist's formula is superior to Oldham's method. We argue that this misconception is due to a failure to recognize that the heterogeneity of individual responses to treatment is a source of regression to the mean in the analysis of the relation between change and initial value. Furthermore, we demonstrate how each method actually answers different research questions, and how confusion arises when this is not always understood.