Mathematical coupling does not account for the association between baseline severity and minimally important change values

Abstract

A number of studies have demonstrated a correlation between baseline severity and minimally important change (MIC) values. However, Browne et al. stated that these studies failed to account for "mathematical coupling," and that, therefore, the correlation between baseline severity and MIC values may be spurious. The present article demonstrates that on the level of individual scores, mathematical coupling causes the observed baseline and change scores to correlate even in the absence of any true correlation between these variables. This phenomenon is because of the fact that change scores can only be estimated by subtracting the baseline score from the follow-up score, causing the baseline and change scores to share a common piece of error variance. However, MIC values are always determined on group level, and mathematical coupling does not affect group-level statistics or the correlation of these statistics across groups. Therefore, mathematical coupling does not account for the association between baseline severity and MIC values as suggested by Browne et al.