Analysis of relative change and initial value of biological studies

In analyzing longitudinal data, the relationship between initial value (ξ₁) and change in response to a maneuver or over time is often interest. This relationship is often determined by the Pearson correlation between χ₁ and subsequent change (χ₂ - χ₁), but a correlation will often be obtained by mathematical necessity even when χ₁ and χ₂ are uncorrelated. It has been suggested that use of relative change, or (χ₂ - χ₁)/χ₁, avoids these mathematical artifacts. By reference to early work by Pearson (Proc. R. Soc. London 60: 489-498, 1897) on an approximation to the correlation between ratios and by computer simulations, this paper shows that this solution is frequently not valid. An alternative approach to the analysis of the relationship between χ₁ and relative change is presented and is illustrated by a study of renal blood flow.