AJP - Regulatory, Integrative and Comparative Physiology, Vol 246, Issue 1 122-R126, Copyright © 1984 by American Physiological Society
Analysis of relative change and initial value in biological studies
G. W. Williams, S. B. Forsythe, S. C. Textor and R. C. Tarazi
In analyzing longitudinal data, the relationship between initial value (x1)
and change in response to a maneuver or over time is often of interest.
This relationship is often determined by the Pearson correlation between x1
and subsequent change (x2 - x1), but a correlation will often be obtained
by mathematical necessity even when x1 and x2 are uncorrelated. It has been
suggested that use of relative change, or (x2 - x1)/x1, 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 x1 and relative change is presented and is
illustrated by a study of renal blood flow.
