### Abstract

In analyzing longitudinal data, the relationship between initial value (ξ_{1}) and change in response to a maneuver or over time is often interest. This relationship is often determined by the Pearson correlation between χ_{1} and subsequent change (χ_{2} - χ_{1}), but a correlation will often be obtained by mathematical necessity even when χ_{1} and χ_{2} are uncorrelated. It has been suggested that use of relative change, or (χ_{2} - χ_{1})/χ_{1}, 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 χ_{1} and relative change is presented and is illustrated by a study of renal blood flow.

Original language | English (US) |
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Pages (from-to) | R122-R126 |

Journal | American Journal of Physiology - Regulatory Integrative and Comparative Physiology |

Volume | 15 |

Issue number | 1 |

State | Published - Jan 1 1984 |

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### ASJC Scopus subject areas

- Physiology
- Physiology (medical)

### Cite this

*American Journal of Physiology - Regulatory Integrative and Comparative Physiology*,

*15*(1), R122-R126.