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Biostatistics Advance Access originally published online on April 14, 2005
Biostatistics 2005 6(3):395-403; doi:10.1093/biostatistics/kxi017
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© The Author 2005. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oupjournals.org.

On the relation between initial value and slope

K. Byth*

NHMRC Clinical Trials Centre, University of Sydney, Locked Bag 77, Camperdown, NSW 1450, Australia and Westmead Millenium Institute, Westmead Hospital, Westmead, NSW 2145, Australia. kbyth{at}ctc.usyd.edu.au

D. R. Cox

Nuffield College, Oxford, OX1 1NF, UK

* To whom correspondence should be addressed.

Suppose measurements of a particular feature are collected at baseline and at a number of subsequent time points and that for each individual there is a roughly linear trend in time. This paper takes three approaches to testing whether there is a relation between the initial value and the slope. It also considers whether the initial value for an individual is a useful predictor of the slope for that individual. The problems are formulated in terms of regression models with random coefficients. The solutions are illustrated using data from an observational study of clinical correlates of disability and progression in Huntington's disease.

Keywords: Huntington's disease; Initial value; Longitudinal data; Regression model with random coefficients; Regression to the mean; Slope


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