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Biostatistics Advance Access originally published online on December 3, 2007
Biostatistics 2008 9(3):419-431; doi:10.1093/biostatistics/kxm041
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© The Author 2007. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org.

Predicting renal graft failure using multivariate longitudinal profiles

Steffen Fieuws* and Geert Verbeke

Biostatistical Centre, Katholieke Universiteit Leuven, Leuven, Belgium steffen.fieuws{at}med.kuleuven.be

Bart Maes

Department of Nephrology, H.-Hartziekenhuis, Roeselare-Menen, Belgium

Yves Vanrenterghem

Department of Nephrology, University Hospital Gasthuisberg, Leuven, Belgium

* To whom correspondence should be addressed.

Patients who have undergone renal transplantation are monitored longitudinally at irregular time intervals over 10 years or more. This yields a set of biochemical and physiological markers containing valuable information to anticipate a failure of the graft. A general linear, generalized linear, or nonlinear mixed model is used to describe the longitudinal profile of each marker. To account for the correlation between markers, the univariate mixed models are combined into a multivariate mixed model (MMM) by specifying a joint distribution for the random effects. Due to the high number of markers, a pairwise modeling strategy, where all possible pairs of bivariate mixed models are fitted, is used to obtain parameter estimates for the MMM. These estimates are used in a Bayes rule to obtain, at each point in time, the prognosis for long-term success of the transplant. It is shown that allowing the markers to be correlated can improve this prognosis.

Keywords: Discriminant analysis; High dimensional; Joint modeling; Longitudinal profiles; Multivariate mixed models

Received December 18, 2006; revised July 27, 2007; revised September 10, 2007; accepted for publication October 12, 2007.


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