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Journal of Probability and Statistics
Volume 2012 (2012), Article ID 194194, 18 pages
http://dx.doi.org/10.1155/2012/194194
Research Article

A Two-Stage Joint Model for Nonlinear Longitudinal Response and a Time-to-Event with Application in Transplantation Studies

1Department of Biostatistics, Erasmus University Medical Center, P.O. Box 2040, 3000 CA Rotterdam, The Netherlands
2I-Biostat, Catholic University of Leuven, B-3000 Leuven, Belgium

Received 7 July 2011; Revised 27 October 2011; Accepted 6 November 2011

Academic Editor: Grace Y. Yi

Copyright © 2012 Magdalena Murawska et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

In transplantation studies, often longitudinal measurements are collected for important markers prior to the actual transplantation. Using only the last available measurement as a baseline covariate in a survival model for the time to graft failure discards the whole longitudinal evolution. We propose a two-stage approach to handle this type of data sets using all available information. At the first stage, we summarize the longitudinal information with nonlinear mixed-effects model, and at the second stage, we include the Empirical Bayes estimates of the subject-specific parameters as predictors in the Cox model for the time to allograft failure. To take into account that the estimated subject-specific parameters are included in the model, we use a Monte Carlo approach and sample from the posterior distribution of the random effects given the observed data. Our proposal is exemplified on a study of the impact of renal resistance evolution on the graft survival.