A two-stage joint model for nonlinear longitudinal response and a time-to-event with application in transplantation studies

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. © 2012 magdalena murawska et al.