ABSTRACT
FIGURE 4.2: Subject-specic longitudinal proles for six patients from the Aortic Valve study.
percentiles of the follow-up times, TypeOpRR denotes the dummy variable for the root replacement type of operation, and we also control for the age of the patients at baseline. To t this model in R we use function ns() from package splines that generates the basis matrix for the natural cubic splines. The corresponding syntax is
The formulation in the random argument in the call to lme() species a diagonal covariance matrix for the random eects b>i = (bi0; : : : ; bi3). For the survival part we t a simple Cox model in which we only include the type of operation as a covariate, i.e.,
hi(t j Mi(t); wi) = h0(t) expf TypeOpRRi + mi(t)g; and we t it in R using
Based on the tted linear mixed and Cox models we t the corresponding joint model, setting also the verbose argument to TRUE,
log-likelihood: -2107.672
betas: 4.275 1.4198 2.4489 2.4651 -0.4827
-0.0201 -0.1128 -0.5105 -1.1762
sigma: 0.6148
gammas: -0.0336
alpha: -0.3875
xi: 0.2721 0.3413 0.431 0.3953 0.9664 0.838 0
D: 0.453 4.4725 1.973 1.2492
.