View PDF Version - RePub - Erasmus Universiteit Rotterdam

Discriminant analysis using a MLMM with a normal mixture 157
a random intercept and time effects (time in months). That is, each matrix Z g
i,r
contains an intercept column and the column of the times at which the markers have
been measured. Hence, in each prognostic group, there are 6-dimensional random
effects. Weakly informative priors as described in Section ’Prior distributions’ have
been used for the model parameters. Models with K = 1 and K = 2 mixture
components have been fitted for comparative purposes. The reported results are
based on 10 000 iterations of 1:10 thinned MCMC after a burn-in period of 5 000
iterations. MCMC sampling took about 120s for Group 0 and about 30s for Group 1
on an Intel Core 2 Duo 3 GHz CPU with 3.25 GB RAM. Convergence of the MCMC
was evaluated using the R package coda (Plummer et al. 26 ).
Tables 1 and 2 show posterior summary statistics for the fixed effects, means and
standard deviations of the random effects and standard deviations of the error terms
in models with K = 2 mixture components. The results for models with K =1are
similar. The mean trajectories for a patient with median values of the covariates and
based on the posterior medians of the model parameters from Table 1 are shown as
black lines in Figure 1. The fitted mean profiles confirm differences between both
prognostic groups and our earlier conclusions taken from the observed longitudinal
profiles. The fact that the observed profiles differ from the fitted mean profiles more
considerably in Group 1 than in Group 0 is seen also from the posterior medians of
Table 1. Dutch PBC Study. Posterior summary statistics for fi xed effects (α) and means of random effects
(β) in models with K = 2.
Group 0 Group 1
Posterior
Median
95% HPD
Interval
Posterior
Median
95% HPD
Interval
Bilirubin
intercept 1.13 (1.07, 1.20) -2.48 (-3.02, -1.98)
time (months) 0.77 · 10-3 (-0.02, 1.61) · 10-3 0.11 (0.06, 0.17)
age (years) -0.78 · 10-2 (-0.87, -0.69) · 10-2 0.056 (0.049, 0.062)
UDCA dosis (mg/day) -0.59 · 10-4 (-1.00, 0.12) · 10-4 0.85 · 10-3 (0.34, 1.34) · 10-3 Albumin
intercept 1.26 (1.21, 1.31) 1.27 (1.13, 1.40)
time (months) -0.30 · 10-3 (-0.50, -0.10) · 10-3 -0.33 · 10-2 (-0.54, -0.12) · 10-2 age (years) -0.11 · 10-2 (-0.27, 0.05) · 10-2 -0.47 · 10-2 (-0.93, 0.00) · 10-2 UDCA dosis (mg/day) -0.35 · 10-4 (-0.96, 0.24) · 10-3 -0.07 · 10-5 (-19.41, 18.63) · 10-5 Alkal. phosph.
intercept 3.66 (3.48, 3.84) 7.38 (6.74, 8.00)
time (months) -0.50 · 10-2 (-0.61, -0.38) · 10-2 -0.021 (-0.042, -0.003)
age (years) -0.30 · 10-1 (-0.32, -0.29) · 10-1 -0.053 (-0.058, -0.046)
UDCA dosis (mg/day) 0.30 · 10-4 (-0.52, 1.12) · 10-4 -0.15 · 10-2 (-0.19, -0.11) · 10-2