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Discriminant analysis using a MLMM with a normal mixture 163
Table 3. Dutch PBC Study, random effect prediction with K=1 and K=2 mixture components. Sensitivity
of the prediction at t=0, 6, 12, 18, 24, 36, 48, 60 months for specifi city of 0.99,0.95, 0.90.
Specifi city
0.99 0.95 0.90
K=1 K=2 K=1 K=2 K=1 K=2
Time Sensitivity
0 months 0.152 0.212 0.545 0.515 0.606 0.667
6 months 0.175 0.175 0.450 0.425 0.675 0.725
12 months 0.081 0.216 0.541 0.486 0.649 0.811
18 months 0.033 0.267 0.467 0.433 0.600 0.733
24 months 0.034 0.414 0.552 0.552 0.759 0.828
36 months 0.115 0.500 0.577 0.692 0.731 0.808
48 months 0.381 0.619 0.619 0.667 0.667 0.810
60 months 0.429 0.500 0.643 0.714 0.714 0.857
Figure 6. Dutch PBC Study. Evolution of the area under the ROC curve over time for random effect
prediction for multivariate model (solid line) , and models with a single marker- bilirubin (dashed line),
albumin (dotted line), log(alkaline phosphatase) (dotted line). In all models K=2 mixture components
were used.
compares the AUC of the random effects prediction from the multivariate mixed
model and the AUCs of the random effects’ prediction from the single models for
each marker. It is seen that prediction based on the multivariate model is better than
with any of the single predictions. With this exercise, it is also seen that bilirubin
provides the most information to predict the patient’s status at T =10years.
Finally, we remark that in this illustration we concentrated on the evaluation of the
discriminant procedure and have not paid much attention to the correct specification
of the mean structure of the underlying mixed models. In fact, we let random