Biomedical Engineering Reference
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of the 95% credible intervals (dashed lines) of the regression coecient from
the 250 replicates. When the true (t) is time independent, all three models
were able to uncover the true value quite well. Not surprisingly, M
1
gave
the narrowest credible intervals because it is parsimoniously and correctly
specied. When the true (t) is time varying, M
1
is misspecified and only
estimates the average temporal effects with overly smaller credible intervals.
Both M
2
and M
3
recovered the true curve reasonably well, but the dynamic
model M
3
gave much narrower credible intervals than M
2
.
Figure 7.2 shows the boxplots of the pairwise differences in LPML and
DIC among all three models. Models with larger LPML and smaller DIC are
preferred. When is constant, the LPML measure seems less ambiguous in
ordering the three models than the DIC measure. On average, M
1
is better
than M
2
, and M
3
is better than M
1
in terms of LPML, as indicated by the
quantiles of the boxplots compared to zero. The DIC measure prefers M
1
to
M
2
, but is indifferent between M
3
and M
1
. It seems to favor M
3
over M
2
,
but the margin is small as the median dierence is close to zero. When is
time varying, the LPML measure again seems to be less ambiguous than the
DIC measure. Both measures prefer M
2
to M
1
. The LPML measure, however,
has a clearer preference of M
3
over M
1
and M
2
because about a fourth of
the time, the former has higher LPML. On the other hand, the DIC measure
seems to be indifferent between M
3
and M
2
.
7.7
Analysis of the Breast Cancer Data
The breast cancer data from Finkelstein (1986) have been analyzed extensively
for illustrating new methods in modeling interval-censored data (e.g., Sinha
et al., 1999; Goetghebeur and Ryan, 2000; Pan, 2000). The objective of the
study was to compare the time to cosmetic deterioration between two groups:
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