Biomedical Engineering Reference
In-Depth Information
46 patients receiving radiotherapy only (x = 0) and 48 patients receiving
radiotherapy plus chemotherapy (x = 1). Because the detection of deteriora-
tion required a clinic visit, the 56 women who experience deterioration were
interval-censored, and the other 38 women who did not were right-censored.
The treatment indicator is the only covariate and hence p = 1.
We fitted the three models given in Section 7.6. The priors and hyper-
parameters of the three models are the same as those in Section 7.6, except
that, for sensitivity analysis, we fitted M
2
and M
3
with two specifications
of (
0
;
0
): (4; 1) or (2; 1). We ran 55,000 iterations of MCMC, discarded the
first 5,000, thinned the rest by 10, and summarized the results based on the
resulting posterior sample of size 5,000.
The Bayesian model selection results are reported in Table 7.1. We observe
that the results of M
2
and M
3
are robust to the choice of hyper parameters
(
0
;
0
). Model M
3
has the smallest, and thus the best LPML measure. The
DIC statistic favors M
2
and M
3
over M
1
but the difference between M
2
and
M
3
is minimal (290.69 versus 290.88). The effective number of parameters
p
D
is 12.45, 14.11, and 5.96, respectively, for models M
1
, M
2
, and M
3
. That
is, M
2
has about 1.6 more parameters than M
1
, which is justified from the
reduction of DIC by 5 to 7; while M
3
has about 8 less parameters than M
2
due to the introduction of dynamic baseline hazards. Although M
3
achieves
the worst goodness-of-t measure D( ), it is still the overall winner because
of the greater reduction in p
D
.
Figure 7.3 shows the estimated coecient with 95% credible intervals for
all three models, where the IG(2; 1) prior is used for w
2
in the two time-varying
coecient models. For M
1
, the marginal posterior of treatment coecient
has mean 0.692 and 95% credible interval (0:160; 1:247), which are close to
published results (Pan, 2000; Goetghebeur and Ryan, 2000). Both M
2
and
M
3
estimate a coecient curve with an increasing trend before 20 days, and
a slowly decreasing trend afterward, with averages over time close to the point
estimate from M
1
. The 95% credible interval from M
2
is much wider than
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