Biomedical Engineering Reference
In-Depth Information
the event has happened or the subject has dropped out. Let = 6 be the
maximum follow-up time. Each gap time was independently generated from a
discrete distribution on equally spaced points over (0;) with increment 0.05
with density
p(t) / 0:5I(t = 0:6) + 0:5LN(t; 0; 0:4);
where LN(t; ;) is the probability density function of a lognormal distri-
bution with mean and standard deviation . This mixture setup mimics
a situation where, on average, 40% of the visits are paid as scheduled with
gap time 0.6, and the remaining 60% of the visits are rescheduled with gaps
following a lognormal distribution. The endpoints of the censoring inverval
are then the two consecutive visit times between which the exact event falls.
An event time greater than 6 was always right-censored, with the last visit
time being the censoring time. Early dropout was accommodated by allowing
a probability 0.02 of dropping out at each new visit time. This setting led to
about one third of the subjects being right censored due to early dropout or
large event time.
For each specication of (t), we generated 250 data sets and rounded the
times to the nearest 0.05. Three models were fitted to each data set: (i) the
time-independent-coecient Cox model (M
1
) with prior (7.6) for h
0
(t); (ii)
the time-varying-coecient Cox model (M
2
) with prior (7.6) for h
0
(t) and
the AR prior (7.11) for (t); and (iii) the dynamic Cox model (M
3
) with
hierarchical AR prior (7.12) for both log h
0
(t) and (t). Because we consider
only a single covariate (p = 1), we drop the subscript j in the hyperparameters.
For both M
1
and M
2
, we set (
k
;
k
) = (0:1; 0:1) in Equation (7.6). The prior
for constant in M
1
was N(0; 10
2
). The hyperparameters in Equation (7.11)
for M
2
and in Equation (7.12) for M
3
were set to c
0
= 100, (
0
;
0
) = (2; 1).
The tuning parameter
0
for M
3
was set at 1.
We ran 6,000 MCMC iterations with a burn-in period of 1,000 for each data
set, and summarized the results based on the remaining 5,000 MCMC samples.
Figure 7.1 shows the median of the posterior mean (solid lines) and the median
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