Biomedical Engineering Reference
In-Depth Information
11.3.3
Coverage Probability on \IntCox"
From the above simulations, we have demonstrated that the \IntCox" can be used to
model interval-censored time-to-event data that gives negligible bias for parameter
estimates with small MSE. The implementation of this ICM-based algorithm in the
R package \IntCox" made it especially easy from a computational aspect. Using this
library, we further conducted a simulation to investigate the coverage probability
for the parameter estimates. We found that the coverage probabilities (CP) for the
parameters are also acceptable. The simulation setup was similar to Section 11.3.1
with true parameters = (
1
;
2
;
3
;
4
) = (0:5;0:5; 0:5; 0:5). The covariates X
1
and X
2
corresponding to the first two parameters
1
and
2
are generated from a
random binomial distribution. This is to illustrate the effect of categorical data, such
as treatment effect. The third covariate was generated from a random uniform dis-
tribution and the fourth was generated from a random standard normal distribution
to illustrate the effect for continuous data. In each simulation, the interval-censored
data were generated based on the Weibull distribution and \intcox" was called to
fit the generated data to obtain the parameter estimates of
^
from that simulation.
Because \intcox" cannot give standard error estimates, the bootstrap resampling
approach was used to bootstrap the simulated data with replacement 300 times,
and the standard errors (SE(
^
)) were estimated from the 300 bootstrap samples.
Based on this bootstrap approach, 95% confidence intervals (CI) were constructed
as (
^
1:96SE(
^
);
^
+ 1:96SE(
^
)) to check whether the true was within the 95%
CI. Eight hundred simulations were performed and the coverage probability was cal-
culated as the percentage of the CIs that contained the true parameter . We found
that the corresponding coverage probability is CP = (90%; 90%; 96%; 95%), which
is acceptable practically even if it is slightly low for categorical covariates.
11.4
HIV Data Analysis
Interval time-to-event data are available on 368 subjects with HIV-1 infection with
hemophilia in \No" and \Low"-dose factor VIII concentration groups from a ve-
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