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CPS1419 Jinheum K. et al.
3. Simulation studies
Extensive simulations are performed to investigate the finite-sample
properties of the estimators proposed in Section 2. We assume a
Weibull distribution with a common shape parameter of 1 as the
baseline transition intensities. However, different values of the scale
parameter of the Weibull distribution are used to impose some
influence on relevant transitions: 01 = 0.006, 02 = 0.003, and 12 =
0.004. We assume a normal distribution with a mean of zero and a
variance of0.1 for the frailty. For generation on covariates, we use a
Bernoulli trial with a success probability of 0.5 on a binary covariate
1
and a standard normal random variate on a continuous covariate .
2
We fix the sample size at 200 and the censoring time at 365. A total
of 500 replications is performed in our simulations.
Table provides the relative bias (‘r.Bias’), standard deviation (‘SD’),
average of the standard errors (‘SEM’), and coverage probability (‘CP’)
of 95% confidence intervals for the regression parameters, and the
variance estimate of the frailty distribution. The SD and SEM are very
close to each other and the CPs of the regression parameters are close
to a nominal level of 0.95 regardless of the types of the regression
coefficients considered in the simulations. Sensitivity analysis is also
conducted to investigate how the parameter estimates behave in
response to different frailty distributions. For simplicity of computation,
we consider only the ‘even’ case for the regression parameters. Three
different frailty distributions are used, along with (0,0.1): uniform,
double exponential (), and gamma () distributions with specific
parameter value(s) set to keep the mean and variance of each
distribution equal to those of the normal distribution. We compare the
results of the three distributions with those of the normal distribution.
The uniform and double exponential distributions are symmetric, like a
normal distribution. However, the uniform distribution has thinner tails
than the normal distribution, while the double exponential distribution
has heavier tails than the normal distribution. Unlike the normal
distribution, the gamma distribution is asymmetric. Despite the
differences among these distributions, overall, there are no differences
in the values of r. Bias and CP when comparing the three distributions
to the normal distribution. This implies that the proposed estimators are
robust to the misspecification of the frailty distribution.

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