The function simGSC() generates simulated recurrent event data from either
a Cox-type model, an accelerated mean model, an accelerated rate model, or a generalized scale-change model.
simGSC(
n,
summary = FALSE,
para,
xmat,
censoring,
frailty,
tau,
origin,
Lam0,
Haz0
)number of observation.
a logical value indicating whether a brief data summary will be printed.
a list of numerical vectors for the regression coefficients
in the joint scale-change model.
The names of the list elements are alpha, beta, eta, and
theta, correspond to \(\alpha\), \(\beta\), \(\eta\), and \(\theta\)
in the joint scale-change model, respectively.
See Details for reReg.
an optional matrix specifying the design matrix.
a numeric variable specifying the censoring times for each of the \(n\) observation.
a numeric variable specifying the frailty variable.
a numeric value specifying the maximum observation time.
a numeric value specifying the time origin.
is an optional function that specifies the baseline cumulative rate function. When left-unspecified, the recurrent events are generated using the baseline rate function of $$\lambda_0(t) = \frac{2}{1 + t},$$ or equivalently, the cumulative rate function of $$\Lambda_0(t) = 2\log(1 + t).$$
is an optional function that specifies the baseline hazard function. When left-unspecified, the recurrent events are generated using the baseline hazard function $$h_0(t) = \frac{1}{5(1 + t)},$$ or equivalently, the cumulative hazard function of $$H_0(t) = \log(1 + t) / 5.$$
The function simGSC() generates simulated recurrent event data over
the interval \((0, \tau)\) based on the specification of the recurrent process and
the terminal events.
Specifically, the rate function, \(\lambda(t)\), of the recurrent process
can be specified as one of the following model:
$$\lambda(t) = Z \lambda_0(te^{X^\top\alpha}) e^{X^\top\beta}, h(t) = Z h_0(te^{X^\top\eta})e^{X^\top\theta}, $$
where \(\lambda_0(t)\) is the baseline rate function,
\(h_0(t)\) is the baseline hazard function,
\(X\) is a \(n\) by \(p\) covariate matrix and \(\alpha\),
\(Z\) is an unobserved shared frailty variable, and
\((\alpha, \eta)\) and \((\beta, \theta)\) correspond to the shape and size parameters of the
rate function and the hazard function, respectively.
Under the default settings, the simGSC() function assumes \(p = 2\)
and the regression parameters to be \(\alpha = \eta = (0, 0)^\top\),
and \(\beta = \theta = (1, 1)^\top\).
When the xmat argument is not specified, the simGSC() function
assumes \(X_i\) is a two-dimensional vector \(X_i = (X_{i1}, X_{i2}), i = 1, \ldots, n\),
where \(X_{i1}\) is a Bernoulli variable with rate 0.5 and
\(X_{i2}\) is a standard normal variable.
With the default xmat, the censoring time $C$ is generated from
an independent uniform distribution in \([0, 2\tau X_{i1} + 2Z^2\tau(1 - X_{i1})]\).
Thus, the censoring distribution is covariate dependent and
is informative when \(Z\) is not a constant.
When the frailty argument is not specified, the frailty variable \(Z\) is generated
from a gamma distribution with a unit mean and a variance of 0.25.
The default values for tau and origin are 60 and 0, respectively.
When arguments Lam0 and Haz0 are left unspecified,
the simGSC() function uses \(\Lambda_0(t) = 2\log(1 + t)\)
and \(H_0(t) = \log(1 + t) / 5\), respectively.
This is equivalent to setting
Lam0 = function(x) 2 * log(1 + x) and Haz0 = function(x) log(1 + x) / 5.
Overall, the default specifications generate the recurrent events and the terminal events
from the model:
$$\lambda(t) = \displaystyle \frac{2Z}{1 + te^{-X_{i1} - X_{i2}}},
h(t) = \displaystyle \frac{Z}{5(1 + te^{X_{i1} + X_{i2}})}, t\in[0, 60].$$
# NOT RUN {
set.seed(123)
simGSC(100, summary = TRUE)
# }
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