reReg (version 1.4.2)

simGSC: Function to generate simulated recurrent event data

Description

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.

Usage

simGSC(
  n,
  summary = FALSE,
  para,
  xmat,
  censoring,
  frailty,
  tau,
  origin,
  Lam0,
  Haz0
)

Arguments

n

number of observation.

summary

a logical value indicating whether a brief data summary will be printed.

para

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.

xmat

an optional matrix specifying the design matrix.

censoring

a numeric variable specifying the censoring times for each of the $n$ observation.

frailty

a numeric variable specifying the frailty variable.

tau

a numeric value specifying the maximum observation time.

origin

a numeric value specifying the time origin.

Lam0

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 $${\mathrm{\Lambda }}_0(t)=2\log (1+t).$$

Haz0

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 $$H_0(t)=\log (1+t)/5.$$

Details

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: $$\lambda (t)=Z{\lambda }_0(t{e}^{X^{\mathrm{\top }}\alpha })e^{X^{\mathrm{\top }}\beta },h(t)=Z{h}_0(t{e}^{X^{\mathrm{\top }}\eta })e^{X^{\mathrm{\top }}\theta },$$ 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 $\alpha =\eta =(0,0{)}^{\mathrm{\top }}$, and $\beta =\theta =(1,1{)}^{\mathrm{\top }}$. When the xmat argument is not specified, the simGSC() function assumes $X_i$ is a two-dimensional vector $X_i=(X_{i1},X_{i2}),i=1,\dots ,n$, 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 ${\mathrm{\Lambda }}_0(t)=2\log (1+t)$ 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: $$\lambda (t)={\displaystyle \frac{2Z}{1+t{e}^{-X_{i1}-X_{i2}}},h(t)={\displaystyle \frac{Z}{5(1+t{e}^{X_{i1}+X_{i2}})},t\in [0,60].}}$$ See online vignette for more examples.

See Also

reReg

Examples

# NOT RUN {
set.seed(123)
simGSC(100, summary = TRUE)
# }