simGSC {reReg}

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

\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(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 exponential distribution with mean \tau X_{i1} + Z^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].

See online vignette for more examples.

See Also

reReg

Examples

set.seed(123)
simGSC(100, summary = TRUE)