Simulate recurrent events from a two-stage model with structured gamma frailties

Simulates recurrent event data with two event types and a terminal event, using a parametric two-stage frailty model. The construction ensures that the marginal rates are approximately correct: conditional on survival, $E(dN_j \mid D > t) \approx$ cumhazj, and the hazard of death equals death.cumhaz.

Usage

sim_recurrentTS(
  n,
  cumhaz,
  cumhaz2,
  death.cumhaz = NULL,
  nu = rep(1, 3),
  share1 = 0.3,
  vargamD = 2,
  vargam12 = 0.5,
  gap.time = FALSE,
  max.recurrent = 100,
  cens = NULL,
  ...
)

Arguments

n: Number of subjects to simulate.
cumhaz: Two-column matrix (time, cumhaz) giving the target marginal cumulative rate of the first recurrent event type.
cumhaz2: Two-column matrix (time, cumhaz) giving the target marginal cumulative rate of the second recurrent event type.
death.cumhaz: Two-column matrix (time, cumhaz) giving the cumulative hazard of the terminal event.
nu: Numeric vector of length 3: the powers $(\nu_1, \nu_2, \nu_3)$ applied to the frailty components (see Details). Must satisfy $\nu_j > -1/\text{shape}$. Default is rep(1, 3).
share1: Proportion of the total death frailty variance assigned to the first component $Z_{d1}$. The remainder goes to $Z_{d2}$. Must be in $(0, 1)$. Default is 0.3.
vargamD: Total variance of the death frailty $Z_\text{death}$. Default is 2.
vargam12: Variance of the shared recurrent-event frailty $Z_{12}$. Default is 0.5.
gap.time: Logical. If TRUE, event times are drawn as gap times rather than calendar times. Default is FALSE.
max.recurrent: Maximum number of recurrent events per subject. Default is 100.
cens: Rate of exponential censoring. If NULL (default), no administrative censoring is applied.
...: Further arguments passed to lower-level simulation functions.

Value

A data frame in counting-process format (one row per event interval per subject) with columns id, start, stop, entry, time, status, and death. Attributes store the (possibly adjusted) cumulative hazards used in simulation and the frailty parameters.

Details

The frailty structure uses three gamma random variables $Z_{d1}$, $Z_{d2}$, $Z_{12}$ to induce dependence: $$Z_\text{death} = Z_{d1} + Z_{d2}, \quad Z_1 = Z_{d1}^{\nu_1} Z_{12}, \quad Z_2 = Z_{d2}^{\nu_2} Z_{12}^{\nu_3}.$$ The parameters share1 and vargamD control how the death frailty splits between the two components, and vargam12 controls the shared recurrent-event frailty. Setting $\nu = (1,1,1)$ with share1 = 0.5 gives a symmetric structure; varying $\nu$ allows asymmetric dependence.

Author

Thomas Scheike

Examples

data(CPH_HPN_CRBSI)
dr    <- CPH_HPN_CRBSI$terminal
base1 <- CPH_HPN_CRBSI$crbsi
base4 <- CPH_HPN_CRBSI$mechanical

rr <- sim_recurrentTS(1000, base1, base4, death.cumhaz = dr)
dtable(rr, ~death + status)
#> 
#>       status    0    1    2
#> death                      
#> 0             138 2394  384
#> 1             861    0    0
mets:::showfitsim(causes = 2, rr, dr, base1, base4)