joineRML (version 0.2.1)

simData: Simulate data from a joint model

Description

This function simulates multivariate longitudinal and time-to-event data from a joint model.

Usage

simData(n = 100, ntms = 5, beta = rbind(c(1, 1, 1, 1), c(1, 1, 1, 1)),
  gamma.x = c(1, 1), gamma.y = c(0.5, -1), sigma2 = c(1, 1), D = NULL,
  model = "intslope", theta0 = -3, theta1 = 1, censoring = TRUE,
  censlam = exp(-3), truncation = TRUE, trunctime = (ntms - 1) + 0.1)

Arguments

n

the number of subjects to simulate data for.

ntms

the maximum number of (discrete) time points to simulate repeated longitudinal measurements at.

beta

a matrix of dim = c(K,4) specifying the coefficients of the fixed effects. The order in each row is intercept, time, a continuous covariate, and a binary covariate.

gamma.x

a vector of length = 2 specifying the coefficients for the time-to-event baseline covariates, in the order of a continuous covariate and a binary covariate.

gamma.y

a vector of length = K specifying the latent association parameters for each longitudinal outcome.

sigma2

a vector of length = K specifying the residual standard errors.

D

a positive-definite matrix specifying the variance-covariance matrix. If model = 'int', the matrix has dimension dim = c(K, K), else if model = 'intslope', the matrix has dimension dim = c(2K, 2K). If D = NULL (default), an identity matrix is assumed.

model

follows the model definition in the joint function. See Details for choices.

theta0, theta1

parameters controlling the failure rate. See Details.

censoring

logical: if TRUE, includes an independent censoring time.

censlam

a scale (\(>0\)) parameter for an exponential distribution used to simulate random censoring times for when censoring = TRUE.

truncation

logical: if TRUE, adds a truncation time for a maximum event time.

trunctime

a truncation time for use when truncation = TRUE.

Value

A list of 2 data.frames: one recording the requisite longitudinal outcomes data, and one recording the time-to-event data.

Details

The function simData simulates data from a joint model, similar to that performed in Henderson et al. (2000). It works by first simulating multivariate longitudinal data for all possible follow-up times using random draws for the multivariate Gaussian random effects and residual error terms. Data can be simulated assuming either random-intercepts only in each of the longitudinal sub-models, or random-intercepts and random-slopes. Currently, all models must have the same structure. The failure times are simulated from proportional hazards time-to-event models using the following methodologies:

model="int"

The baseline hazard function is specified to be an exponential distribution with $$\lambda_0(t) = \exp{\theta_0}.$$ Simulation is conditional on known time-independent effects, and the methodology of Bender et al. (2005) is used to simulate the failure time.

model="intslope"

The baseline hazard function is specified to be a Gompertz distribution with $$\lambda_0(t) = \exp{\theta_0 + \theta_1 t}.$$ In the usual representation of the Gompertz distribution, \(\theta_1\) is the shape parameter, and the scale parameter is equivalent to \(\exp(\theta_0)\). Simulation is conditional on on a predictable (linear) time-varying process, and the methodology of Austin (2012) is used to simulate the failure time.

References

Austin PC. Generating survival times to simulate Cox proportional hazards models with time-varying covariates. Stat Med. 2012; 31(29): 3946-3958. Bender R, Augustin T, Blettner M. Generating survival times to simulate Cox proportional hazards models. Stat Med. 2005; 24: 1713-1723. Henderson R, Diggle PJ, Dobson A. Joint modelling of longitudinal measurements and event time data. Biostatistics. 2000; 1(4): 465-480.

Examples

beta <- rbind(c(0.5, 2, 1, 1),
c(2, 2, -0.5, -1))
D <- diag(4)
D[1, 1] <- D[3, 3] <- 0.5
D[1, 2] <- D[2, 1] <- D[3, 4] <- D[4, 3] <- 0.1
D[1, 3] <- D[3, 1] <- 0.01

sim <- simData(n = 250, beta = beta, D = D, sigma2 = c(0.25, 0.25),
               censlam = exp(-0.2), gamma.y = c(-.2, 1), ntms = 8)