MST (version 2.2)

rmultime: Random Multivariate Survival Data

Description

Generates multivariate survival data

Usage

rmultime(N = 100, K = 4, beta = c(-1, 2, 1, 0, 0), cutoff = c(0.5, 0.5, 0, 0),
  digits = 1, icensor = 1, model = c("gamma.frailty", "log.normal.frailty",
  "marginal.multivariate.exponential", "marginal.nonabsolutely.continuous",
  "nonPH.weibull"), v = 1, rho = 0.65, a = 1.5, lambda = 0.1)

Arguments

N

Number of clusters (ids)

K

Number of units per cluster

beta

Vector of beta coefficients (first number is baseline hazard coefficient (\(\beta_{0}\)), remaining numbers are slope coefficients for covariates (\(\beta_{1}\)))

cutoff

Cutoff values for each covariate

digits

Rounding digits

icensor

Control for censoring rate: 1 - 50%

model

Model for simulating data: must be either "gamma.frailty", "log.normal.frailty", "marginal.multivariate.exponential", "marginal.nonabsolutely.continuous", or "nonPH.weibull"

v

Scale parameter for "gamma.frailty" and "nonPH.weibull" or variance parameter for "log.normal.frailty" models. Not used in marginal models

rho

Correlation for marginal models. Not used in other models

a

Parameter for "nonPH.weibull" model. Not used in other models

lambda

Parameter for "nonPH.weibull" model. Not used in other models

Value

dat

The simulated data

model

The model used

Details

This function generates multivariate survival data. Letting \(i=1,...,N\) number of clusters, \(j=1,...,K\) number of units per cluster, and \(X_{ij}\) be a candidate covariate, the following multivariate survival models can be used:

gamma.frailty: \(\hspace{2mm}\) \(\lambda_{ij}(t)=\exp(\beta_{0}+\beta_{1} \cdot I(X_{ij} \leq c)) w_{i}\) with \(w_{i} \sim \Gamma(1/v, 1/v)\)

log.normal.frailty: \(\hspace{2mm}\) \(\lambda_{ij}(t)=\exp(\beta_{0}+\beta_{1} \cdot I(X_{ij} \leq c) + w_{i})\) with \(w_{i} \sim N(0, v)\)

marginal.multivariate.exponential: \(\hspace{2mm}\) \(\lambda_{ij}(t)=\exp(\beta_{0}+\beta_{1} \cdot I(X_{ij} \leq c))\) absolutely continuous

marginal.nonabsolutely.continuous: \(\hspace{2mm}\) \(\lambda_{ij}(t)=\exp(\beta_{0}+\beta_{1} \cdot I(X_{ij} \leq c))\) not absolutely continuous

nonPH.weibull: \(\hspace{2mm}\) \(\lambda_{ij}(t)=\lambda_{0}(t) \exp(\beta_{0}+\beta_{1} \cdot I(X_{ij} \leq c)) w_{i}\) with \(w_{i} \sim \Gamma(1/v ,1/v)\) and

\(\hspace{96mm}\) \(\lambda_{0}(t)=\alpha \lambda t^{\alpha-1}\)

The user specifies the coefficients (\(\beta_{0}\) and \(\beta_{1}\)), the cutoff values, the censoring rate, and the model with the respective parameters.

References

Fan J., Nunn M., Su X. (2009) Multivariate exponential survival trees and their application to tooth prognosis. Computational Statistics and Data Analysis, 53(4), 1110--1121.

Su X., Fan J., Wang A., Johnson M. (2006) On Simulating Multivariate Failure Times. International Journal of Applied Mathematics & Statistics, 5, 8--18

See Also

genSurv, complex.surv.dat.sim, survsim

Examples

# NOT RUN {
randMarginalExp <- rmultime(N = 200, K = 4, beta = c(-1, 2, 2, 0, 0), cutoff = c(0.5, 0.5, 0, 0),
    digits = 1, icensor = 1, model = "marginal.multivariate.exponential", rho = .65)$dat

randFrailtyGamma <- rmultime(N = 200, K = 4, beta = c(-1, 1, 3, 0), cutoff = c(0.4, 0.6, 0),
    digits = 1, icensor = 1, model = "gamma.frailty", v = 1)$dat
# }