sim_weibdf {discfrail}

Simulation of grouped time-to-event data with Weibull baseline hazard and discrete shared frailty distribution

Description

This function returns a dataset generated from a Weibull proportional hazards model with a shared discrete frailty term, for given Weibull parameters, hazard ratios, distribution of groups among latent populations, frailty values for each latent population, and randomly-generated covariate values.

Usage

sim_weibdf(J, N = NULL, lambda, rho, beta, p, w_values, cens_perc)

Arguments

J

number of groups in the data

N

number of individuals in each group

lambda

Weibull baseline rate parameter (see below), interpreted as the rate parameter with covariate values of 0 and frailty ratio 1. For rho=1 this is the baseline hazard.

rho

Weibull shape parameter (see below)

beta

covariate effects in the Weibull distribution, interpreted as log hazard ratios (see below)

p

vector of K elements. The kth element gives the proportion of groups in the kth latent population of groups.

w_values

vector of K distinct frailty values, one for each latent population.

cens_perc

cens_perc percentage of censored events. Censoring times are assumed to be distributed as a Normal with variance equal to 1.

Details

The "proportional hazards" parameterisation of the Weibull distribution is used, with survivor function S(t) = exp(-\lambda t^{\rho} w exp(x^T {\beta}) ). Note this is different from the "accelerated failure time" parameterisation used in, e.g. dweibull. Distribution functions for the proportional hazards parameterisation can be found in the flexsurv package.

Value

A data frame with one row for each simulated individual, and the following columns:

family: the group which the individual is in (integers 1, 2, ...)

time: the simulated event time.

status: the simulated survival status. Censoring times are generated from a Normal distribution with standard deviation equal to 1 and the mean is estimated in order to guarantee the determined percentage of censored events. The event time is observed (status=1) if it is less than the censoring time, and censored otherwise (status=0).

x: matrix of covariate values, generated from a standard normal distribution.

belong: the frailty hazard ratio corresponding to the cluster of groups in which the individual's group has been allocated.

References

Wan, F. (2017). Simulating survival data with predefined censoring rates for proportional hazards models. Statistics in medicine, 36(5), 838-854.

Examples

J <- 100
N <- 40
lambda <- 0.5
beta <- 1.6
rho <- 1
p <- c( 0.8, 0.2 )
w_values <- c( 0.8, 1.6 )
cens_perc <- 0.2
data <- sim_weibdf( J, N, lambda, rho, beta, p, w_values, cens_perc)
head( data )