sim_weibdf {discfrail} R Documentation

## 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)