Simulation of survival times

library(survobj)
library(survival)

Introduction

Following Bender, Augustin, and Blettner (2003) and Leemis (1987), simulation of survival times is possible if there is function that invert the cumulative hazard ($H^{-1}$), Random survival times for a baseline distribution can be generated from an uniform distribution between 0-1 $U$ as: $$T = H^{-1}(-log(U))$$ For a survival distribution object, this can be accomplished with the function rsurv(s_object, n) which will generate n number of random draws from the distribution s_object. All objects of the s_distribution family implements a function that inverts the survival time with the function invCum_Hfx()

The function ggplot_survival_random() helps to graph Kaplan-Meier graphs and cumulative hazard of simulated times from the distribution

s_obj <- s_exponential(fail = 0.4, t = 2)
ggplot_survival_random(s_obj, timeto =2, subjects = 1000, nsim= 10, alpha = 0.3)

Generation of Proportional Hazard times

Survival times with hazard proportional to the baseline hazard can be simulated $$T = H^{-1}\left(\frac{-log(U)}{HR}\right)$$ where $HR$ is a hazard ratio.

The function rsurv_hr(s_object, hr) can generate random number with hazards proportionals to the baseline hazard. The function produce as many numbers as the length of the hr vector. for example:

s_obj <- s_exponential(fail = 0.4, t = 2)
group <- c(rep(0,500), rep(1,500))
hr_vector <- c(rep(1,500),rep(2,500))
times <- rsurvhr(s_obj, hr_vector)
plot(survfit(Surv(times)~group), xlim=c(0,5))

The function ggplot_survival_hr() can plot simulated data under proportional hazard assumption.

s_obj <- s_exponential(fail = 0.4, t = 2)
ggplot_survival_hr(s_obj, hr = 2, nsim = 10, subjects = 1000, timeto = 5)

Generation of Acceleration Failure Times

Survival times with accelerated failure time to the baseline hazard can be simulated $$T = \frac{H^{-1}(-log(U))}{AFT}$$ where $AFT$ is a acceleration factor, meaning for example an AFT of 2 have events two times quicker than the baseline

The function rsurv_aft(s_object, aft) can generate random numbers accelerated by an AFT factor. The function produce as many numbers as the length of the aft vector. for example:

s_obj <- s_lognormal(scale = 2, shape = 0.5)
ggplot_survival_aft(s_obj, aft = 2, nsim = 10, subjects = 1000, timeto = 5)

In this example, the scale parameter of the Log-Normal distribution represents the mean time and it this simulation and accelerated factor of 2 move the average median from 2 to 1

If the proportional hazard and the accelerated failure is combined and accelerated hazard time is generated. This can be accomplished with the function rsurvah() function and the ggplot_random_ah() functions

References

Bender, R., Thomas Augustin, and Maria Blettner. 2003. “Generating Survival Times to Simulate Cox Proportional Hazards Models.” Universitätsbibliothek Der Ludwig-Maximilians-Universität München. https://doi.org/10.5282/UBM/EPUB.1716.

Leemis, Lawrence M. 1987. “Variate Generation for Accelerated Life and Proportional Hazards Models.” Operations Research 35 (6): 892–94.