knitr::opts_chunk$set( collapse = TRUE, comment = "#>" )

library(survobj) library(survival)

Following @bender2003 and @leemis1987, 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)

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)

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

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