Generate Random Survival Times From A Hazard Function Applying A Hazard Rate with flexsurv - r

Question

Please consider the following:
My aim is to draw random survival times from a flexible parametric multi-state model fitted with flexsurvreg (more specifically msfit.flexsurvreg) and applying some hazard ratio (HR, in this example set to 0.2).
I found an example to generate random survival times using any hazard function here. This is also were I apply the HR.
Problem
With the actual data, I receive an error once the HR is below the value of 0.2: Error in uniroot((function(x) { : no sign change found in 1000 iterations.
This does not happen in the reproducible example below.
Questions
Is there another, better way than the one below to draw random survival times while applying a HR?
Can someone indicate why the "no sign change" error may occur and how this can be fixed?
Any help is greatly appreciated!
Minimal reproducible example
# Load package
library(flexsurv)
#> Loading required package: survival
# Load data
data("bosms4")
# Define hazard ratio
hr <- 0.2
# Fit model (weibull)
crwei <- flexsurvreg(formula = Surv(years, status) ~ trans + shape(trans),
data = bosms3, dist = "weibull")
# Create transition matrix
Q <- rbind(c(NA,1,2),c(NA,NA,3), c(NA,NA,NA))
# Capture parameters
pars <- pars.fmsm(crwei, trans=Q, newdata=data.frame(trans=1:3))
# Code from https://eurekastatistics.com/generating-random-survival-times-from-any-hazard-function/ ----
inverse = function(fn, min_x, max_x){
# Returns the inverse of a function for a given range.
# E.g. inverse(sin, 0, pi/2)(sin(pi/4)) equals pi/4 because 0 <= pi/4 <= pi/2
fn_inv = function(y){
uniroot((function(x){fn(x) - y}), lower=min_x, upper=max_x)[1]$root
}
return(Vectorize(fn_inv))
}
integrate_from_0 = function(fn, t){
int_fn = function(t) integrate(fn, 0, t)
result = sapply(t, int_fn)
value = unlist(result["value",])
msg = unlist(result["message",])
value[which(msg != "OK")] = NA
return(value)
}
random_survival_times = function(hazard_fn, n, max_time=10000){
# Given a hazard function, returns n random time-to-event observations.
cumulative_density_fn = function(t) 1 - exp(-integrate_from_0(hazard_fn, t))
inverse_cumulative_density_fn = inverse(cumulative_density_fn, 0, max_time)
return(inverse_cumulative_density_fn(runif(n)))
}
# Run with data ----
random_survival_times(hazard_fn = function(t){crwei$dfns$h(t, pars[[1]][1], pars[[1]][2]) * hr}, n = 100)
#> Error in integrate(fn, 0, t): non-finite function value
# Adapt random_survival time function replacing 0 with 0.1 ----
random_survival_times <- function(hazard_fn, n, max_time=10000){
# Given a hazard function, returns n random time-to-event observations.
cumulative_density_fn = function(t) 1 - exp(-integrate_from_0(hazard_fn, t))
inverse_cumulative_density_fn = inverse(cumulative_density_fn, 0.1, max_time)
return(inverse_cumulative_density_fn(runif(n)))
}
# Run again with data ----
random_survival_times(hazard_fn = function(t){crwei$dfns$h(t, pars[[1]][1], pars[[1]][2]) * hr}, n = 100)
#> Error in uniroot((function(x) {: f() values at end points not of opposite sign
# Adapt inverse adding extendedInt = "yes" ----
inverse <- function(fn, min_x, max_x){
# Returns the inverse of a function for a given range.
# E.g. inverse(sin, 0, pi/2)(sin(pi/4)) equals pi/4 because 0 <= pi/4 <= pi/2
fn_inv <- function(y){
uniroot((function(x){fn(x) - y}), lower=min_x, upper=max_x,
extendInt = "yes" # extendInt added because of error on some distributions: "Error in uniroot((function(x) { : f() values at end points not of opposite sign. Solution found here: https://stackoverflow.com/questions/38961221/uniroot-solution-in-r
)[1]$root
}
return(Vectorize(fn_inv))
}
# Run again with data ----
res <- random_survival_times(hazard_fn = function(t){crwei$dfns$h(t, pars[[1]][1], pars[[1]][2]) * hr}, n = 100)
res[1:5]
#> [1] 1.074281 13.688663 30.896637 159.643827 15.805103
Created on 2022-10-18 with reprex v2.0.2

Answer 1

This method of sampling survival times basically works by sampling a random uniform(0,1) number p and finding x for which the survival probability is p. The uniroot step is used to solve S(x) = p by a numerical search. In your case, it is having difficulty finding a solution after 1000 steps.
I've seen this happen, and fixed by adding, e.g. uniroot(..., maxiter=10000) to tell it to try a bit harder to find the solution. That's always been enough in my tests, though those may be limited. If that doesn't work, I'd advise digging in by hand and examining the survival curve that you are trying to invert - it may be invalid due to some parameter value being extreme.
(This kind of thing is done in the function qgeneric in the flexsurv package, though it borrows a vectorised version of uniroot from the rstpm2 package which is faster.)