[R] parfm unable to fit models when hazard rate is small

[Alexander Pate]

Hello, I would like to use the parfm package: https://cran.r-project.org/web/packages/parfm/parfm.pdfhttps://cran.r-project.org/web/packages/parfm/parfm.pdf in my work. This package fits parametric frailty models to survival data. To ensure I was using it properly, I started by running some small simulations to generate some survival data (without any random effects), and analyse the data using the parfm package. I am using an exponential baseline hazard. When the baseline hazard rate drops to 0.001, I get the following error when trying to fit the model:

Error in optimHess(par = ESTIMATE, fn = Mloglikelihood, obs = obsdata,  :
  non-finite finite-difference value [1]
In addition: Warning message:
In log(pars) : NaNs produced

Has anybody else come across this issue, or could suggest why parfm struggles with low event rates? Or could someone please run my code to see if they get the same issue? Full reproducible code is presented below.

Many thanks for any help,
Alex

CODE:

### Create function to generate data
simulWeib <- function(N, lambda, rho, beta1, beta2, beta3, beta4, rateC, sigma)
{
  # covariate --> N Bernoulli trials
  x1 <- sample(x=c(0, 1), size=N, replace=TRUE, prob=c(0.5, 0.5))

  # Now create random effect stuff
  # Create one vector of length N, all drawn from same normal distribution
  rand.effect <- rnorm(N,0,sigma)

  # Weibull latent event times
  v <- runif(n=N)
  Tlat <- round((- log(v) / (lambda * exp(x1 * beta1 + rand.effect)))^(1 / rho))
  multiplier = exp(x1 * beta1 + rand.effect)
  haz=lambda * exp(x1 * beta1 + rand.effect)

  # censoring times
  #C <-rep(100000,N)
  C <- rexp(n=N, rate=rateC)

  # follow-up times and event indicators
  time <- pmin(Tlat, C)
  #status <- as.numeric(rep(1,N))
  status <- as.numeric(Tlat <= C)

  # data set
  data.frame(id=1:N,
             id10=ceiling(1:N/10),
             time=time,
             status=status,
             x1 = as.factor(x1),
             re=rand.effect,
             multiplier=multiplier,
             haz=haz)
}

### The reason it doesn't work is becayse the event rate gets so small!!
set.seed(101)

# Note that although data generated is for weibull, I set rho = 1 so it reduces to an exponential hazard, with rate = lambda
# Also note sigma = 0, so random effect is not present

## Create data and fit model, lambda = 0.1
data0<-simulWeib(10000,lambda=0.1,rho=1,rateC=0.0000000001, beta1=0.25,beta2=0,beta3=0,beta4=0, sigma = 0)
fit.cox0<-parfm(Surv(time,status) ~ x1, data=data0, dist="exponential")
fit.cox0

## Create data and fit model, lambda = 0.01
data0<-simulWeib(10000,lambda=0.01,rho=1,rateC=0.0000000001, beta1=0.25,beta2=0,beta3=0,beta4=0, sigma = 0)
fit.cox0<-parfm(Surv(time,status) ~ x1, data=data0, dist="exponential")
fit.cox0

## Create data and fit model, lambda = 0.001
data0<-simulWeib(10000,lambda=0.001,rho=1,rateC=0.0000000001, beta1=0.25,beta2=0,beta3=0,beta4=0, sigma = 0)
fit.cox0<-parfm(Surv(time,status) ~ x1, data=data0, dist="exponential")
fit.cox0

## Create data and fit model, lambda = 0.0001
data0<-simulWeib(10000,lambda=0.0001,rho=1,rateC=0.0000000001, beta1=0.25,beta2=0,beta3=0,beta4=0, sigma = 0)
fit.cox0<-parfm(Surv(time,status) ~ x1, data=data0, dist="exponential")
fit.cox0

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