R help - Apr 2018 - parfm unable to fit models when hazard rate is small

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

	[[alternative HTML version deleted]]

Possible hint:

1. Look at the error message.

2.
> 1/0
[1] Inf


Cheers,
Bert


Bert Gunter

"The trouble with having an open mind is that people keep coming along
and sticking things into it."
-- Opus (aka Berkeley Breathed in his "Bloom County" comic strip )


On Wed, Apr 4, 2018 at 6:37 AM, Alexander Pate
<alexander.pate at manchester.ac.uk> wrote:
> 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
>
>         [[alternative HTML version deleted]]
>
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