[R] Competing risks Kalbfleisch & Prentice method

[Eleni Rapsomaniki]

Dear Prof. Therneau, 

Thank you for your views on this subject. I think all R users who play
with survival analysis are most grateful for the functions you have
already supplied us with.

I'm guessing Ravi is wondering why you have not implemented the
smoothing of the baseline hazard from the Cox model. 

I actually tried to do this originally, inspired from this thread (i.e
use sm.spline to smooth the hazard):
https://stat.ethz.ch/pipermail/r-help/2004-July/053843.html

but it overestimated the CI (perhaps I implemented it wrong). I was then
advised to treat CI as a step function, rather than continuous, which
means that F(t+1, cause k)-F(t, cause k) will be 0 unless an event of
cause k has occurred in that interval (see also "Competing Risks, by
Melanie Pintilie, page 62). This is obviously problematic if one wants
to estimate the CI at times that are not close to observed events for
either cause (perhaps a parametric model could be used in this case).
But then again, this was not an issue wtih my data. 

Eleni Rapsomaniki
 Research Associate
Strangeways Research Laboratory
Department of Public Health and Primary Care
University of Cambridge
 

-----Original Message-----
From: Terry Therneau [mailto:therneau at mayo.edu] 
Sent: 27 March 2009 13:53
To: Eleni Rapsomaniki; tuechler at gmx.at; Ravi Varadhan
Cc: r-help at r-project.org
Subject: RE: Competing risks Kalbfleisch & Prentice method

Ravi's last note finished with
>  I am wondering why Terry Therneau's "survival" package doesn't
>  have this option.  

  The short answer is that there are only so many hours in a day.  

  I've recently moved the code base from an internal Mayo repository to
R-forge, 
one long term goal with this is to broaden the developer base to n>2 (me
and 
Thomas Lumley).  
  
  A longer statistical answer:
  
  I'm not sure if the "this" of Ravi's question is a. smoothed hazards,
b. the 
K&P cumulative incidence or c. the Fine & Gray model.
  
  b. I like the CI model and am using it more.  We also have local code.
The 
latest version of survival (on rforge, likely in the next default R
release) has 
added simple CI curves to the survfit function.  Adding code for survfit
on Cox 
models is on the todo list.  But -- this release also fixes up
survfit.coxph to 
handle weighted Cox models and that was on my list for approx 10 years,
i.e., 
don't hold your breath.  I don't release something until it also has a
set of 
worked out test cases to add to the 'tests' directory.
  
  a. smoothed hazards.  For the case at hand I don't see any particular 
advantage of this.  On the other hand, I often would like to display
hazard 
functions instead of CI functions for Cox models; with time dependent
covariates 
I don't think a survival curve makes sense.  But I haven't had the time
to think 
through exactly which methods should be added.
  
  c. Fine & Gray model, i.e., where covariates have a direct influence
on the 
competing risk.  I find the model completely untenable from a biologic
point of 
view, so have no interest in adding it.  (Due to finite time, everything
in the 
survival package is code that I needed for an analysis; medical research
is what 
pays my salary.)  Assume that I have competing processes/risks, say
progression 
of a tumor and heart disease;  I expect that the tumor process pays no
attention 
whatsoever to what is going on in the heart.  But this is necessary if 
"type=squamous" is modeled as an absolute beta=__ increase in the CI for
cancer. 
 The squamous cells need to "step up the pace" of invasion if heart
failure 
threatens, like jockeys in a horse race. 
  
   Terry T.