[R] competing risks survival analysis

Thomas Lumley thomas at biostat.washington.edu
Mon Oct 30 06:00:04 CET 2000

On Thu, 26 Oct 2000, Bill Simpson wrote:

> I will have data in the following form:
> Time    resp type       stim type
> 300     a               A
> 200     b               A
> 155     a               B
> 250     b               B
> 80      c               A
> 1000    d               B
> ...
> c is left censored observation; d is right censored
> This sort of problem is discussed in Chap 9 of Cox & Oakes Analysis of
> Survival Data under the name "competing risks".
> Observations are obtained from n independent individuals in the form
> (t_i,r_i;s_i) where t_i is the time of the event (failure), r_i is the
> response type (failure type), and s_i is the stimulus type (explanatory
> variable).
> I am wondering if it is possible to use survfit5 to fit parametric and
> nonparametric models to data like these, and if so how to do it. I
> read the documentation for survfit5 and Surv() did  not seem to allow for
> the type of model I need. If I can't use survfit5, any suggestions on how
> to proceed? I am pretty ignorant of survival analysis at this point.
> (Maybe I can just do separate survival analysis runs for the type a and
> type b responses?)
> Thanks very much for any help.
> Bill
> PS In the end I would like to have a plot of phat_a(t) vs t: probablity of
> a failure of type a as a function of time (just like Cox and Oakes fig
> 9.1)

The mixture of left and right censoring is a problem -- survival5 can only
handle this for parametric models.

I don't have a copy of Cox & Oakes, but if you just want to know the
probability of a failure of type a before time t you can easily handle the
competing risks issue. If someone has a failure of type b then you know
that they don't have a failure of type a before time t, so you can set
their failure time to a very large number (effective infinity).  If it
weren't for the left censoring you could just use survfit to get the
cumulative  incidence of events of type a.  With the left censoring it's a
bit messy, since none of the available parametric distributions will fit
(none of them has mass at infinity), so there isn't a very good
solution. What sort of parametric models were you thinking of? In
principle you can specify your own models to survreg(), but there isn't
much documentation.

If you want to do something more complicated involving what might have
happened to the type b failures if they didn't have a type b failure then
the problem is impossible (there are several solutions in the literature
but that doesn't change the fact that it's impossible).  


Thomas Lumley
Assistant Professor, Biostatistics
University of Washington, Seattle

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