[R] competing risks survival analysis

Thomas Lumley thomas at biostat.washington.edu
Mon Oct 30 17:44:21 CET 2000

On Mon, 30 Oct 2000, gb wrote:
> > 
> > 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
> Hold it! I think you should _right censor_ the observation at t. This
> doesn't matter, of course, if you only are interested of _one_ particular
> t, but usually one wants to do the estimation for a range of  t  values.

It does matter, even for one particular t (unless it's the first one), and
I meant what I said.  If someone has a failure of one type you know for
certain that they will not have a failure of another type: for 
any t, P(failure of other type before t)=0.  Censoring the
observation would imply that their chance of having a failure of another
type was the same as for someone who hadn't failed.

You would censor failures from other causes if you wanted to estimate the
cause-specific hazard function, but it seems that Bill wants to estimate
the crude incidence of failure of one type.  

Censoring the failures of other types and computing a survival function
gives you a quantity that AFAIK has no useful interpretation except under
untestable and usually implausible assumptions like independence of
causes. The crude incidence of failure is admittedly not always a very
interesting quantity, but it has the definite advantage of being


Thomas Lumley
Assistant Professor, Biostatistics
University of Washington, Seattle

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