[R] Estimate hazard function from right-censored data only

(Ted Harding) Ted.Harding at nessie.mcc.ac.uk
Wed Nov 5 04:06:44 CET 2003

On 05-Nov-03 John Fox wrote:
> Dear Monica,
> I'm not sure what the muhaz function is (it's not in the survival
> package), but regardless, unless I'm seriously mistaken, there's no
> information to estimate the hazard function if you haven't observed
> any events.
> I hope that this helps,
>   John

Well, there is _some_ information, to the extent that such data rule
out high levels of hazard ...

I recall seeing a paper by I.J. Good many years ago (can't locate the
reference now) in which he made a Bayesian inference of the probability
of nuclear war (none having occurred).

Basically he assumed a homogeneous Poisson process of nuclear war,
with improper prior (? 1/mu ) for the mean, and got a posterior
distribution for it.
Consequently a probability of NW within the next (say) 20 years could
be evaluated (though I seem to remember th\t a certain amount of
footwork was involved).

In the present case, without going so far as to be Bayesian, assuming
a constant hazard lambda would lead to an upper confidence limit for
lambda given that there had been no events within the observed
intervals (e.g. as the largest value of lambda such that the probability
of no events was not less than 0.05). You don't need survival-data
techniques for this ...

However, I certainly agree with the above to the extent that there
is no information which would support an estimate of a non-constant
hazard function.

Best wishes,

E-Mail: (Ted Harding) <Ted.Harding at nessie.mcc.ac.uk>
Fax-to-email: +44 (0)870 167 1972
Date: 05-Nov-03                                       Time: 03:06:44
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