Hi,
The fundamental relation b/w hazard (h), survival (S), and density (f)
functions is:
f(t) = h(t) * S(t)
Where S(t) = exp ( - int_{0} ^{t} h(u) du )
mean life time = int_{0} ^{\inf} f(u) du
If you have a piecewise constant h(t), you can either smooth it and compute
the required integrals using the smoothed version, or compute the areas
using tapezoidal or simpson's rule (if data is equally spaced).
Ravi.
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Ravi Varadhan, Ph.D.
Assistant Professor, The Center on Aging and Health
Division of Geriatric Medicine and Gerontology
Johns Hopkins University
Ph: (410) 502-2619
Fax: (410) 614-9625
Email: [EMAIL PROTECTED]
Webpage: http://www.jhsph.edu/agingandhealth/People/Faculty/Varadhan.html
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-----Original Message-----
From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On
Behalf Of Alan Cox
Sent: Friday, September 26, 2008 11:31 AM
To: r-help@r-project.org
Subject: [R] Computing Mean Lifetime from Hazard
Hello,
If all I have access to is an empirically calculated hazard function, is it
possible to compute an approximate value for the mean lifetime?
I know that if the hazard function is essentially constant, the mean
lifetime is 1/hazard rate. But if I'm confident that the empirical hazard
function is not constant, I'm not sure how to go about calculating an
estimate of mean lifetime.
For instance, suppose someone goes about generating a muhaz object by doing
the following:
> haz <- muhaz(runif(1000,30,40))
and then gives me only the haz object. I can plot it, and see pretty
quickly that it isn't constant. The person who generated the muhaz object
would know that the average lifetime is approx. 35. Is there anyway that I
can learn that from looking only haz?
Does the process for doing this differ based on whether the lifetimes are
generated from a well-known distribution?
Thanks for your help,
Alan
--
Alan Cox
Director, User Experience
iContact, Corp.
p 919.459.1038 f 919.287.2475
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