Re: independent right-censor in survival analysis

water <waterloo2005@xxxxxxxxx> wrote in
news:a16cbd3c-01c0-4852-a630-79ce502f8339@xxxxxxxxxxxxxxxxxxxxxxxxxxxx:

On 3ÔÂ22ÈÕ, ÉÏÎç5ʱ48·Ö, David Winsemius <doe_s...@xxxxxxxxxxx>
wrote:
water <waterloo2...@xxxxxxxxx> wrote
innews:3463ff3a-6b65-47f8-a61b-85fd3f
4d885b@xxxxxxxxxxxxxxxxxxxxxxxxxxxx:



If the censor is independent, we have
P{T in [t,t+h) | x,T >= t } P{T in [t,t+h) | x,T
>t ,Y(t) = 1}
lim ---------------------------- = lim
------------------------------------
h->0 h h->0
h

here T is failure time variable, Y(t)=1 indicates that the
individual has neithere failed nor been censored prior to time t.

Let me guess ... Kalpfleisch and Prentice 2nd ed., top of p 13?

Why?

Isn't that just saying that the instantaneous value of:

P{T in [t,t+h) | x,T >= t }
-------------------------- = lambda(x;t)
h

...which is the failure rate for an event given x's (covariates)in
the interval (t,t+h), is the same for the survivors as it was for
the whole cohort at the beginning of any interval?

--
David Winsemius

Thanks, wrapping makes my formula unreadable.
Yes,it is on top of p.13 in Kalpfleisch and Prentice 2nd ed.
P{T in [t,t+h) | x,T >= t }
lim --------------------------- h->0 h
P{T in [t,t+h) | x,T >= t,Y(t) = 1}
lim -----------------------------------
h->0 h

Y(t)=1 indicates that the individual
has neithere failed nor been censored prior to time t.

Why independent makes the formula hold?
Thanks


If the act of removing a censored case has no biasing impact on the
estimated hazard function, then the censoring process is independent of
the event process. And vice versa. If a censoring process is
independent for the event process, then there is no bias in the
estimates under consitions of censoring. It is a mathematical statement
of equivalency.

If you desire to take it to the next level, then you end up in
stochastic calculus territory. That's chapter 5 in K&P.

--
David Winsemius
.

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