[R] coxph

Peter Dalgaard p.dalgaard at biostat.ku.dk
Sun Feb 1 21:43:21 CET 2004

```Prof Brian Ripley <ripley at stats.ox.ac.uk> writes:

> On 1 Feb 2004, Peter Dalgaard wrote:
>
> > Jim Clark <jimclark at duke.edu> writes:
> >
> > [twice...]
> > > Where are the estimates of the baseline hazard for coxph?
> >
> > That's not an estimable quantity. However, estimates of the integrated
> > hazard or the survival function can be obtained with basehaz(fit)
> > resp. survfit(fit).
>
> Not estimable?  Well, neither is the cumulative hazard/survival fnction
> then, as you only get estimates at the event times.
>
> In both cases you need further assumptions on the hazard, which can be
> smoothness or sum of delta functions or ....

Well.... This *is* quibbling you know.

The relation is basically the same as with densities and distribution
functions.

You can of course, if you want to, define the estimated hazard as a
sum of delta functions. However, it won't converge to the true hazard
function in any of the standard senses as n increases (although it
will in the distribution sense, but that is basically the point of
saying that its indefinite integral is estimable).

In contrast, you can define the integrated hazard function by
extending the value at event times as a right-continuous step function
and it will converge pointwise under relatively mild conditions (the
censoring mechanism cannot be too harsh and the regressors should
behave sensibly).

--
O__  ---- Peter Dalgaard             Blegdamsvej 3
c/ /'_ --- Dept. of Biostatistics     2200 Cph. N
(*) \(*) -- University of Copenhagen   Denmark      Ph: (+45) 35327918
~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk)             FAX: (+45) 35327907

```