[R] non-cumulative hazard in Cox model with time-dependent covariates

[Thomas Lumley]

On Fri, Oct 7, 2011 at 9:27 AM, David Winsemius <dwinsemius at comcast.net> wrote:
>
> On Oct 6, 2011, at 7:00 AM, koshihaku wrote:
>
>> Dear all,
>> Is there a way to calculate the non-cumulative hazard (instantaneous
>> hazard), which is the product of baseline hazard and exp{beta*covariate} ?
>> I knew in survfit, we can get the estimator of cumulative baseline hazard,
>> but how can we get the non-cumulative one?
>>
>
> The instantaneous hazard is just (dS/dt)/ S. It should be fairly easy to
> calculate that value at each event from the estimated baseline survival,
> S_0(t).  I don't know if there is an intermediate result in the coxph or
> survfit internals that could be exported as the "baseline hazard function".
> Most of the presentation of the theory in Therneau and Grambsch uses the
> cumulative hazard function.
>

It's actually quite tricky to get a good estimate unless the sample
size is very large.  S_0(t) is a step function, so you need to smooth,
and the smoothing bandwidth needs to increase with t, as the sample
size at risk decreases. And there's a boundary at the left but not at
the right, to add complications for kernel smoothing.

   -thomas

-- 
Thomas Lumley
Professor of Biostatistics
University of Auckland