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?
Thank you very much!
Koshihaku
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non-cumulative hazard in Cox model with time-dependent covariates
3 messages · koshihaku, David Winsemius, Thomas Lumley
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. Therneau suggests: "Users are strongly advised to use the newdata argument. Note that this data set needs to contain values for the main effects but not for any interaction terms." The "baseline survival" has the same problems in interpretation that are discussed on the opening paragraph for the Details section in help(survfit.coxph).
David Winsemius, MD West Hartford, CT
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