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

[David Winsemius]

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