[R] predicting cumulative hazard for coxph using predict

[Terry Therneau]

> I am estimating the following coxph function with stratification and 
> frailty, where each person had multiple events.

> m <- coxph(Surv(dtime1,status1) ~ gender +cage +uplf+ strata(enum)+ 
>               frailty(id), xmodel)

>I want to predict the cumulative hazard for each person for their next event at
> a given time in future.What is the best way to compute it? 

 There are two issues.  The first is that what you are asking for -- it is not 
at all clear to me exactly how this should be computed, and as a consequence the 
coxph routines/documentation are not clear.  When there is a random effect in 
the model, should the baseline hazard be computed before or after integrating 
out the random effect?  How should one define the cumulative hazard for a 
subject?  These are hard questions, or at least I've found them so.
 
 What is currently done: The basline hazard is computed treating each of the 
fitted random effects (one per id) as it if were a known fixed value.  The 
predict function treats the random effects as just another coefficient, which is 
clearly the wrong thing to do wrt a new subject who was not in the original data 
set. 
   If you think of the frailty term as a shrinkage estimator, with no particular 
connection to random effects, then what is currently done makes reasonable 
sense.  The "random effects" are just more coefficients in the model.   
   
   Terry Therneau