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