coxph
Prof Brian Ripley <ripley at stats.ox.ac.uk> writes:
On 1 Feb 2004, Peter Dalgaard wrote:
Jim Clark <jimclark at duke.edu> writes: [twice...]
Where are the estimates of the baseline hazard for coxph?
That's not an estimable quantity. However, estimates of the integrated hazard or the survival function can be obtained with basehaz(fit) resp. survfit(fit).
Not estimable? Well, neither is the cumulative hazard/survival fnction then, as you only get estimates at the event times. In both cases you need further assumptions on the hazard, which can be smoothness or sum of delta functions or ....
Well.... This *is* quibbling you know. The relation is basically the same as with densities and distribution functions. You can of course, if you want to, define the estimated hazard as a sum of delta functions. However, it won't converge to the true hazard function in any of the standard senses as n increases (although it will in the distribution sense, but that is basically the point of saying that its indefinite integral is estimable). In contrast, you can define the integrated hazard function by extending the value at event times as a right-continuous step function and it will converge pointwise under relatively mild conditions (the censoring mechanism cannot be too harsh and the regressors should behave sensibly).
O__ ---- Peter Dalgaard Blegdamsvej 3 c/ /'_ --- Dept. of Biostatistics 2200 Cph. N (*) \(*) -- University of Copenhagen Denmark Ph: (+45) 35327918 ~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk) FAX: (+45) 35327907