It happens from time to time that I would like to estimate the excess hazard instead of the hazard ratios in a survival analysis - often because I am asked to do so by reviewers on researchpapers. So to say, an additive hazard model instead of an multiplicative.
There are several ways to do this. One very elegant way has been described by Lin et al (reference below). In this very general model we still have a non-parametric baseline-hazard as known from cox-regression, but then there can be both a multiplicative effect and/or an additive effect. The hazardfunction then takes the form
where S is stratum, i is individual i, lambda0S is the baseline hazard. g and h is user defines link-funktions and W and X is covariates and t is a time on the underlying time axis. It turns out that it is surprisingly simple to estimate the parameters beta and gamma. An example of the model is the cox-regression where g=0, and h=exp(). An excess hazard model could for instance be where g(x)=x and h()=1.
My suggestion is to develop a procedure where the user can specify the two link functions arbitrary. This will give a procedure which can estimate parameters in a large family of hazard-models.
something like this is my suggestion:
proc hazardregression data=survivaldata;
gclass A B C;
hclass D E;
model (entry exit)*censur(0)=gmodel(A B C) hmodel( D E) /ties=breslow hlink=exp glink=id;
run;
the user has then then to specify both the hlink and glink as either already buildin SAS-functions, or as userdefined function specified with fcmp (I assume above that A B C D and E are covariates). Notice the similarity with phreg.
I hope what I suggest makes sense.
Reference:
Semiparametric Analysis of General Additive-Multiplicative Hazard Models for Counting Processes The Annals of Statistics, Vol. 23, No. 5. (1995), pp. 1712-1734, by D. Y. Lin, Zhiliang Ying
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