[R] Prediction in Cox Proportional-Hazard Regression
Thomas Lumley
tlumley at u.washington.edu
Thu Jun 9 15:57:49 CEST 2005
On Thu, 9 Jun 2005 Giuseppe.Palermo at bo.infn.it wrote:
> I only have an other question:
>
> since h(t) = h0(t) exp(B1*X1+ B2*X2 + B3*X3 + B4*X4)
> represent the hazard at time t.
>
> In a linear prediction,
> what Value = B1*(X1-mean(X1)) + B2*(X2-mean(X2)) + ....
> represent?
>
coxph() parametrizes the model so that
h(t)=h_0(t)exp(B1(X1-mean(X1))+B2(X2-mean(X2))
as Brian pointed out. This doesn't affect the coefficients B1, B2,..., it
just redefines h_0 to be the hazard at mean covariates rather than at zero
covariates.
The reason is that this makes h_0(t) more likely to be a useful thing to
estimate. For example, if one covariate is age then extrapolating the
baseline hazard to age zero is numerically unreliable and not very
interesting.
-thomas
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