[R] Prediction in Cox Proportional-Hazard Regression

[Thomas Lumley]

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