R help - Feb 2010 - survival - ratio likelihood for ridge coxph()

It seems to me that R returns the unpenalized log-likelihood for the ratio
likelihood test when ridge regression Cox proportional model is implemented. Is
this as expected?

In the example below, if I am not mistaken, fit$loglik[2] is unpenalized
log-likelihood for the final estimates of coefficients. I would expect to get
the penalized log-likelihood. I would like to check if this is as expected. If
not, I am prepared to give more details. Cheers,DK.

For example, if we have a model
> fit <- coxph(Surv(futime, fustat) ~ ridge(rx, age, ecog.ps,
theta=1),data=ovarian)
> fit$loglik
[1] -34.98494 -27.17558
> fit
Call:
coxph(formula = Surv(futime, fustat) ~ ridge(rx, age, ecog.ps, 
    theta = 1), data = ovarian)

               coef   se(coef) se2    Chisq DF p     
ridge(rx)      -0.780 0.5862   0.5589  1.77 1  0.1800
ridge(age)      0.123 0.0387   0.0356 10.15 1  0.0014
ridge(ecog.ps)  0.104 0.5729   0.5478  0.03 1  0.8600

Iterations: 1 outer, 4 Newton-Raphson
Degrees of freedom for terms= 2.7 
Likelihood ratio test=15.6  on 2.67 df, p=0.000941  n= 26
> fit$loglik[2]
[1] -27.17558


 		 	   		  
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> It seems to me that R returns the unpenalized log-likelihood for the
> ratio likelihood test when ridge regression Cox proportional model is
> implemented. Is this as expected?
It is easy to verify that this is correct:
> fit1 <- coxph(Surv(time, status) ~ ridge(age) + ph.ecog, lung)
> fit2 <- coxph(Surv(time, status) ~ age + ph.ecog, lung,
      init=fit1$coef, iter=0)  # A model with pre-fixed
coefficients
> c(fit1$loglik[2], fit2$loglik[2])
[1] -735.0954 -735.0954

It this intentional?  Yes.  Is it optimal?  Probably not. The dominating
design goal for the penalized Cox code was extensibility --- you can
actually add your own penalized methods.  It also meant that individual
plugins such as frailty, pspline, and ridge have compromises.  However,
I am not aware of anyone ever using this extensibility; given this
experience the design priorities would be different if I were to write
it anew.  Hindsight is always 20/20.

BUT -- I would be quite happy to have someone write a better ridge()
plugin.  Interested?

Terry Therneau