[R] survival - ratio likelihood for ridge coxph()

Terry Therneau therneau at mayo.edu
Tue Feb 16 16:28:21 CET 2010

> 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

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