# [R] Cox ridge regression

Ljubomir Buturovic ljubomir at sfsu.edu
Sat Aug 1 22:38:12 CEST 2009

```Hello,

I have questions regarding penalized Cox regression using survival
package (functions coxph() and ridge()). I am using R 2.8.0 on Ubuntu
Linux and survival package version 2.35-4.

Question 1. Consider the following example from help(ridge):

> fit1 <- coxph(Surv(futime, fustat) ~ rx + ridge(age, ecog.ps, theta=1), ovarian)

As I understand, this builds a model in which `rx' is the predictor,
whereas ridge penalty term contains variables `age' and
`ph.ecog'. Could someone explain what it means to regularize on
parameters which are not part of the model?  Based on definition of
Cox ridge regression (see for example ), or any other regularized
regression, the penalty term is a function of the coefficients
corresponding to the predictor variables, and nothing else.

Question 2. Consider a similar example:

> library(survival)
> lfit2 <- coxph(Surv(time, status) ~ age+ph.ecog + ridge(age, ph.ecog, theta=1), cancer)
> print(lfit2)
Call:
coxph(formula = Surv(time, status) ~ age + ph.ecog + ridge(age,
ph.ecog, theta = 1), data = cancer)

coef     se(coef) se2      Chisq DF p
age            1.13e-02 0.111    9.32e-03 0.01  1  0.92
ph.ecog        4.43e-01 1.398    1.16e-01 0.10  1  0.75
ridge(age)     2.60e-21 0.110    4.85e-17 0.00  1  1.00
ridge(ph.ecog) 5.14e-22 1.393             0.00  1  1.00

Iterations: 1 outer, 3 Newton-Raphson
Degrees of freedom for terms= 0 0 0
Likelihood ratio test=19.1  on 0.01 df, p=3.54e-08
n=227 (1 observation deleted due to missingness)
Warning message:
In sqrt((diag(x\$var2))[kk]) : NaNs produced

What is the meaning of the ridge(age) and ridge(ph.ecog) coefficients?
Again, based on the definition of Cox ridge regression, it simply adds
a penalty term to the standard Cox regression function, and doesn't
introduce any new predictors. What to make of the ridge(age) and
ridge(ph.ecog) rows in the output?

Question 3. What is the origin and significance of the warning in the
previous example:

Warning message:
In sqrt((diag(x\$var2))[kk]) : NaNs produced

Thank you very much for your help,

Ljubomir

 Bovelstad et al., Predicting survival from microarray data - a
comparative study (Bioinformatics, Vol. 23, no. 16, 2007,
pp. 2080-2087).

```