# [R] p values in coxph()

Terry Therneau therneau at mayo.edu
Fri Sep 23 15:31:23 CEST 2011

``` 1) The p values in the printout are a Wald test.  The Wald, score, and
likelihood ratio tests are asymptotically equivalent, but may differ
somewhat in finite samples.  (The Wald and score are both Taylor series
approximations to the LR).  If you want to do an LR test, fit the two
models and use the anova command.  But beware if your second variable
has missing values: the two fits have to be on the same sample.

2) Yes, coxph(Surv(time, status) ~1) is a valid Cox model.  Not a
particularly interesting one -- it's the LR for the overall fit of the
baseline hazard which is equivalent to a Kaplan Meier when there are no
covariates.

Terry T.

-------begin inclusion ------

I'm interested in building a Cox PH model for survival modeling, using 2
covariates (x1 and x2).   x1 represents a 'baseline' covariate, whereas
x2
represents a 'new' covariate, and my goal is to figure out where x2 adds
significant predictive information over x1.

Ideally, I could get a p-value for doing this.  Originally, I thought of
doing some kind of likelihood ratio test (LRT), where i measure the
(partial) likelihood of the model with just x1, then with x1 and x2,
then it
becomes a LRT with 1 degree of freedom.  But when i use the summary()
function for coxph(), i get the following output (shown at the bottom).

I have two questions:

1) What exactly are the p-values in the Pr(>|z|) representing?  I
understand
that the coefficients have standard errors, etc., but i'm not sure how
the
p-value there is calculated.

2) At the bottom, where it shows the results of an LRT with 2df, i don't
quite understand what model the ratio is being tested against.  If the
current model has two variables (x1 and x2), and those are the extra
degrees
of freedom, then the baseline should then have 0 variables, but that's
not
really a Cox model?

thanks for any help.

```