[R] Cox regression and p-values

[Duncan Murdoch]

On 9/18/2007 12:41 PM, Daniel Brewer wrote:
> Hello,
> I might be barking up the wrong tree here, but I want to make sure I
> have a full understanding of this.  What I would like to know is what
> tests are performed to give the p-values for each variable in the table
> that is the result of coxph regression when the variables are
> categorical only.
> 
> More specifically, when expected counts are less than 5 is the Fisher's
> exact test used instead of the Chi^2 test?

I think you need to check the reference (Anderson and Gill) or the 
source to be sure, but I wouldn't expect either of those tests to be 
used here.

I'd guess these are generalized likelihood ratio tests:  fit the model 
with the variable, fit it without, and look at the difference in 
(partial) log likelihood.  If the variable does not affect the response 
then twice the difference in log likelihood would have an asymptotic 
chi-square distribution.

Fisher's exact test and the Pearson chi-square test are not appropriate 
here, because the individuals are not exchangeable under the null 
hypothesis.

Duncan Murdoch