[R] Cox regression and p-values

Terry Therneau therneau at mayo.edu
Wed Sep 19 15:51:34 CEST 2007

  Fisher's "exact" test is for comparing two proportions, which is a completely 
different problem than Cox regression, and so the test has no relevance to this 
problem.  It has, however, sparked a large literature of debate; already alluded 
to by many of the responses.

  The tests in the coxph table are Wald tests, beta/ se(beta).  For large sample 
sizes the Wald, score, and likelihood ratio tests will be equivalent, but for 
small samples the prevailing wisdom is that the likelihood ratio tests are the 
most reliable.  To do the LR test, you need to refit the Cox model without the 
variable of interest.  Then compare the two printouts, one for the full model 
and one for the reduced model: both will contain a line "Likelihood ratio test = 
xxx on y df" where xxx and y are numbers.  The LR test for the omitted variable 
is the difference in the two "xxx" values, which is chi-squared with degrees of 
freedom equal to the difference in the "y" values.
  	Terry Therneau

>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?

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