[R] the output of coxph

[Zheng Zhao]

Dear All:

I have some questions about the output of coxph.

Below is the input and output:

----------------------------------------
 > coxph(formula = Surv(futime, fustat) ~ age + rx + ecog.ps, data =
+  ovarian, x = TRUE)

Call:
coxph(formula = Surv(futime, fustat) ~ age + rx + ecog.ps, data =
    ovarian, x = TRUE)


           coef exp(coef) se(coef)     z      p
age      0.147     1.158   0.0463  3.17 0.0015
rx      -0.815     0.443   0.6342 -1.28 0.2000
ecog.ps  0.103     1.109   0.6064  0.17 0.8600

Likelihood ratio test=15.9  on 3 df, p=0.00118  n= 26
---------------------------------------
Question One:
As I know, the p-value of "age" is the significance level. However what 
is the exact meaning of the parameter, and how do we calculate the 
parameter? If the sample size is small (20~40), is this estimation still 
reliable?

Question Two:
the p-value in the last line (Likelihood ratio test=15.9 on 3 df, 
p=0.00118) is asymptotically equivalent tests of the omnibus null 
hypothesis that all of the Î²â€™s are zero, according to John Fox's "Cox 
Proportional-Hazards Regression for Survival Data" 
(http://cran.r-project.org/doc/contrib/Fox-Companion/appendix-cox-regression.pdf)
Can anybody explain that why this true? (As I know, the p-value is 
obtained by 1-pchisq(2*log Likelihood ratio), and this is because 
2*log(likelihood ratio) is approximately chi-square for nested models.)

Thank you very much.

Sincerely,
Alan
2005-11-27