[R] REPOST: Need help interpreting output from rcorrp.cens with Cox regression

[Peter Jepsen]

I am reposting my message from April 8th because I never received a response to the original post:

Dear R-listers, 

I am an MD and clinical epidemiologist developing a measure of comorbidity severity for patients with liver disease. Having developed my comorbidity score as the linear predictor from a Cox regression model I want to compare the discriminative ability of my comorbidity measure with the "old" comorbidity measure, Charlson's Comorbidity Index. I have nearly 10,000 deaths and 36 candidate comorbidities.
 
I wish to compare the discrimination of the two comorbidity measures, i.e. I have two non-nested Cox models. I get the following output with
 
> rcorrp.cens(myscore.lp, charlson.lp, Surv(time, dead), method=1): 


x1 = My comorbidity score, x2 = Charlson 
                   [,1]
Dxy                "-0.0605"
S.D.               "0.00648"
x1 more concordant "0.4697"
x2 more concordant "0.5302"
n                  "1.369e+04"
missing            "0"
uncensored         "9411"
Relevant Pairs     "1.587e+08"
Uncertain          "2.861e+07"
C X1               "0.395"
C X2               "0.401"
Dxy X1             "-0.21"
Dxy X2             "-0.198"

 
I am aware that because a high hazard means short survival I must subtract C X1 and C X2 from 1, so my comorbidity score has marginally better discrimination than the Charlson score (C = 0.605 vs. 0.599). Question: Is it true that my score is more discriminative than the Charlson score in 53% of patient pairs?
 
I have done the same analysis with 'method = 2', i.e. 
> rcorrp.cens(myscore.lp, charlson.lp, Surv(time, dead), method=2): 


x1 = My comorbidity score, x2 = Charlson 
                   [,1]
Dxy                "-0.006002"
S.D.               "0.001102"
x1 more concordant "0.04018"
x2 more concordant "0.04618"
n                  "1.369e+04"
missing            "0"
uncensored         "9411"
Relevant Pairs     "1.587e+08"
Uncertain          "2.861e+07"
C X1               "0.395"
C X2               "0.401"
Dxy X1             "-0.21"
Dxy X2             "-0.198"

 
Question: How do I interpret the 'x1/x2 more concordant' numbers in a Cox regression setting? My guess: My comorbidity score concordant in 4.6% of pairs in which Charlson's score is not. And Charlson's score is concordant in 4.0% of pairs in which my comorbidity score is not.
 
Thank you in advance for your insight and help. 

Best regards, 
Peter Jepsen 
Aarhus, Denmark