R help - Sep 2009 - rcorrp.cens and U statistics

I have two alternative Cox models with C-statistics 0.72 and 0.78. My question
is if 0.78 is significantly greater than 0.72. I'm using rcorrp.cens. I
cannot find the U statistics in the output of the function. This is the output
of the help example:
> x1 <- rnorm(400)
> x2 <- x1 + rnorm(400)
> d.time <- rexp(400) + (x1 - min(x1))
> cens   <- runif(400,.5,2)
> death  <- d.time <= cens
> d.time <- pmin(d.time, cens)
> rcorrp.cens(x1, x2, Surv(d.time, death))
               Dxy               S.D. x1 more concordant x2 more concordant     
n            missing         uncensored     Relevant Pairs
     -8.902077e-03       2.649712e-01       4.955490e-01       5.044510e-01     
4.000000e+02       0.000000e+00       4.000000e+00       1.348000e+03
         Uncertain               C X1               C X2             Dxy X1     
Dxy X2
      1.582520e+05       9.955490e-01       9.762611e-01       9.910979e-01     
9.525223e-01

Should I manually calculate the U statistics interpreting the fraction "x1
more concordant" and "x2 more concordant" of the "Relevant
Pairs" as Uxy and Uyx?

many thanks for any help or suggestion

Pietro Bulian

pietro bulian wrote:
> I have two alternative Cox models with C-statistics 0.72 and 0.78. My
question is if 0.78 is significantly greater than 0.72. I'm using
rcorrp.cens. I cannot find the U statistics in the output of the function. This
is the output of the help example:
> 
>> x1 <- rnorm(400)
>> x2 <- x1 + rnorm(400)
>> d.time <- rexp(400) + (x1 - min(x1))
>> cens   <- runif(400,.5,2)
>> death  <- d.time <= cens
>> d.time <- pmin(d.time, cens)
>> rcorrp.cens(x1, x2, Surv(d.time, death))
>                Dxy               S.D. x1 more concordant x2 more concordant
n            missing         uncensored     Relevant Pairs
>      -8.902077e-03       2.649712e-01       4.955490e-01       5.044510e-01
4.000000e+02       0.000000e+00       4.000000e+00       1.348000e+03
>          Uncertain               C X1               C X2             Dxy X1
Dxy X2
>       1.582520e+05       9.955490e-01       9.762611e-01       9.910979e-01
9.525223e-01
> 
> Should I manually calculate the U statistics interpreting the fraction
"x1 more concordant" and "x2 more concordant" of the
"Relevant Pairs" as Uxy and Uyx?
> 
> many thanks for any help or suggestion
Everything you want is right there in the output.  The test statistic is 
Dxy;  z statistic is -8.9e-3 / .265.

Note that even though this test is more powerful than comparing two ROC 
areas, it is not as powerful as a likelihood ratio chi-square test.

Frank
> 
> Pietro Bulian
> 
> 
> 
> 
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-- 
Frank E Harrell Jr   Professor and Chair           School of Medicine
                      Department of Biostatistics   Vanderbilt University