[R] rcorrp.cens and U statistics

[Frank E Harrell Jr]

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