[R] Standard error for the area under a smoothed ROC curve?

[Dan Bolser]

Hello, 

I am making some use of ROC curve analysis. 

I find much help on the mailing list, and I have used the Area Under the
Curve (AUC) functions from the ROC function in the bioconductor project...

http://www.bioconductor.org/repository/release1.5/package/Source/
ROC_1.0.13.tar.gz 

However, I read here...

http://www.medcalc.be/manual/mpage06-13b.php

"The 95% confidence interval for the area can be used to test the
hypothesis that the theoretical area is 0.5. If the confidence interval
does not include the 0.5 value, then there is evidence that the laboratory
test does have an ability to distinguish between the two groups (Hanley &
McNeil, 1982; Zweig & Campbell, 1993)."

But aside from early on the above article is short on details. Can anyone
tell me how to calculate the CI of the AUC calculation?


I read this...

http://www.bioconductor.org/repository/devel/vignette/ROCnotes.pdf

Which talks about resampling (by showing R code), but I can't understand
what is going on, or what is calculated (the example given is specific to
microarray analysis I think).

I think a general AUC CI function would be a good addition to the ROC
package.




One more thing, in calculating the AUC I see the splines function is
recomended over the approx function. Here...

http://tolstoy.newcastle.edu.au/R/help/04/10/6138.html

How would I rewrite the following AUC functions (adapted from bioconductor
source) to use splines (or approxfun or splinefun) ...

> spe # Specificity
 [1] 0.02173913 0.13043478 0.21739130 0.32608696 0.43478261 0.54347826
 [7] 0.65217391 0.76086957 0.89130435 1.00000000 1.00000000 1.00000000
[13] 1.00000000

> sen # Sensitivity
 [1] 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 0.9302326 0.8139535
 [8] 0.6976744 0.5581395 0.4418605 0.3488372 0.2325581 0.1162791

trapezint(1-spe,sen)
my.integrate(1-spe,sen)

## Functions
## Nicked (and modified) from the ROC function in bioconductor.
"trapezint" <-
function (x, y, a = 0, b = 1)
{
    if (x[1] > x[length(x)]) {
      x <- rev(x)
      y <- rev(y)
    }
    y <- y[x >= a & x <= b]
    x <- x[x >= a & x <= b]
    if (length(unique(x)) < 2)
        return(NA)
    ya <- approx(x, y, a, ties = max, rule = 2)$y
    yb <- approx(x, y, b, ties = max, rule = 2)$y
    x <- c(a, x, b)
    y <- c(ya, y, yb)
    h <- diff(x)
    lx <- length(x)
    0.5 * sum(h * (y[-1] + y[-lx]))
}

"my.integrate" <-
function (x, y, t0 = 1)
{
    f <- function(j) approx(x,y,j,rule=2,ties=max)$y
    integrate(f, 0, t0)$value
}





Thanks for any pointers,
Dan.