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.
I don't see why the above formulas are being used. The Bamber-Hanley-McNeil-Wilcoxon-Mann-Whitney nonparametric method works great. Just get the U statistic (concordance probability) used in Wilcoxon. As Somers' Dxy rank correlation coefficient is 2*(1-C) where C is the concordance or ROC area, the Hmisc package function rcorr.cens uses U statistic methods to get the standard error of Dxy. You can easily translate this to a standard error of C.
Frank
--
Frank E Harrell Jr Professor and Chair School of Medicine
Department of Biostatistics Vanderbilt University______________________________________________ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
