topic PROC LOGISTIC (ROC statement) - why Wald 95% CI with Mann-Whitney AUCs? in Statistical Procedures

PROC LOGISTIC (ROC statement) - why Wald 95% CI with Mann-Whitney AUCs?

penlight — Fri, 15 Oct 2010 21:37:38 GMT

I am relatively new to working with ROC curves and associated AUC statistic, thus had a question regarding the output from PROC LOGISTIC when you use the ROC statement.

I understand that the AUC is equivalent to the result obtained with Mann-Whitney test.

However if Mann-Whitney is a nonparametric test, how can it be associated with a Wald 95% CI's? I thought that Wald assumed an approximate normal distribution? I suspect this is related to the central limit theorem, however the ROC results show that Mann-Whitney is the overall header for the AUC, the Wald SE, and the Wald 95% CI. Is it that the Mann-Whitney is used to calculate the AUC, however a normal distribution is assumed to calculate a Wald SE.

How would this be reported in a journal paper? "AUC were calculated using Mann-Whitney statistic with associated Wald 95% confidence intervals."

thank you for the advice and assistance,
- mike

Re: PROC LOGISTIC (ROC statement) - why Wald 95% CI with Mann-Whitney AUCs?

SPR — Mon, 18 Oct 2010 20:43:20 GMT

Hello PenLight,

As far as I know PROC LOGISTIC produces AUC (c-stat) without confidence intervals. There is a book by Mithat Gohen "Analyzing Receiver Operating Curves with SAS" which contains all aspects of AUC calcultion with SAS. In partucular, the author suggests using PROC FREQ to calulcate AUC with confidence intervals using Somer's D statictics:

proc freq data=;
table target*predictor / noprint measures;
run;

Sincerely, SPR

Re: PROC LOGISTIC (ROC statement) - why Wald 95% CI with Mann-Whitney AUCs?

StatDave — Tue, 26 Oct 2010 19:11:16 GMT

As noted in the LOGISTIC documentation:

"Asymptotic normality of the estimated area follows from U-statistic theory..."

See the "Details: Receiver Operating Characteristic Curves: ROC Computations" section of the LOGISTIC documentation:
http://support.sas.com/documentation/cdl/en/statug/63347/HTML/default/logistic_toc.htm