# Re: st: Roctab and binomial exact confidence interval

 From ymarchenko@stata.com (Yulia Marchenko, StataCorp LP) To statalist@hsphsun2.harvard.edu Subject Re: st: Roctab and binomial exact confidence interval Date Fri, 30 Oct 2009 12:28:13 -0500

```Garry Anderson <g.anderson@unimelb.edu.au> asks about the binomial confidence
interval reported by -roctab- when the estimated area under the receiver
operating characteristics curve is one:

>
>                      ROC                    -- Binomial Exact --
>           Obs       Area     Std. Err.      [95% Conf. Interval]
>         --------------------------------------------------------
>           109     1.0000       0.0000        0.00023     0.05006
>
>
> How does one interpret the 95% CI of 0.00023 to 0.05006 when the ROC area is
> 1.00?  I have seen a dataset (n=47, 15 +ve) where the ROC area was 1.00 and
> I wish to determine the lower 95%CI.

Garry discovered a bug in -roctab- with the -binomial- option when the ROC
area estimate is one.  We will fix this in the next update.  Meanwhile, Garry
can obtain the lower bound for the ROC area estimate by using -cii-.  For the
above example the lower bound is 0.9667233:

. cii 109 109

Variable |        Obs        Mean    Std. Err.       [95% Conf. Interval]
-------------+---------------------------------------------------------------
|        109           1           0        .9667233           1*

(*) one-sided, 97.5% confidence interval

For a dataset with 47 observations the lower bound is 0.9245153:

. cii 47 47

-- Binomial Exact --
Variable |        Obs        Mean    Std. Err.       [95% Conf. Interval]
-------------+---------------------------------------------------------------
|         47           1           0        .9245143           1*

(*) one-sided, 97.5% confidence interval

-- Yulia
ymarchenko@stata.com
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