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RE: st: Roctab and binomial exact confidence interval


From   Garry Anderson <g.anderson@unimelb.edu.au>
To   statalist@hsphsun2.harvard.edu
Subject   RE: st: Roctab and binomial exact confidence interval
Date   Mon, 02 Nov 2009 18:07:39 +1100

Many thanks Al and Yulia for your alternative solution and fix.
Cheers, Garry 

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Yulia
Marchenko, StataCorp LP
Sent: Saturday, 31 October 2009 4:28 AM
To: statalist@hsphsun2.harvard.edu
Subject: Re: st: Roctab and binomial exact confidence interval

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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