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Re: st: what's wrong with ROC curves


From   rgutierrez@stata.com (Roberto G. Gutierrez, StataCorp.)
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: what's wrong with ROC curves
Date   Mon, 15 Sep 2003 11:41:14 -0500

Alvine Bissery <Alvine.BISSERY@hop.egp.ap-hop-paris.fr> asks:

> I have a problem with the roctab function.
> I have 2 variables : "groupe " : 1 for disease, 0 for no disease
> 		        "outcome" wich is a continous variable measuring
> PTH, with values from 12 to 58

> - roctab groupe outcome, d - gives :

> Detailed report of Sensitivity and Specificity
> ----------------------------------------------------------------------------
> --
>                                            Correctly
> Cut point     Sensitivity   Specificity   Classified          LR+
> LR-
> ----------------------------------------------------------------------------
> --
> ( >= 12 )           0.00%       100.00%       60.00%
> 1.0000
> ( >= 14 )           8.33%       100.00%       63.33%

[...]

> How is it possible to have a specificity = 100% and sensitivity = 0% for the
> first cut point ? all people >= 12 have to be classifed has "disease people"
> because test is abnormal and so sensivity must be 100% and specificity = 0 %

One assumption of ROC is that as the classification variable increases, so
does the risk of abnormality.  For your data, the risk of abnormality
decreases as the classifaction variable increases, in which case -roctab-
begins by classifying everyone as normal to begin with (>=12, for your data)
and goes from there.

Admittedly, this fact needs to be better documented.

--Bobby
rgutierrez@stata.com
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