> Arnold Kester <mailto:[email protected]> wrote in response to my posting:
>
> > I don't agree, it's not my point whether the analysis is proper for
> these data. Even when the data are 'pathological', which I doubt, the
> ROC curve should be drawn as it is defined. And by definition, the curve
> cannot be non-monotone. If the curve is drawn wrong in this case, how
> can we be confident that it will be correct in other instances?
I misunderstood Arnold's intent. I assumed that he was trying to make sense of his data and not trying to indicate that there was a bug in -roctab-. In respond to that, I used Arnold's data and recalculated the sensitivity and specificity at every possible cut-point and plotted the results. The plot I produced was identical to that from -roctab-, indicating that Arnold's results were not caused by a bug in -roctab-. The problem is that in Arnold's data, as Joseph Coveney <[email protected]> pointed out, "the diagnostic test (slightly) predicts the diametric opposite of the truth" thus, for Arnold's diagnostic test higher values are associated with lower risk, violating the assumption that "The rating or outcome of the diagnostic test must be at least ordinal with higher values indicating higher risk".
What is important is that the peculiar results that Arnold obtained were not cause by a bug in -roctab-, and thus, user can be confident that -roctab- will generate the correct results in all instances where the assumptions are met.
Here is the code used to calculate the sensitivity and specificity at every possible cut-point in the data.
insheet using roc_data.out, names clear
count if y==0
local y0=r(N)
count if y==1
local y1=r(N)
sort x
gen sens=.
gen spec=.
local N=_N
local i 1
while `i'<=`N' {
tempvar g
gen `g'=0
replace `g'=1 if x>x[`i']
count if `g'==0 & y==0
local sp=r(N)/`y0'
count if `g'==1 & y==1
local se=r(N)/`y1'
replace spec=`sp' in `i'
replace sens=`se' in `i'
drop `g'
local i= `i'+1
noi di in red `i'
}
local nN=`N' +2
set obs `nN'
local pu=_N-1
replace spec=0 in `pu'
replace sens=1 in `pu'
replace spec=1 in l
replace sens=0 in l
gen onesp=1- spec
sort onesp
gr sens onesp, c(l) ylab xlab sort
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