[R] Usage of p/d/qnorm

[Martyn Plummer]

On 12-Jan-00 ralf.herold at charite.de wrote:
> Hello,
> 
> could You please help: I am looking for a way to formulate test accuracy
> measures such as test sensitivity, specificity, predictive values, and
> correct classification rate using p/d/qnorm. The tests' primary values
> follow a bimodal distribution, which is modelled by a mixture of two normal
> distributions:
> 
>      p  * dnorm ((x - u1) / s1) / s1 +
> (1 - p) * dnorm ((x - u2) / s2) / s2)
> 
> {written like in Venables & Ripley, 2nd Ed., p. 288}. So, the first and
> second summand would correspond to truly negative and positive status,
> respectively, whereas the test would be termed negative or positive with
> respect to a varying x cut off value.
> 
> How could one possibly formulate using p/d/qnorm e.g. the specificity:
> f(x)= number of positive tests at cut off x / total number of truly
> positives ?

That's not the specificity. It looks like (an estimate of) the 
sensitivity, except the numerator should be the number of truly positives
who test positive.

Sensitivity = Pr (Test status +ve | True status +ve)
            = 1 - pnorm((x-u2)/s2)

Specificity = Pr (Test status -ve | True status -ve)
            = pnorm((x-u1)/s1)

The mixture proportions are irrelevant, since you're conditioning
on true status. (I'm assuming that u2 > u1 and values above x are
considered positive.  This is true in every example I've seen).

Martyn
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