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 ?
Thank You,
Ralf Herold
# Charite Campus Virchow-Klinikum
# Medizinische Fakultaet der Humboldt-Universitaet
# Augustenburger Platz 1, D-13353 Berlin
# ralf.herold at charite.de pgp welcome
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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 -.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.- r-help mailing list -- Read http://www.ci.tuwien.ac.at/~hornik/R/R-FAQ.html Send "info", "help", or "[un]subscribe" (in the "body", not the subject !) To: r-help-request at stat.math.ethz.ch _._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._