[R-sig-Epi] [R-sig-epi] Sensitivity, specificity, and predictive values

[Michael Hills]

All of the examples cited in this discussion assume that a single sample
of subjects is taken from a population and then classified as disease
positive or negative, using the reference test. When this is the case
the true prevalence can also be obtained from the sample, but in many
situations separate samples are taken to estimate sensitivity and
specificity, so that the proportion of subjects who are disease positive
depends on the sample sizes chosen, and no estimate of prevalence is
possible. 

In this case the sensitivity and specificity can be estimated as before
and then applied to a population in which the true prevalence of the
disease is p to give the predictive odds of a positive test in that
population, namely

p/(1-p) x Sens/(1-Spec) = p/(1-p) x LR

so the CI for the predictive odds of a positive test is directly related
to the CI for the LR.

The epicentre package does provide an interval for the LR but it seems
likely that this is based on a single sample not two separate samples.
For two separate samples a method for finding the CI for the ratio of
two independent proportions (Sens and 1-Spec) is required. Any
suggestions for doing this in R?

Michael Hills