Comment (too long for 'comment' format):
When dealing with 'prevalence', 'specificity', 'specificity', and so on. It is important to be clear to what population each probability applies. Prevalence is strictly a property of the population (although the proportion of the population infected might have been be estimated using screening test test data).
Sensitivity and specificity are properties of the test. For example,
$$\eta = \mathrm{Specificity}
= P(\mathrm{Pos.\; test\; |\; Subj.\; infected} )\\
=\frac{P(\mathrm{Pos.\; test\; AND\;Subj.\; infected})}
{P(\mathrm{Subj.\; infected})}.$$
So in combining specificity data, you have to look at the total number of infected subjects involved for each determination of specificity.
You can't just average sensitivity determinations from two different studies--one
using 100 infected subjects and one using 1000 infected subjects. If
$\hat\eta_1 = \frac{92}{100} = 0.920$ and $\hat\eta_2 = \frac{893}{1000} = 0.893,$
then the combined estimate of sensitivity from the two studies is
$\hat \eta_c = \frac{985}{1100} = 0.896.$
Depending on the method used to make confidence intervals for estimates of
sensitivity, the CI for the first study might be $(0.847, 0.961),$
the CI for the second might be $(0.872, 0.911),$ and the CI using the combined
estimate $(0.876, 0.912).$ [I have used 95% Agresti-Coull ("Plus-4") confidence intervals for consistency because one sample size is less than 1000. Computations use R.
Perhaps see Wikipedia on binomial confidence intervals.]
eta.1 = 94/104; pm = c(-1,1)
CI.1 = eta.1 + pm*1.96*sqrt(eta.1*(1-eta.1)/104); round(CI.1,3)
[1] 0.847 0.961
eta.2 = 895/1004
CI.2 = eta.2 + pm*1.96*sqrt(eta.2*(1-eta.2)/1004); round(CI.2,3)
[1] 0.872 0.911
eta.c = 987/1104
CI.c = eta.c + pm*1.96*sqrt(eta.c*(1-eta.c)/1104); round(CI.c,3)
[1] 0.876 0.912
Moreover, I should point out that the terminologies 'false positive' and
'false negative' have been so often carelessly used in discussions about
screening tests that one must be careful what they mean in each paper.
For example, one common meaning for the proportion of false negatives is
$P(\mathrm{Neg.\; test\;|\; Subj,\; infected}) = 1-\eta$ and another is
$P(\mathrm{Neg.\; test\; AND\; Subj,\; infected})$ where the denominator
would be all subjects (not just infected subjects).
Finally, predictive powers of positive and negative tests are simultaneously
properties of the type of test used and of the population being tested.
So, for each probability associated with a screening test, it is crucial to
understand whether it depends on the test used, the population tested, or both.
(I have used some of the terminology and notation above in a
previous post
about estimating prevalence from screening test data.)
