I'm trying to thing about how to calculate confidence intervals in the presence of known measurement error for some test protocol.
Let's assume we're doing a sample survey in which we're performing some test on the participants. This test has known sensitivity and specificity.
I'm assuming one could run a simulation where nspecificity of the positives are removed, and 1/sensitivity(number of true positives) are added randomly, and then computing confidence intervals in that manner, but it feels clunky at best.
I"m also interested in combining the variability induced by the test with general variance estimation techniques, such as bootstrapping the survey weights.