  Diagnostic tests are almost never perfect. Studies quantifying their
performance use knowledge of the true health status, measured with a reference
diagnostic test. Researchers commonly assume that the reference test is
perfect, which is not the case in practice. When the assumption fails,
conventional studies identify "apparent" performance or performance with
respect to the reference, but not true performance. This paper provides the
smallest possible bounds on the measures of true performance - sensitivity
(true positive rate) and specificity (true negative rate), or equivalently
false positive and negative rates, in standard settings. Implied bounds on
policy-relevant parameters are derived: 1) Prevalence in screened populations;
2) Predictive values. Methods for inference based on moment inequalities are
used to construct uniformly consistent confidence sets in level over a relevant
family of data distributions. Emergency Use Authorization (EUA) and independent
study data for the BinaxNOW COVID-19 antigen test demonstrate that the bounds
can be very informative. Analysis reveals that the estimated false negative
rates for symptomatic and asymptomatic patients are up to 3.17 and 4.59 times
higher than the frequently cited "apparent" false negative rate.
