Sensitivity and Specificity Measurement Using an Imperfect Gold Standard: Identification and Inference
Abstract
Diagnostic test performance is measured with respect to the true health status commonly determined using an imperfect reference test. To attain point identification, researchers often assume that the references are infallible, risking misleading conclusions. Without the assumption sensitivity and specificity are partially identified. I derive their smallest possible joint identification regions in standard test performance studies when reference test performance measures are either known precisely or to be in some bounded set. I formalize existing informally stated assumptions on dependence between the reference and tests of interest and characterize smaller identification regions when they hold. In my discussion, I provide an inference procedure that yields confidence sets that are uniformly consistent in level over the class of relevant of distributions. I outline two important use-cases for the identification regions: $1)$ bounding prevalence for population screening tests; $2)$ bounding predictive values. Finally, I analyze the performance of the Abbott BinaxNow COVID-19 rapid antigen tests using the framework. I provide estimated identification regions and confidence sets for all currently available COVID-19 rapid antigen tests in the US under the Emergency Use Authorization.
