| To estimate the sensitivity and specificity of a diagnostic test requires verification of true disease status for each study patient. In practice, not all study patients have disease status verified, and using only verified cases when estimating sensitivity and specificity often leads to biased results, commonly known as verification bias. Due to the incompleteness of data, Kosinski and Barnhart conducted global sensitivity analysis and proposed a test ignorance region (TIR) containing all sensitivity and specificity values consistent with the observed data. In our research, we give the uncertainty interval for the general bounds of the TIR, and the joint uncertainty envelope for TIR. We also give the sample size computations for diagnostic test evaluation with partially missing gold standard with MAR missing data mechanism and with no knowledge of the missing data mechanism based on the uncertainty interval and joint uncertainty envelope. The goal is to achieve the precision defined by a complete data design. Our third research topic is to restrict the TIR with additional information, for example, the range of probability of disease among the unverified subjects, additional subjects taking gold standard later. If unverified subjects take another two diagnostic tests, we propose a non-ignorance model to estimate sensitivity and specificity for the primary diagnostic test. |
