A Sensitivity And Specificity Analysis Of A Medical Diagnostic Test When The Data Is Incomplete

Current technological advances enable less invasive or less expensive and more convenient diagnostic tools in identifying disease status. Before adopting a new diagnostic procedure, it is essentially important to assess whether the diagnostic accuracy of the new procedure is non-inferior(or equivalent)to that of the definitive gold standard procedure. When a diagnostic test is evaluated against a gold standard test, one often finds that some of the patients with test results may not have verified disease status for some reasons. The sensitivity and specificity estimates based only on the patients with verified disease are often biased. This bias is called verification bias. Many authors deal with this based on the assumption of independence between disease status and election for verification conditionally on the test result. But this assumption may not be valid mostly. Because the reason for verification depends on the test results and other factors. For example, patients may not have been verified because they were too sick to undergo the gold standard test, or maybe they felt themselves were rather healthy. So, the verification bias is nonignorable.In this paper, we present an odds ratio analysis, a sensitivity analysis and a specificity analysis with the incomplete data. During this process, we do not ignore the verification bias and consider all possible situations of the missing data. The analysis is not limited to a chosen model. Then we derive a ragion of all odds ratio values, a curved surface, consistent with all possible combinations of the incomplete data and get the projection of the surface. In order to assess the consistency of two diagnostic measures, we calculate the probability of odds ratio through the projected area. The further discussion is taken when the prior distribution is given. Finally, two examples are presented to illustrate the method.