How to deal with double partial verification when evaluating two index tests in relation to a reference test?

Research into the diagnostic accuracy of clinical tests is often hampered by single or double partial verification mechanisms, that is, not all patients have their disease status verified by a reference test, neither do all patients receive all tests under evaluation (index tests). We show methods that reduce verification bias introduced when omitting data from partially tested patients. Adjustment techniques are well established when there are no missing index tests and when the reference test is 'missing at random'. However, in practice, index tests tend to be omitted, and the choice of applying a reference test may depend on unobserved variables related to disease status, that is, verification may be missing not at random (MNAR). We study double partial verification in a clinical example from reproductive medicine in which we analyse the diagnostic values of the chlamydia antibody test and the hysterosalpingography in relation to a diagnostic laparoscopy. First, we plot all possible combinations of sensitivity and specificity of both index tests in two test ignorance regions. Then, we construct models in which we impose different assumptions for the verification process. We allow for missing index tests, study the influence of patient characteristics and study the accuracy estimates if an MNAR mechanism would operate. It is shown that data on tests used in the diagnostic process of the same population are preferably studied jointly and that the influence of an MNAR verification process was limited in a clinical study where more than half of the patients did not have the reference test.