A global sensitivity analysis of performance of a medical diagnostic test when verification bias is present

Current advances in technology provide less invasive or less expensive diagnostic tests for identifying disease status. When a diagnostic test is evaluated against an invasive or expensive gold standard test, one often finds that not all patients undergo the gold standard test. The sensitivity and specificity estimates based only on the patients with verified disease are often biased. This bias is called verification bias. Many authors have examined the consequences of verification bias and have proposed bias correction methods based on the assumption of independence between disease status and election for verification conditionally on the test result, or equivalently on the assumption that the disease status is missing at random using missing data terminology. This assumption may not be valid and one may need to consider adjustment for a possible non-ignorable verification bias resulting from the non-ignorable missing data mechanism. Such an adjustment involves ultimately uncheckable assumptions and requires sensitivity analysis. The sensitivity analysis is most often accomplished by perturbing parameters in the chosen model for the missing data mechanism, and it has a local flavour because perturbations are around the fitted model. In this paper we propose a global sensitivity analysis for assessing performance of a diagnostic test in the presence of verification bias. We derive a region of all sensitivity and specificity values consistent with the observed data and call this region a test ignorance region (TIR). The term 'ignorance' refers to the lack of knowledge due to the missing disease status for the not verified patients. The methodology is illustrated with two clinical examples.