Bayesian estimation of the receiver operating characteristic curve for a diagnostic test with a limit of detection in the absence of a gold standard

The receiver operating characteristic (ROC) curve is commonly used for evaluating the discriminatory ability of a biomarker. Measurements for a diagnostic test may be subject to an analytic limit of detection leading to immeasurable or unreportable test results. Ignoring the scores that are beyond the limit of detection of a test leads to a biased assessment of its discriminatory ability, as reflected by indices such as the associated area under the curve (AUC). We propose a Bayesian approach for the estimation of the ROC curve and its AUC for a test with a limit of detection in the absence of gold standard based on assumptions of normally and gamma-distributed data. The methods are evaluated in simulation studies, and a truncated gamma model with a point mass is used to evaluate quantitative real-time polymerase chain reaction data for bovine Johne's disease (paratuberculosis). Simulations indicated that estimates of diagnostic accuracy and AUC were good even for relatively small sample sizes (n=200). Exceptions were when there was a high per cent of unquantifiable results (60 per cent) or when AUC was ≤0.6, which indicated a marked overlap between the outcomes in infected and non-infected populations.