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A receiver operating characteristic (ROC) curve is often used to assess the discriminatory ability of a continuous diagnostic test, which is summarized by its corresponding area under the curve (AUC). For tests that are subject to a limit of detection and especially when a reference standard is not available, unquantifiable test scores beyond the limit of detection introduces bias in AUC estimation. We propose a Bayesian approach for estimating AUC that are facilitated by the presence of covariates for a no reference standard scenario. We develop methods for AUC estimation where both an absence of a reference standard and a limit of detection co-exist for both a normally- and gamma-distributed test scores. Our work extends previous developments to the scenarios involving the presence of a limit of detection for the test and also varying degrees of censoring due to the extent of the detection limit that could affect AUC estimation. Simulations suggested that AUC estimates are accurate except when covariates information is ignored, when there is a high percentage of unquantifiable scores (e.g., 60%), or when substantial overlap exits between diseased and non-diseased populations (e.g., true AUC = 0.6) that could result in marginally less precise AUC estimates. When a continuous test is subject to a limit of detection and in the absence of a reference standard, covariate information could help with a more accurate distinction of the latent disease status for individuals.

communications in statistics - simulation and computation

Covariate-adjusted Bayesian estimation of the performance of a continuous diagnostic test with a limit of detection in the absence of a reference standard: a simulation study