Biometrical Journal

ROC curve inference for best linear combination of two biomarkers subject to limits of detection

Journal Article


The receiver operating characteristic (ROC) curve is a tool commonly used to evaluate biomarker utility in clinical diagnosis of disease. Often, multiple biomarkers are developed to evaluate the discrimination for the same outcome. Levels of multiple biomarkers can be combined via best linear combination (BLC) such that their overall discriminatory ability is greater than any of them individually. Biomarker measurements frequently have undetectable levels below a detection limit sometimes denoted as limit of detection (LOD). Ignoring observations below the LOD or substituting some replacement value as a method of correction has been shown to lead to negatively biased estimates of the area under the ROC curve for some distributions of single biomarkers. In this paper, we develop asymptotically unbiased estimators, via the maximum likelihood technique, of the area under the ROC curve of BLC of two bivariate normally distributed biomarkers affected by LODs. We also propose confidence intervals for this area under curve. Point and confidence interval estimates are scrutinized by simulation study, recording bias and root mean square error and coverage probability, respectively. An example using polychlorinated biphenyl (PCB) levels to classify women with and without endometriosis illustrates the potential benefits of our methods.

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Published features on are checked for statistical accuracy by a panel from the European Network for Business and Industrial Statistics (ENBIS)   to whom Wiley and express their gratitude. This panel are: Ron Kenett, David Steinberg, Shirley Coleman, Irena Ograjenšek, Fabrizio Ruggeri, Rainer Göb, Philippe Castagliola, Xavier Tort-Martorell, Bart De Ketelaere, Antonio Pievatolo, Martina Vandebroek, Lance Mitchell, Gilbert Saporta, Helmut Waldl and Stelios Psarakis.