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

Neil J. Perkins, Enrique F. Schisterman, Albert Vexler

Research output: Contribution to journalArticlepeer-review

15 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)464-476
Number of pages13
JournalBiometrical Journal
Issue number3
StatePublished - May 2011
Externally publishedYes


  • Area under the curve
  • Best linear combinaton
  • Left censoring
  • Limit of detection
  • ROC

ASJC Scopus subject areas

  • Statistics and Probability
  • Medicine(all)
  • Statistics, Probability and Uncertainty


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