title: Multivariate normally distributed biomarkers subject to limits of detection and receiver operating characteristic curve inference.
abstract: OBJECTIVE
  Biomarkers are of ever-increasing importance to clinical practice and epidemiologic research. Multiple biomarkers are often measured per patient. Measurement of true biomarker levels is limited by laboratory precision, specifically measuring relatively low, or high, biomarker levels resulting in undetectable levels below, or above, a limit of detection (LOD). Ignoring these missing observations or replacing them with a constant are methods commonly used although they have been shown to lead to biased estimates of several parameters of interest, including the area under the receiver operating characteristic (ROC) curve and regression coefficients.
  
  
  METHODS
  We developed asymptotically consistent, efficient estimators, via maximum likelihood techniques, for the mean vector and covariance matrix of multivariate normally distributed biomarkers affected by LOD. We also developed an approximation for the Fisher information and covariance matrix for our maximum likelihood estimations (MLEs). We apply these results to an ROC curve setting, generating an MLE for the area under the curve for the best linear combination of multiple biomarkers and accompanying confidence interval.
  
  
  RESULTS
  Point and confidence interval estimates are scrutinized by simulation study, with bias and root mean square error and coverage probability, respectively, displaying behavior consistent with MLEs. An example using three polychlorinated biphenyls to classify women with and without endometriosis illustrates how the underlying distribution of multiple biomarkers with LOD can be assessed and display increased discriminatory ability over naïve methods.
  
  
  CONCLUSIONS
  Properly addressing LODs can lead to optimal biomarker combinations with increased discriminatory ability that may have been ignored because of measurement obstacles.
authors.affiliation: Division of Epidemiology, Statistics and Prevention Research, Eunice Kennedy Shriver National Institute of Child Health and Human Development, National Institutes of Health, DHHS, 6100 Executive Boulevard, Bethesda, MD 20852, USA. perkinsn@mail.nih.gov
authors.forename: Neil J
authors.initials: NJ
authors.lastname: Perkins
authors.forename: Enrique F
authors.initials: EF
authors.lastname: Schisterman
authors.forename: Albert
authors.initials: A
authors.lastname: Vexler
mesh_terms: D015415:Biomarkers / Q000378:metabolism; D003198:Computer Simulation; D016001:Confidence Intervals; D004715:Endometriosis / Q000378:metabolism*; D005260:Female; D006801:Humans; D016013:Likelihood Functions; D057230:Limit of Detection; D015233:Models, Statistical; D015999:Multivariate Analysis; D016011:Normal Distribution; D011078:Polychlorinated Biphenyls / Q000378:metabolism; D011336:Probability; D012372:ROC Curve; D012680:Sensitivity and Specificity
chemical_list: D015415:Biomarkers; D011078:Polychlorinated Biphenyls