American Journal of Epidemiology Advance Access originally published online on November 16, 2006
American Journal of Epidemiology 2007 165(3):325-333; doi:10.1093/aje/kwk011
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ORIGINAL CONTRIBUTIONS |
Receiver Operating Characteristic Curve Inference from a Sample with a Limit of Detection
1 Division of Epidemiology, Statistics, and Prevention Research, National Institute of Child Health and Human Development, National Institutes of Health, Department of Health and Human Services, Bethesda, MD
2 Department of Mathematics and Statistics, American University, Washington, DC
Correspondence to Dr. Enrique F. Schisterman, Division of Epidemiology, Statistics, and Prevention Research, National Institute of Child Health and Human Development, 6100 Executive Boulevard, Bethesda, MD 20852 (e-mail: schistee{at}mail.nih.gov).
The receiver operating characteristic curve is a commonly used tool for evaluating biomarker usefulness in clinical diagnosis of disease. Frequently, biomarkers being assessed have immeasurable or unreportable samples below some limit of detection. Ignoring observations below the limit of detection leads to negatively biased estimates of the area under the curve. Several correction methods are suggested in the areas of mean estimation and testing but nothing regarding the receiver operating characteristic curve or its summary measures. In this paper, the authors show that replacement values below the limit of detection, including those suggested, result in the same biased area under the curve when properly accounted for, but they also provide guidance on the usefulness of these values in limited situations. The authors demonstrate maximum likelihood techniques leading to asymptotically unbiased estimators of the area under the curve for both normally and gamma distributed biomarker levels. Confidence intervals are proposed, the coverage probability of which is scrutinized by simulation study. An example using polychlorinated biphenyl levels to classify women with and without endometriosis illustrates the potential benefits of these methods.
censoring; curve estimation; detection; maximum likelihood; receiver operating characteristic
Abbreviations: A, area under the curve; LOD, limit of detection; MLE, maximum likelihood estimate; p(c), specificity; q(c), sensitivity; RMSE, root mean square error; ROC, receiver operating characteristic