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Assessing the diagnostic power of variables measured with a detection limit

Author

Listed:
  • Bochao Jia

    (University of Science Technology of China
    University of Florida)

  • Yuan-chin Ivan Chang

    (Academia Sinica)

  • Zhanfeng Wang

    (University of Science Technology of China)

Abstract

The phenomenon of the limit of detection (LoD) often happens in many practical situations because of technique and instrument limitations. In the literature, some reports show that, in general, to apply conventional methods to evaluate the diagnostic power of variables while ignoring LoD could be seriously biased. Although the area under the receiver operating characteristic (ROC) curve can be estimated consistently if the distribution of variables are known. In practical situation, such information is usually not available. On the other hand, it has been proved that the area under ROC curve of a variable with a LoD and no distribution assumptions is usually biased no matter what kinds of replacement strategies are used. However, there is a lack of similar studies on the partial area under ROC curve (pAUC), and because this measure is usually preferred in practice, it is of interest to examine whether the estimate of pAUC of a variable measured with a LoD behaves the same. In this study, we found that for some LoD scenarios, and even without distribution assumption, consistent estimate of pAUC can be constructed. When the consistent estimate of pAUC cannot be obtained, the bias can be ineffectual in practical situations, and the proposed estimator can be a good approximation of pAUC. Numerical studies using simulated data sets and real data examples are reported.

Suggested Citation

  • Bochao Jia & Yuan-chin Ivan Chang & Zhanfeng Wang, 2016. "Assessing the diagnostic power of variables measured with a detection limit," Computational Statistics, Springer, vol. 31(4), pages 1287-1303, December.
    • Handle: RePEc:spr:compst:v:31:y:2016:i:4:d:10.1007_s00180-015-0628-0
    DOI: 10.1007/s00180-015-0628-0
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    References listed on IDEAS

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    1. Albert Vexler & Aiyi Liu & Ekaterina Eliseeva & Enrique F. Schisterman, 2008. "Maximum Likelihood Ratio Tests for Comparing the Discriminatory Ability of Biomarkers Subject to Limit of Detection," Biometrics, The International Biometric Society, vol. 64(3), pages 895-903, September.
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