Abstract
We discuss the implicit or explicit trade-offs between false positive and false negative tests errors provided by the information from the Receiver Operating Characteristic (ROC) curve. We discuss its impact for the evaluation of the performance of a new medical diagnostic test in comparison with an already established test. We discuss the comparability of a new test N with respect to a standard test S in terms of the seriousness of a False Positive error relative to a False Negative error using information from the ROC curve.
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Appendix
Appendix
Cost may be expressed as: cost = CFN (1 − sensitivity) ρ + CFP (1 − sensitivity) (1 − ρ).
Therefore, when operating the test at False Positive Fraction or (1 − specificity) = t, the cost is
cost(t) = CFN (1 − ROC(t)) ρ + CFP (t) (1 − ρ).
Solving ∂cost(t)/∂t = 0 provides the result for the slope m = ∂ROC(t)/∂t = (CFP /CFN)(1 − ρ)/ρ.
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Pantoja-Galicia, N., Pennello, G. (2019). What Is the Right Comparison? ROC Curve and Trade-Off Between Key Diagnostic Test Errors (ROCKE). In: Zhang, L., Chen, DG., Jiang, H., Li, G., Quan, H. (eds) Contemporary Biostatistics with Biopharmaceutical Applications. ICSA Book Series in Statistics. Springer, Cham. https://doi.org/10.1007/978-3-030-15310-6_18
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DOI: https://doi.org/10.1007/978-3-030-15310-6_18
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