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Abstract:
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The Receiver Operating Characteristic (ROC) curve, which is an effective tool for evaluating the performance of the discrimination ability of various diagnostic tests/biomarkers, can be compared by the Area under the Curve (AUC). The existing methods of estimating AUC are either under normality assumption or nonparametric, which may suffer from substantial loss of efficiency and accuracy when the assumptions are violated. In this paper, our investigation is under the assumption that the data from both the case group and the control group can be transformed to uncorrelated normal distribution by Box-Cox transformation. The case when both groups share the same transformation parameters has been well studied. However, when it's not the case, an exact Box-Cox transformation adjusted estimation of AUC is proposed and compared with traditional estimators in terms of asymptotic mean squared error. It was shown by numerical calculation and simulation results that the traditional methods are inferior when they are compared with our proposed method. The result is also exemplified by real data from a maternal choline intake case-control study among women with NTD-affected pregnancy.
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