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Abstract:
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While receiver operating characteristic (ROC) curves and the area under the curves (AUC) are often used to compare the discriminatory ability of potentially correlated biomarkers, in many practical settings, the partial area under the curves (pAUC) is more appealing. For example, in screening research, it is often of interest to estimate the pAUC in the region of very small false-positive rates. Many biomarkers are subject to limit of detection (LOD) due to the instrumental limitation in measurements and may not be normally distributed. Existing parametric methods with normality assumptions can lead to biased results when the assumption is violated. We propose new estimation and inference procedures for the pAUC of biomarkers subject to LOD by using the semiparametric transformation model allowing for heteroscedasticity. We obtain the nonparametric maximum likelihood estimator of the pAUC and establish its large sample properties. The proposed method is robust to nonnormality and outliers with little loss of efficiency compared to its parametric counterpart. This is demonstrated by extensive simulation studies using C. An application to an autism study is provided.
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