A semiparametric method for comparing the discriminatory ability of biomarkers subject to limit of detection

Receiver operating characteristic curves and the area under the curves (AUC) are often used to compare the discriminatory ability of potentially correlated biomarkers. Many biomarkers are subject to limit of detection due to the instrumental limitation in measurements and may not be normally distributed. Standard parametric methods assuming normality can lead to biased results when the normality assumption is violated. We propose new estimation and inference procedures for the AUCs of biomarkers subject to limit of detection by using the semiparametric transformation model allowing for heteroscedasticity. We obtain the nonparametric maximum likelihood estimators by maximizing the likelihood for the observed data with limit of detection. The proposed estimators are shown to be consistent, asymptotically normal, and asymptotically efficient. Additionally, we propose a Wald type test statistic to compare the AUCs of 2 potentially correlated biomarkers with limit of detection. Extensive simulation studies demonstrate that the proposed method is robust to nonnormality while performing as well as its parametric counterpart when the normality assumption is true. An application to an autism study is provided.