Estimating the AUC with a graphical lasso method for high-dimensional biomarkers with LOD

This manuscript estimates the area under the receiver operating characteristic curve (AUC) of combined biomarkers in a high-dimensional setting. We propose a penalization approach to the inference of precision matrices in the presence of the limit of detection. A new version of expectation-maximization algorithm is then proposed for the penalized likelihood, with the use of numerical integration and the graphical lasso method. The estimated precision matrix is then applied to the inference of AUCs. The proposed method outperforms the existing methods in numerical studies. We apply the proposed method to a data set of brain tumor study. The results show a higher accuracy on the estimation of AUC compared with the existing methods.