Empirical likelihood ratio confidence interval estimation of best linear combinations of biomarkers.

A novel smoothed empirical likelihood (EL) approach that incorporates kernel estimation of the area under the receiver operating characteristic curve (AUC) to construct nonparametric confidence intervals of AUC based on the best linear combination (BLC) of biomarkers is proposed. The method has several advantages including the feasibility to use gradient-based techniques for fast computation of BLC coefficients and to employ powerful likelihood methods without specification of underlying data distributions. Simulation results show that the new method performs well even when the distribution of biomarkers is skewed, a situation commonly met in practice. A data set from a clinical experiment related to atherosclerotic coronary heart disease is used to illustrate the efficiency of the proposed method.