Estimators for ROC curves with missing biomarkers values and informative covariates

In this paper, we present three estimators of the ROC\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\hbox {ROC}}$$\end{document} curve when missing observations arise among the biomarkers. Two of the procedures assume that we have covariates that allow to estimate the propensity and and from this information, the estimators are obtained using an inverse probability weighting method or a smoothed version of it. The third one assumes that the covariates are related to the biomarkers through a regression model which enables us to construct convolution–based estimators of the distribution and quantile functions. Consistency results are obtained under mild conditions. Through a numerical study we evaluate the finite sample performance of the different proposals. A real data set is also analysed.