Empirical likelihood confidence interval for sensitivity to the early disease stage

Abstract

Disease status can naturally be classified into three or more ordinal stages rather than just being binary stages. Many works have been done for the estimation and inference procedure regarding three ordinal disease stages, which are non‐disease, early disease, and full disease stages. The early disease stage can be very important for therapeutic intervention and prevention potentiality. As a diagnostic measure, sensitivity to the early disease stage is often used. In this article, we propose confidence intervals for the sensitivity to early disease stage based on given target specificity for non‐disease stage and target sensitivity to full disease stage using both empirical likelihood (EL) and adjusted EL procedures. We compare the performance of the proposed EL confidence intervals with other procedures in our simulation study. The proposed procedures are further applied to Alzheimer's Disease Neuroimaging Initiative data set.

Interval estimation in three-class receiver operating characteristic analysis: A fairly general approach based on the empirical likelihood

“…Here, we compare the performance of our proposed methods ELQB in Section (2.2) with the existing nonparametric approaches, i.e. ELP, ELB, and BTII, 15 IF, 17 PEL and AEL, 16 through scenarios in Table 1. Under each scenario, we fixed the values θ 10 and θ 30, and generated 5000 random samples.…”

“…To estimate the unknown scale constant, the authors proposed, as alternatives, a method involving kernel density estimators, and a bootstrap-based procedure. A different profile empirical log-likelihood for θ 2, and an adjusted version, have been proposed by Rahman and Zhao, 16 referred to as PEL and AEL. They have the advantage of having the standard χ 2 distribution as approximating distribution, but they are more complicated to compute than the competitors mentioned above.…”

A review of recent advances in empirical likelihood

“…Chen et al (2021) conducted the inference under the complex survey design with scrambled responses by the sample empirical likelihood approach. Rahman and Zhao (2022) constructed confidence intervals for the sensitivity to early disease stage by the empirical likelihood method. The EL methods have been also applied to genetics and omics studies.…”