Bayesian and influence function‐based empirical likelihoods for inference of sensitivity to the early diseased stage in diagnostic tests

Abstract

In practice, a disease process might involve three ordinal diagnostic stages: the normal healthy stage, the early stage of the disease, and the stage of full development of the disease. Early detection is critical for some diseases since it often means an optimal time window for therapeutic treatments of the diseases. In this study, we propose a new influence function-based empirical likelihood method and Bayesian empirical likelihood methods to construct confidence/credible intervals for the sensitivity of a test to patients in the early diseased stage given a specificity and a sensitivity of the test to patients in the fully diseased stage. Numerical studies are performed to compare the finite sample performances of the proposed approaches with existing methods. The proposed methods are shown to outperform existing methods in terms of coverage probability. A real dataset from the Alzheimer's Disease Neuroimaging Initiative (ANDI) is used to illustrate the proposed methods.

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.…”

“…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. Finally, Hai et al 17 proposed to obtain a confidence interval for 𝜃 2 (given 𝜃 1 and 𝜃 3 ) by using an estimated EL pivot based on an estimated version of the so-called influence function of an estimator for 𝜃 2 . The proposed pivot has a standard 𝜒 2 asymptotic distribution, but the estimation of the influence function involves kernel density estimation.…”

“…Finally, Hai et al. 17 proposed to obtain a confidence interval for θ 2 (given θ 1 and θ 3) by using an estimated EL pivot based on an estimated version of the so-called influence function of an estimator for θ 2. The proposed pivot has a standard χ 2 asymptotic distribution, but the estimation of the influence function involves kernel density estimation.…”