Bayesian and influence function-based empirical likelihoods for inference of sensitivity in diagnostic tests

Abstract

In medical diagnostic studies, a diagnostic test can be evaluated based on its sensitivity under a desired specificity. Existing methods for inference on sensitivity include normal approximation-based approaches and empirical likelihood (EL)-based approaches. These methods generally have poor performance when the specificity is high, and some require choosing smoothing parameters. We propose a new influence function-based empirical likelihood method and Bayesian empirical likelihood methods to overcome such problems. Numerical studies are performed to compare the finite sample performance of the proposed approaches with existing methods. The proposed methods are shown to perform better in terms of both coverage probability and interval length. A real data set from Alzheimer’s Disease Neuroimaging Initiative (ANDI) is analyzed.

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

“…Hai et al. (2020) initially provided influence function‐based EL methods for sensitivity of two‐stage diagnostic tests. However, the extension of the results for the two stage in Hai et al.…”

“…With a similar motivation to BEL inference for sensitivity of two‐stage diagnostic tests in Hai et al. (2020), we propose two types of BEL methods for better interval estimation of sensitivity of a three‐stage diagnostic test to early stage disease in this section.…”

“…Yu et al (2012) proposed EL methods based on influence functions of parameters of interest. Hai et al (2020) proposed an influence function-based EL method for inference of sensitivity of two-stage diagnostic tests. Motivated by Yu et al (2012) and Hai et al (2020), we propose an influence function and EL-based confidence interval for 𝑃 2 at a given value of the pair (𝑃 1 , 𝑃 3 ), that is, the sensitivity of the test to the early diseased stage at a specificity and a sensitivity of the test to the fully diseased stage.…”

“…Hai et al. (2020) proposed an influence function‐based EL method for inference of sensitivity of two‐stage diagnostic tests. Motivated by Yu et al.…”

“…(2012) and Hai et al. (2020), we propose an influence function and EL‐based confidence interval for P 2 at a given value of the pair $$(P_1, P_3)$$, that is, the sensitivity of the test to the early diseased stage at a specificity and a sensitivity of the test to the fully diseased stage. The idea is to replace the estimating function in the EL with an influence function of the sensitivity to the early stage.…”