Empirical likelihood inference and goodness-of-fit test for logistic regression model under two-phase case-control sampling

• Published in: Statistical theory and related fields Vol. 6; no. 4; pp. 265 - 276
• Main Authors: Sheng, Zhen, Liu, Yukun, Qin, Jing
• Format: Journal Article
• Language: English
• Published: Taylor & Francis 25.11.2022; Taylor & Francis Group
• Subjects: Bootstrap; case-control data; empirical likelihood; goodness-of-fit test; two-phase case-control sampling
• ISSN: 2475-4269; 2475-4277
• DOI: 10.1080/24754269.2021.1946373

Due to cost-effectiveness and high efficiency, two-phase case-control sampling has been widely used in epidemiology studies. We develop a semi-parametric empirical likelihood approach to two-phase case-control data under the logistic regression model. We show that the maximum empirical likelihood estimator has an asymptotically normal distribution, and the empirical likelihood ratio follows an asymptotically central chi-square distribution. We find that the maximum empirical likelihood estimator is equal to Breslow and Holubkov (1997)'s maximum likelihood estimator. Even so, the limiting distribution of the likelihood ratio, likelihood-ratio-based interval, and test are all new. Furthermore, we construct new Kolmogorov-Smirnov type goodness-of-fit tests to test the validation of the underlying logistic regression model. Our simulation results and a real application show that the likelihood-ratio-based interval and test have certain merits over the Wald-type counterparts and that the proposed goodness-of-fit test is valid.