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

Zhen Sheng, Yukun Liu and Jing Qin

Statistical Theory and Related Fields, 2022, vol. 6, issue 4, 265-276

Abstract: 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.

Date: 2022
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DOI: 10.1080/24754269.2021.1946373

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