Statistics and Its Interface

Volume 11 (2018)

Number 3

A unified semi-empirical likelihood ratio confidence interval for treatment effects in the two sample problem with length-biased data

Pages: 531 – 540

DOI: http://dx.doi.org/10.4310/SII.2018.v11.n3.a14

Authors

Tao Li (School of Statistics and Management, Shanghai University of Finance and Economics, Shanghai, China)

Mengyun Wu (School of Statistics and Management, Shanghai University of Finance and Economics, Shanghai, China)

Yong Zhou (Academy of Mathematics and System Sciences, Chinese Academy of Science, Beijing, China; and School of Statistics and Management, Shanghai University of Finance and Economics, Shanghai, China)

Abstract

In two sample studies, the treatment effects that we are interested in may have different types, such as mean difference, the difference of probabilities, etc. In this work, we apply semi-parametric empirical likelihood principle to length biased data and derived a unified empirical likelihood ratio confidence interval for treatment effects. The empirical likelihood ratio is shown to be asymptotically distributed as chi-squared. Simulation studies show that the proposed confidence interval has a better performance compared with its counterpart which is based on normal approximation. The severe effect caused by ignoring the length bias is also illustrated by simulation. The proposed method is applied to Oscar data to study the effect of high socio-economic status on lifetime.

Keywords

empirical likelihood, estimating equation, treatment effect, censored data, length-biased

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Li’s work was supported by State Key Program of NNSF of China (91546202). Wu’s work was supported by NNSF of China (61402276). Zhou’s work was supported by the State Key Program of NNNSF of China (71331006) and the State Key Program in the Major Research Plan of NNSF of China (91546202).

Received 26 December 2016