Iranian Statistical Society Journal of the Iranian Statistical Society 1726-4057 23 2 2024 12 01 Analysis of Restricted Mean Survival Time for Length-biased Data via Empirical Likelihood 69 96 725133 10.22034/jirss.2025.2013325.1040 EN Vahid Fakoor Department of Statistics, Ordered and Spatial Data Center of Excellence, Ferdowsi University of Mashhad, Mashhad, Iran Zahra Mohammadian Department of Statistics, Ordered and Spatial Data Center of Excellence, Ferdowsi University of Mashhad, Mashhad, Iran Arezou Habibirad Department of Statistics, Ordered and Spatial Data Center of Excellence, Ferdowsi University of Mashhad, Mashhad, Iran Hadi Jabbari Department of Statistics, Ordered and Spatial Data Center of Excellence, Ferdowsi University of Mashhad, Mashhad, Iran 0000-0002-7028-9052 Journal Article 2023 10 12 The restricted mean survival time (RMST) in the context of length-biased data is an important addition to clinical studies. The RMST is a widely used measurement for evaluating survival over a specific period, and the area under the survival function is a key component of this metric. However, when the data under study are length-biased, traditional parametric and classical methods for examining the RMST are not applicable. Nonparametric and semi-parametric methods are used to address this issue. We utilize the empirical likelihood (EL) method to investigate RMST.<br />Our proposed EL procedure provides a reliable approach for inferential analysis of RMST in the presence of length-biased data. We have shown that the limiting distribution of the empirical log-likelihood ratio is a chi-square distribution with one degree of freedom. We also demonstrated that the likelihood ratio exhibits weak convergence to a mean-zero Gaussian process, which we used to construct a confidence band.<br />In our simulation section, we compared the confidence intervals obtained from the normal approximation (NA) and EL methods. We showed that the EL method has a better coverage probability than the NA method. Additionally, we provided a real data application using bank customers' monthly taxes to illustrate further the effectiveness of our proposed method. https://jirss.irstat.ir/article_725133_831279af3fa26f20a847ce04894300b4.pdf