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 measure- ment 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. 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. 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 ap- plication using bank customers’ monthly taxes to illustrate further the effectiveness of our proposed method.

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