Adjusted empirical likelihood analysis of restricted mean survival time for length-biased data

The Restricted Mean Survival Time (RMST) serves as a valuable and extensively utilized metric in clinical trials. However, its application becomes intricate when dealing with data affected by length-biased sampling, rendering traditional inference strategies inadequate. To overcome this challenge, we advocate for the adoption of nonparametric techniques. One notably promising approach is the Empirical Likelihood (EL) method, which furnishes robust results without the need for stringent parametric assumptions. In practical scenarios, the underlying sampling distributions often remain elusive, necessitating adjustments in the case of parametric methodologies. The EL method has demonstrated its efficacy in addressing such complexities. Consequently, this paper introduces the EL method for computing RMST in situations involving both length-biased and right-censored data. Additionally, we introduce the concept of adjusted empirical likelihood (AEL) to further enhance the coverage probability, particularly when dealing with smaller sample sizes. To gauge the performance of the EL and AEL methods, we conduct simulations and rigorously compare their results. The findings unequivocally demonstrate that AEL-based confidence intervals consistently provide superior coverage probability when juxtaposed with EL-based intervals. Lastly, we substantiate the practical applicability of our proposed method by employing it in the analysis of a real dataset.