Two-sample test based on empirical likelihood ratio under semi-competing risks data

This article considers the two-sample testing problem of the survival function of the non terminal event time under semi-competing risks data. The empirical likelihood function is constructed for the survival function estimation of the non terminal event time, then maximize it by the PSO (Particle swarm optimization) algorithm to obtain the MLE. For the testing problem, the article develops the empirical likelihood ratio test to compare the two survival curves. From simulation studies, it shows the performance of the proposed approaches is good. Finally, a real data analysis is presented for illustration.