Ball divergence for the equality test of crossing survival curves

It is a very common problem to test survival equality using the right-censored time-to-event data in clinical research. Although the log-rank test is popularly used in various studies, it may become insensitive when the proportional hazards assumption is violated. As follows, there have a variety of statistical methods being proposed to identify the discrepancy between crossing survival curves or hazard functions. The omnibus tests against general alternatives are usually preferred due to their wide applicability to complicated scenarios in real applications. In this paper, we propose two novel statistics to estimate the ball divergence using the right-censored survival data, and then implement them in the equality test on survival time in two independent groups. The simulation analysis demonstrates their efficiency in identifying the survival discrepancy. Compared to the existing methods, our proposed methods present higher power in situations with complex distributions, especially when there is a scale shift between groups. Real examples illustrate its advantage in practical applications.