生存分析中，最重要的一项研究是治疗方法间的比较。右删失数据下，生存曲线或风险率出现交叉（即风险率成比例假设失效）的情况频频发生，无论是基于风险率差的加权log-rank等检验，还是基于生存率差的加权Kaplan-Meier等检验均无法完全避免交叉点前后差异相互抵消导致的检验效能降低，甚至给出错误的结果。由于生存曲线能直接表达生存状态的高低，项目组提出以两条生存曲线间绝对面积为基础的非参数检验方法，能避免“交叉”带来的问题，并在此基础上发展任意时间段（如长期效应）、固定时间点上的组间差异比较方法。竞争风险下，累积发生率或部分分布风险率出现交叉又是另一种复杂生存数据，常用的Gray检验也有交叉点前后差异抵消造成的检验效能降低的问题，本课题基于上述类似思想提出基于两条累积发生率间绝对面积的非参数检验法，以及任意时间段、点上的非参数检验。同时研究以上新检验法在多组比较时的方法，及交叉点的估计方法。

To evaluate treatment effect in cases of survival data, we often need to compare two hazard rate functions or survival curves of the treatment and control groups. For right censoring data, the phenomenon of crossing hazard rates or crossing survival curves is common in applications. Whether the methods based on the difference between the hazard rates such as weighted log-rank test, or the methods based on the difference between the survival rates such as weighted Kaplan-Meier test will lose power, because early positive differences between the two groups are canceled out by later differences of the opposite sign. Since the survival curves can be expressed directly to the level of survival, the project team plans to develop a non-parametric test based on the absolute area between the two survival curves which can avoid the "cross" problems, and detect early or late survival differences, and compare survival rates at a fixed point in time. For competing risks data, the Gray test will lose power when crossing cumulative incidence rates or the subdistribution hazard rates are presence. This project will propose a new non-parametric test based on the area between two cumulative incidence rates, and detect early or late survival differences, and compare survival rates at a fixed point in time. Moreover, the new test methods in the multi-group comparison, and the estimation of the crossing point.