The ABC (area between curves) statistic is an $L^1$-distance which targets an easy-to-interpret estimand. Defined as the (normalized) integrated absolute distance between two survival curves it is a meaningful quantity even when survival functions are crossing. Based on right-censored time-to-event data, estimation is based on Kaplan-Meier curves obtained from two independent sample groups. In the present paper, we develop the large sample properties of the ABC statistic and investigate various resampling options for approximating the statistic's distribution which is possibly non-normal in the limit. These breakthroughs enable the construction of equivalence tests which can be used to establish that differences between two survival functions are practically irrelevant. Alternatively, the point estimator can be accompanied with confidence intervals that comprehensibly quantify the difference between the curves. An extensive simulation study explores these inferential methods under various scenarios: proportional, crossing, and partially equal survival functions. An application to data on overall and progression-free survival in a lung cancer trial illustrates the methods' benefits and some points of consideration.

翻译：ABC（曲线间面积）统计量是一种针对易于解释的估计量的$L^1$距离。该统计量定义为两条生存曲线之间（归一化）积分绝对距离，即使在生存函数交叉时也具有明确意义。基于右删失事件时间数据，估计过程依赖于两个独立样本组所获得的Kaplan-Meier曲线。本文发展了ABC统计量的大样本性质，并研究了多种重抽样方法以近似该统计量的分布（该分布在极限情形下可能非正态）。这些突破使得能够构建等价检验，用于证明两条生存函数间的差异在实际上可忽略不计。此外，点估计量可辅以置信区间，直观地量化曲线间的差异。通过涵盖比例风险、交叉及部分相等生存函数等多种场景的广泛模拟研究，本文探讨了这些推断方法。在肺癌试验总生存期与无进展生存期数据上的应用案例展示了该方法的优势及若干需注意的要点。