A Better Comparison under right-censoring: ABC Statistic for Equivalence Testing and Quantification

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.