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

2026-06-02

AI Summary

This study addresses the challenge of equivalence comparison in right-censored survival data when survival curves may cross, rendering traditional methods inadequate. The authors propose a novel L¹ distance metric based on the difference in areas between survival curves (ABC), constructing a test statistic using Kaplan–Meier estimates to quantify discrepancies between two groups. They establish, for the first time, the large-sample asymptotic theory for the ABC statistic and develop resampling-based inference procedures—such as bootstrap—to accommodate its non-normal limiting distribution, thereby enabling rigorous equivalence testing and confidence interval estimation. Simulation studies demonstrate the method’s robust performance under proportional hazards, crossing survival curves, and partial equivalence scenarios. The approach is successfully applied to a lung cancer clinical trial, yielding interpretable quantifications of differences in both overall survival and progression-free survival.

Abstract

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. %in opposition to tests for exact equality of survival curves. 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.

Problem

• right-censoring
• survival curves
• equivalence testing
• ABC statistic
• time-to-event data

Innovation

• ABC statistic
• equivalence testing
• right-censoring
• survival analysis
• resampling