A Nonparametric Statistical Method for Two Crossing Survival Curves

TL;DR

This paper introduces a nonparametric method using the area between survival curves and a permutation test to evaluate treatment benefits when survival curves cross, overcoming limitations of traditional methods.

Contribution

It proposes a novel robust statistical approach with an R package for analyzing crossing survival curves, improving assessment accuracy in complex survival data scenarios.

Findings

Permutation test has acceptable type I error rate.

Method shows superior power in crossing survival curves.

Provides intuitive quantification of treatment differences.

Abstract

In comparative research on time-to-event data for two groups, when two survival curves cross each other, it may be difficult to use the log-rank test and hazard ratio (HR) to properly assess the treatment benefit. Our aim was to identify a method for evaluating the treatment benefits for two groups in the above situation. We quantified treatment benefits based on an intuitive measure called the area between two survival curves (ABS), which is a robust measure of treatment benefits in clinical trials regardless of whether the proportional hazards assumption is violated or two survival curves cross each other. Additionally, we propose a permutation test based on the ABS, and we evaluate the effectiveness and reliability of this test with simulated data. The ABS permutation test is a robust statistical inference method with an acceptable type I error rate and superior power to detect differences in treatment effects, especially when the proportional hazards assumption is violated. The ABS can be used to intuitively quantify treatment differences over time and provide reliable conclusions in complicated situations, such as crossing survival curves. The R Package "ComparisonSurv" contains the proposed methods and is available from https://CRAN.R-project.org/package=ComparisonSurv. Keywords: Survival analysis; Area between two survival curves; Crossing survival curves; Treatment benefit