Crossing points in survival analysis sensitively depend on system conditions

TL;DR

Crossing points in survival analysis are highly sensitive to individual survival curve errors, which complicates their interpretation and suggests the need for careful variability analysis before advanced methods.

Contribution

This paper reveals the exponential dependence of crossing points on survival curves and highlights their sensitivity to small errors, proposing cautious analysis strategies.

Findings

Crossing points depend exponentially on survival curves.

Small errors in survival data can cause large errors in crossing point location.

Most crossing points are sensitive to individual survival errors.

Abstract

Crossing survival curves complicate how we interpret results from a clinical trial's primary endpoint. We find the function to determine a crossing point's location depends exponentially on individual survival curves. This exponential relationship between survival curves and the crossing point transforms small survival curve errors into large crossing point errors. In most cases, crossing points are sensitive to individual survival errors and may make accurately locating a crossing point unsuccessful. We argue more complicated analyses for mitigating crossing points should be reserved only after first exploring a crossing point's variability, or hypothesis tests account for crossing point variability.