# Introducing the Event‐Adjusted Rank Sum (EARS) Test: A Simple Approach to Survival Analysis Independent of Proportional Hazards

## TL;DR

The EARS test is a new survival analysis method that works well even when traditional assumptions are violated, making it a reliable and accessible alternative for researchers.

## Contribution

The EARS test introduces a nonparametric survival analysis method that does not rely on the proportional hazards assumption.

## Key findings

- EARS and log-rank tests agreed in 96.6% of simulated cases.
- EARS identified significant differences in 94.4% of PH-violating datasets.
- EARS showed consistent results with established tests in clinical cohorts.

## Abstract

Survival analyses often violate the proportional hazards (PH) assumption, compromising the validity of widely used statistical tests such as the log‐rank test and Cox regression. To address this limitation, we introduce the event‐adjusted rank sum (EARS) test, a nonparametric method designed to provide robust time‐to‐event data analysis without relying on PH.

The EARS test adjusts survival times by dividing each event time by the proportion of events within its respective group. These adjusted survival times are then compared using the Kruskal–Wallis test. To account for censoring, the resulting p value is adjusted based on the overall proportion of censored observations. We validated the EARS test through simulations involving 1000 cohorts with group sizes ranging from 50 to 1000 patients and censoring rates between 5% and 75%. Additionally, we compared the performance of EARS to the log‐rank test and restricted mean survival time (RMST) under both PH and non‐PH conditions using both simulated and clinical datasets.

In simulation studies, the EARS and log‐rank tests agreed in 96.6% of cases. Under the null hypothesis, the EARS test demonstrated a Type I error rate of 2% across two to five groups, slightly higher than the log‐rank test′s 1%. Power analyses revealed that EARS detected true differences in 63% of cases compared to 68% for the log‐rank test. In 1000 datasets violating the PH assumption, EARS identified significant differences in 94.4% of cases versus 98.0% for RMST, with both methods agreeing 96.4% of the time on null hypothesis rejection. Analyses of clinical cohorts further confirmed the reliability of the EARS test, showing consistent alignment with established tests in most scenarios.

The EARS test offers a simple, nonparametric alternative for survival analysis that remains reliable across diverse conditions and varying censoring distributions. Its accessibility and robust performance make it a valuable tool for researchers and clinicians, especially in settings where the PH assumption is violated or advanced statistical software is unavailable. An R package implementing the EARS test is openly available.