Normalized area above quantile: An alternative measure to restricted mean survival time
Chenyang Zhang, Jiaqi Gu, Yuanshan Wu, Guosheng Yin
The Annals of Applied Statistics · 2025 · Volume 19 · Issue 4
Abstract
The restricted mean survival time (RMST), which quantifies the average survival time within an investigational time interval, has been widely used to evaluate treatment effects, especially when comparing treatment survival profiles across treatments where the proportional hazards assumption does not hold. However, in the ENACT trial, we observed significant differences in follow-up periods across treatment groups (34 months vs. 20 months), and analysis relying on the RMST difference could result in a substantial loss of useful survival information. As an alternative, we propose integrating the survival curve along the quantile axis instead of the time axis to retain more information, which leads to a new clinical measure called the normalized area above quantile (NAAQ). The NAAQ discards survival information below a chosen quantile τ and assesses the conditional expected survival time among patients with 100(1−τ)% shortest survival time (corresponding to the worst (1−τ) survivors). For right-censored survival data, we propose a nonparametric NAAQ estimator from the Kaplan–Meier curve and prove its asymptotic properties under mild conditions. Simulation studies demonstrate the promising performance of the NAAQ estimator and the NAAQ-based test, which are further applied to two real clinical trials to illustrate the broad practical value of NAAQ.
Keywords
nonparametric estimator; quantile; Right-censored data; RMST; Survival analysis;
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