Assessing dominance in survival functions: A test for right-censored data
Félix Belzunce, Carolina Martínez-Riquelme, Jaime Valenciano
TL;DR
The paper tackles testing stochastic dominance between two survival functions under right-censoring, where survival curves may cross. It introduces a supremum-based test statistic $\Delta_{n,m}=\left(\frac{nm}{n+m}\right)^{1/2}\sup_{t\in(0,\tau)}\{\hat{S}_{T,n}(t)-\hat{S}_{U,m}(t)\}$ and derives an asymptotic Gaussian-process distribution for inference, with consistency under the alternative. Implementations rely on a multivariate normal approximation (via the mvtnorm package) and grid discretization, and the method is demonstrated on real datasets (lung cancer survival and catheter infection times) showing detection of crossings where standard tests may fail. The approach provides a more informative alternative to the log-rank for scenarios involving dominance and crossing, with practical implications for medical and reliability studies.
Abstract
This paper proposes a new statistical test to assess the dominance of survival functions in the presence of right-censored data. Traditional methods, such as the log-rank test, are inadequate for determining whether one survival function consistently dominates another, especially when survival curves cross. The proposed test is based on the supremum of the difference between Kaplan-Meier estimators and allows for distinguishing between dominance and crossing survival curves. The paper presents the test's asymptotic properties, along with simulations and applications to real datasets. The results demonstrate that the test has high sensitivity for detecting crossings and dominance compared to conventional methods.