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.