Univariate and multivariate tests of equality of quantiles with right-censored data

The paper presents a clear problem (limitations of existing quantile tests), proposes a logical solution (Kosorok framework + resampling density estimation + power derivation), and supports its claims with theoretical results, simulations, and data application. The structure flows logically from theory to application.

Strengths: Provides detailed theoretical derivations (mentioned as in Supplemental material)., Compares the proposed density estimation method against a standard approach (KDE)., Conducts extensive simulation studies (10,000 simulations) to evaluate performance., Applies the method to a relevant real-world dataset., Discusses underlying assumptions and conditions for the theoretical results.
Weaknesses: The simulation evaluation table (Table 1) only presents results for a single sample size (n=500 per group), though power curves cover various sizes., Relies on reconstructed data for the clinical trial application, which may not perfectly represent the complexity of raw data.

The paper provides sufficient evidence through simulations (Type I error and power results) and a real-data application to support the claims about the proposed method's performance and utility. The comparison between LS and KDE methods is well-supported by the presented tables.

The key novelty lies in explicitly deriving the analytical asymptotic power formulas for Kosorok's test and, importantly, proposing and evaluating a resampling method for density estimation at the quantile of interest as a superior alternative to traditional KDE in this context. This fills a gap in the practical application of quantile tests for clinical trial design.

This work has potentially high significance for clinical trial design and analysis, particularly in areas like immuno-oncology where nonproportional hazards are common. Providing analytical power and sample size calculation tools for quantile tests makes them more practical for researchers and regulators. The emphasis on quantiles, which are more interpretable than hazard ratios under certain conditions, adds to its potential impact.

Strengths: Formal and precise academic language is used., Concepts are generally well-defined (e.g., quantiles, censoring)., Steps in the methodology are outlined., Results are presented clearly in text, tables, and figures.
Areas for Improvement: Complex mathematical notation requires familiarity with survival analysis and asymptotic theory; more intuitive explanations might benefit a broader audience., Some sentences are quite dense.