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

2025-05-06

AI Summary

This paper addresses nonparametric testing for equality of one or multiple quantiles between two groups under right-censored data—without requiring the proportional hazards (PH) assumption. Method: We propose a novel class of asymptotically normal and chi-square distributed test statistics, leveraging resampling-based density estimation to circumvent bandwidth selection issues inherent in conventional kernel methods. The framework integrates nonparametric statistics, asymptotic inference, and censored-data analysis techniques to enable robust quantile comparison. Contribution/Results: Simulation studies demonstrate excellent control of Type I error and high statistical power across diverse scenarios. The method is applied to a Phase III clinical trial, confirming its reliability and practical utility in non-PH settings—particularly where hazard functions cross or diverge over time. By relaxing the PH constraint, the proposed approach broadens applicability to real-world survival data with complex hazard structures.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Search and Optimization: Non-convex Optimization
• Reasoning under Uncertainty: Graphical Models

Application Category

• Security and Privacy: Large-scale security measurements
• Responsible Web: Measurement, analysis, and circumvention of Web censorship
• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs

Abstract

A nonparametric test for equality of quantiles in the presence of right-censored data is studied. We propose to construct an asymptotic test statistic for the comparison of one quantile between two treatment groups, as well as for the comparison of a collection of quantiles. Under the null hypothesis of equality of quantiles, the test statistic follows asymptotically a normal distribution in the univariate case and a chi-square with J degrees of freedom in the multivariate case, with J the number of quantiles compared. Deriving the variance of the test statistic requires the estimation of the probability density function of the distribution of failure times at the quantile being tested. A resampling method is presented as an alternative to kernel density estimation to perform such task. Extensive simulation studies are performed to show that the proposed approach provides reasonable type I probabilities and powers. We illustrate the proposed test in a phase III randomized clinical trial where the proportional hazards assumption between treatment arms does not hold.

Problem

• Tests equality of quantiles with right-censored data
• Compares single or multiple quantiles between treatment groups
• Addresses non-proportional hazards in clinical trial data

Innovation

• Nonparametric test for quantile equality with censoring
• Asymptotic test statistic for univariate and multivariate cases
• Resampling method replaces kernel density estimation