Empirical likelihood based tests for stochastic ordering under right censorship

Area of Science:

• Biostatistics
• Survival Analysis
• Statistical Inference

Background:

• Comparing probability distributions is crucial in many scientific fields.
• Right-censored data is common in clinical trials and survival studies.
• Existing methods like log-rank tests have limitations with certain data patterns.

Purpose of the Study:

• To develop a novel statistical test for stochastic ordering between two univariate distributions.
• To address the challenges posed by right-censored data.
• To improve upon existing methods in terms of statistical power.

Main Methods:

• An empirical likelihood approach was developed.
• A maximally selected local empirical likelihood statistic was utilized.
• The asymptotic null distribution was determined using Brownian bridge theory.

Main Results:

• The proposed empirical likelihood test demonstrated superior power compared to log-rank and weighted Kaplan-Meier tests.
• This advantage was particularly evident under crossing hazard alternatives.
• The method's performance was validated through simulation studies.

Conclusions:

• The new empirical likelihood method provides a powerful tool for testing stochastic ordering with right-censored data.
• It offers a valuable alternative to traditional methods, especially when hazard rates cross.
• The approach is applicable to real-world data, as shown in an alcoholic hepatitis clinical trial.