Empirical-likelihood-based semiparametric inference for the treatment effect in the two-sample problem with censoring

Area of Science:

• Statistics
• Biostatistics
• Survival Analysis

Background:

• Comparing two samples with censored data is common in biostatistics.
• Existing methods often assume similar models (parametric or nonparametric) for both samples.
• A gap exists in methods that can handle mixed model assumptions for censored data.

Purpose of the Study:

• To develop a unified semiparametric inference framework for comparing two censored data samples.
• To accommodate situations where one sample follows a parametric model and the other a nonparametric model.
• To improve confidence interval estimation for parameters of interest, such as mean differences or survival probabilities.

Main Methods:

• Proposing a unified semiparametric inference approach.
• Utilizing the empirical likelihood principle for confidence interval construction.
• Establishing the asymptotic chi-squared distribution for the empirical likelihood ratio.

Main Results:

• The semiparametric inference method provides improved confidence intervals compared to standard estimating equations.
• Empirical likelihood-based confidence intervals demonstrate superior performance.
• Simulation experiments confirm the substantial outperformance of the empirical likelihood method.

Conclusions:

• The proposed unified semiparametric inference is effective for comparing censored data with mixed model assumptions.
• The empirical likelihood principle offers a robust and advantageous method for statistical inference in such scenarios.
• The method is validated through simulations and real-world data analysis.