Novel empirical likelihood inference for the mean difference with right-censored data

Area of Science:

• Biostatistics
• Statistical Inference
• Survival Analysis

Background:

• Existing methods for confidence intervals with right-censored data often rely on synthetic data approaches.
• These methods can result in a scaled chi-squared distribution, necessitating scale parameter estimation.
• This estimation introduces complexity and potential inaccuracies in confidence interval construction.

Purpose of the Study:

• To develop an improved empirical likelihood method for constructing confidence intervals for the difference between two means with right-censored data.
• To address the limitations of existing methods, particularly the need for scale parameter estimation.
• To enhance coverage accuracy, especially in small sample scenarios.

Main Methods:

• Utilizing an empirical likelihood method combined with an independent and identically distributed (i.i.d.) random functions representation.
• Employing Kaplan-Meier weights within the empirical likelihood ratio to achieve a standard chi-squared distribution.
• Applying adjusted empirical likelihood for improved small-sample coverage accuracy.
• Investigating a novel mean empirical likelihood method.

Main Results:

• The proposed empirical likelihood method yields a standard chi-squared distribution, avoiding scale parameter estimation.
• Adjusted empirical likelihood demonstrates improved coverage accuracy for small sample sizes.
• Extensive simulations indicate that the proposed empirical likelihood-based confidence interval outperforms existing methods in terms of coverage accuracy.
• The findings are validated using a real-world dataset.

Conclusions:

• The developed empirical likelihood method provides a more accurate and robust approach for confidence intervals with right-censored data.
• This method simplifies the construction process by eliminating the need for scale parameter estimation.
• The study highlights the potential of adjusted and mean empirical likelihood methods for enhancing statistical inference in survival analysis.