Empirical Likelihood Comparison of Absolute Risks.

Area of Science:

• Biostatistics
• Survival Analysis
• Statistical Inference

Background:

• Estimating the t-year absolute risk, or cumulative incidence function, is crucial in competing risks settings.
• The standard nonparametric Aalen-Johansen estimator, while robust for large samples, exhibits limitations in small sample performance.
• Inaccurate confidence interval coverage and inconsistent conclusions between risk differences and risk ratios are noted issues.

Purpose of the Study:

• To introduce an alternative empirical likelihood approach for estimating absolute risks in competing risks.
• To address the limitations of the Aalen-Johansen estimator in small sample scenarios.
• To ensure consistent statistical significance conclusions when comparing absolute risks using both risk differences and risk ratios.

Main Methods:

• Developed an empirical likelihood approach for absolute risk estimation.
• Derived formulas and algorithms for constrained nonparametric maximum likelihood estimation (NPMLE).
• Implemented the novel approach in the R package 'timeEL' for practical application.

Main Results:

• The empirical likelihood approach yields consistent conclusions for risk difference and risk ratio comparisons.
• Simulation studies indicate improved accuracy in small sample inference compared to traditional methods.
• Confidence intervals and p-values can be computed using this approach, supported by asymptotic properties.

Conclusions:

• The proposed empirical likelihood method offers a more reliable alternative for absolute risk estimation and comparison in competing risks.
• This approach enhances the accuracy of statistical inference in small sample sizes.
• The 'timeEL' R package facilitates the application of this method, demonstrated with bone marrow transplant data analysis.