P-values and confidence intervals of linear rank tests for left-truncated data under truncated binomial design

Area of Science:

• Statistics
• Biostatistics
• Survival Analysis

Background:

• Accurate statistical inference is crucial for analyzing left-truncated data, common in survival studies.
• Existing methods for approximating p-values may have limitations in accuracy for such data.
• The mid-p-value offers a potentially less biased alternative to traditional p-values.

Purpose of the Study:

• To compare the accuracy of saddlepoint and normal approximation methods for mid-p-values.
• To evaluate these methods for Wilcoxon and log-rank tests with left-truncated data.
• To assess performance using both real and simulated data.

Main Methods:

• Computational comparison of approximation methods.
• Application of Wilcoxon and log-rank tests.
• Utilizing a truncated binomial design for left-truncated data.
• Inversion of tests for confidence interval construction.

Main Results:

• The saddlepoint approximation demonstrated superior accuracy in approximating mid-p-values compared to the normal approximation.
• Both methods were evaluated using real-world datasets and extensive simulations.
• Confidence intervals were successfully derived through test inversion.

Conclusions:

• The saddlepoint approximation is recommended for improved accuracy in mid-p-value calculations for left-truncated data.
• This finding has implications for statistical testing in survival analysis and related fields.
• The study provides a robust comparison supporting the use of saddlepoint approximations.