Accurate and efficient P-values for rank-based independence tests with clustered data using a saddlepoint...

Area of Science:

• Biostatistics
• Statistical Inference
• Clinical Trials

Background:

• Clustered data in multi-center trials and longitudinal studies present statistical inference challenges due to within-cluster correlation.
• Rank-based tests (logrank, Wilcoxon) are robust but can have inflated Type I errors with standard approximations.
• Exact permutation tests are accurate but computationally infeasible for large datasets.

Purpose of the Study:

• To develop a computationally efficient and accurate statistical method for analyzing clustered data.
• To provide reliable p-values and confidence intervals for rank-based tests in the presence of within-cluster correlation.
• To address the methodological gap between the accuracy of permutation tests and the practicality of asymptotic methods.

Main Methods:

• A novel double saddlepoint approximation framework is proposed.
• The method utilizes a permutation distribution reformulation via block urn design to maintain cluster integrity.
• This reformulation allows the test statistic's distribution to be represented as a sum of independent conditional random variables for saddlepoint computation.

Main Results:

• The double saddlepoint method accurately controls Type I error rates for rank-based tests on clustered data.
• Performance is statistically equivalent to exact permutation tests but with significantly reduced computational cost.
• The approach handles right-censored survival data and tied ranks effectively.

Conclusions:

• The proposed double saddlepoint approximation offers a practical, efficient, and statistically rigorous tool for biostatisticians analyzing clustered data.
• It overcomes the computational limitations of permutation tests while maintaining accuracy.
• The method can prevent false-positive conclusions sometimes arising from standard asymptotic approximations in clinical trial data.