Accurate and Efficient P-value Calculation via Gaussian Approximation: a Novel Monte-Carlo Method.

Area of Science:

• Statistics
• Genetics
• Bioinformatics

Background:

• Testing the significance of multiple covariates is crucial in statistical analysis, particularly in genome-wide association studies (GWAS).
• Methods like minimum p-value, higher criticism, and Berk-Jones tests are effective for sparse effects but face challenges with correlated covariates and non-Gaussian data.
• Permutation testing provides accurate p-values but is computationally intensive, limiting its application in large-scale hypothesis testing.

Purpose of the Study:

• To develop a computationally efficient method for calculating p-values in hypothesis testing for sparse covariate effects.
• To address the challenges posed by covariate correlations and non-Gaussian response distributions.
• To offer an accurate and faster alternative to permutation testing in statistical genetics.

Main Methods:

• Proposed a Gaussian approximation method utilizing a Monte Carlo scheme.
• Derived non-asymptotic approximation error bounds, demonstrating validity even when covariates exceed sample size.
• Compared the proposed method against permutation testing and asymptotic distribution methods using simulations and real GWAS data.

Main Results:

• The Gaussian approximation method achieves comparable accuracy to permutation testing.
• The proposed method demonstrates significantly improved computational efficiency over permutation testing.
• Error bounds indicate the method's robustness even with a large number of covariates relative to sample size.

Conclusions:

• The Gaussian approximation method offers a computationally efficient and accurate approach for hypothesis testing with sparse covariate effects.
• This method is particularly beneficial for large-scale genetic studies where computational cost is a major concern.
• The derived error bounds provide theoretical support for the method's reliability across various data scenarios.