Efficient calculation of P-value and power for quadratic form statistics in multilocus association testing

Area of Science:

• Genetics
• Statistical Genetics
• Bioinformatics

Background:

• Association studies often employ test statistics with quadratic forms.
• Accurate distribution estimation is crucial for significance testing, especially in genome-wide scans and complex genetic analyses.
• Current methods like permutation procedures can be computationally intensive or challenging under specific conditions.

Purpose of the Study:

• To develop efficient and accurate methods for estimating the asymptotic and approximate distributions of quadratic form test statistics in association studies.
• To provide a computationally feasible alternative to permutation procedures for p-value estimation.
• To address challenges in genome scans and haplotype frequency inference using the Expectation-Maximization (EM) algorithm.

Main Methods:

• Representing the test statistic D = X(T)AX as a linear combination of independent chi-squared (χ²) random variables with a shift.
• Approximating the distribution of D using a single χ² distribution or the difference of two χ² distributions.
• Applying these methods to multivariate normal data with general similarity matrices and potentially singular variance matrices.

Main Results:

• Demonstrated that the quadratic form statistic D can be expressed as a linear combination of independent chi-squared variables.
• Showcased that the distribution of D can be effectively approximated by chi-squared distributions.
• Validated the utility of the method for scenarios requiring stringent significance levels (e.g., genome scans) and computationally intensive tasks like EM-based haplotype inference.

Conclusions:

• The proposed method offers an efficient and accurate approach for estimating the distributions of quadratic form test statistics.
• This technique provides a valuable alternative to computationally demanding permutation tests in genetic association studies.
• The general applicability to various quadratic form statistics makes this method broadly relevant for statistical genetics research.