P-value evaluation, variability index and biomarker categorization for adaptively weighted Fisher's meta-analysis method in omics applications

Meta-analysis methods have been widely used to combine results from multiple clinical or genomic studies to increase statistical power and ensure robust and accurate conclusion. Adaptively weighted Fisher's method (AW-Fisher) is an effective approach to combine p-values from $K$ independent studies and to provide better biological interpretation by characterizing which studies contribute to meta-analysis. Currently, AW-Fisher suffers from lack of fast, accurate p-value computation and variability estimate of AW weights. When the number of studies $K$ is large, the $3^K - 1$ possible differential expression pattern categories can become intractable. In this paper, we apply an importance sampling technique with spline interpolation to increase accuracy and speed of p-value calculation. Using resampling techniques, we propose a variability index for the AW weight estimator and a co-membership matrix to characterize pattern similarities between genes. The co-membership matrix is further used to categorize differentially expressed genes based on their meta-patterns for further biological investigation. The superior performance of the proposed methods is shown in simulations. These methods are also applied to two real applications to demonstrate intriguing biological findings.