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

Abstract

Motivation: Meta-analysis methods have been widely used to combine results from multiple clinical or genomic studies to increase statistical powers and ensure robust and accurate conclusions. The adaptively weighted Fisher's method (AW-Fisher), initially developed for omics applications but applicable for general meta-analysis, is an effective approach to combine P-values from K independent studies and to provide better biological interpretability by characterizing which studies contribute to the meta-analysis. Currently, AW-Fisher suffers from the lack of fast P-value computation and variability estimate of AW weights. When the number of studies K is large, the 3K - 1 possible differential expression pattern categories generated by AW-Fisher can become intractable. In this paper, we develop an importance sampling scheme with spline interpolation to increase the accuracy and speed of the P-value calculation. We also apply bootstrapping to construct a variability index for the AW-Fisher weight estimator and a co-membership matrix to categorize (cluster) differentially expressed genes based on their meta-patterns for intuitive biological investigations.

Results: The superior performance of the proposed methods is shown in simulations as well as two real omics meta-analysis applications to demonstrate its insightful biological findings.

Availability and implementation: An R package AWFisher (calling C++) is available at Bioconductor and GitHub (https://github.com/Caleb-Huo/AWFisher), and all datasets and programing codes for this paper are available in the Supplementary Material.

Supplementary information: Supplementary data are available at Bioinformatics online.

Fig. 1.

Six meta-pattern modules of biomarkers from mouse metabolism example. Each gene module (Modules I, II, …, VI) shows a set of detected biomarkers with similar meta-pattern of differential signals. (A) Heatmaps of detected genes (on the rows) and samples (on the columns) for each tissue (brown fat, heart, liver), where each tissue represents a study. In the heatmap, red color represents higher expression level, and the green color represents lower expression level. Black color bar on top represents wild-type (control) and orange color bar on top represents VLCAD−/− mice (case). Number of genes is shown on the left under each module number. (B) Variability index (genes on the rows and studies on the columns). Variability index is described in Section 2.2. Gray heatmap range from 0 (black) to 1 (white), which is the maximum of the variability index. Genes of each module are sorted based on the mean variability index. (C) Signed AW-Fisher weights ${\widehat{v}}_{\mathit{gk}}$ for gene g and study k. Light blue represents$\mathrm{ }{\widehat{v}}_{\mathit{gk}}=1$, yellow corresponds to ${\widehat{v}}_{\mathit{gk}}=-1$ and black for$\mathrm{ }{\widehat{v}}_{\mathit{gk}}=0$. Representative signed AW-Fisher weights for each module are shown on the right. Note brown represents brown fat tissue. (Color version of this figure is available at Bioinformatics online.)