Hypothesis setting and order statistic for robust genomic meta-analysis

TL;DR

This paper introduces the rOP order statistic method for meta-analysis of genomic studies, improving detection of differentially expressed genes across multiple datasets with better statistical properties.

Contribution

It proposes the rOP method for meta-analysis, including parameter estimation, asymptotic analysis, and applications to real genomic data, showing advantages over classical methods.

Findings

rOP outperforms Fisher's, Stouffer's, and p-value min/max methods in power.

rOP is connected to vote counting and offers a generalized, robust approach.

Applied to microarray data for diseases like depression, brain cancer, and diabetes.

Abstract

Meta-analysis techniques have been widely developed and applied in genomic applications, especially for combining multiple transcriptomic studies. In this paper we propose an order statistic of $p$-values ($r$th ordered $p$-value, rOP) across combined studies as the test statistic. We illustrate different hypothesis settings that detect gene markers differentially expressed (DE) 'in all studies," "in the majority of studies"' or "in one or more studies," and specify rOP as a suitable method for detecting DE genes "in the majority of studies." We develop methods to estimate the parameter $r$ in rOP for real applications. Statistical properties such as its asymptotic behavior and a one-sided testing correction for detecting markers of concordant expression changes are explored. Power calculation and simulation show better performance of rOP compared to classical Fisher's method, Stouffer's method, minimum $p$-value method and maximum $p$-value method under the focused hypothesis setting. Theoretically, rOP is found connected to the na\"{i}ve vote counting method and can be viewed as a generalized form of vote counting with better statistical properties. The method is applied to three microarray meta-analysis examples including major depressive disorder, brain cancer and diabetes. The results demonstrate rOP as a more generalizable, robust and sensitive statistical framework to detect disease-related markers.