Background: Meta-analysis has become increasingly popular in recent years, especially in genomic data analysis, due\nto the fast growth of available data and studies that target the same questions. Many methods have been developed,\nincluding classical ones such as Fisherââ?¬â?¢s combined probability test and Stoufferââ?¬â?¢s Z-test. However, not all meta-analyses\nhave the same goal in mind. Some aim at combining information to find signals in at least one of the studies, while\nothers hope to find more consistent signals across the studies. While many classical meta-analysis methods are\ndeveloped with the former goal in mind, the latter goal has much more practicality for genomic data analysis.\nResults: In this paper, we propose a class of meta-analysis methods based on summaries of weighted ordered\np-values (WOP) that aim at detecting significance in a majority of studies. We consider weighted versions of classical\nprocedures such as Fisherââ?¬â?¢s method and Stoufferââ?¬â?¢s method where the weight for each p-value is based on its order\namong the studies. In particular, we consider weights based on the binomial distribution, where the median of the\np-values are weighted highest and the outlying p-values are down-weighted. We investigate the properties of our\nmethods and demonstrate their strengths through simulations studies, comparing to existing procedures. In addition,\nwe illustrate application of the proposed methodology by several meta-analysis of gene expression data.\nConclusions: Our proposed weighted ordered p-value (WOP) methods displayed better performance compared to\nexisting methods for testing the hypothesis that there is signal in the majority of studies. They also appeared to be\nmuch more robust in applications compared to the rth ordered p-value (rOP) method (Song and Tseng, Ann. Appl.\nStat. 2014, 8(2):777ââ?¬â??800). With the flexibility of incorporating different p-value combination methods and different\nweighting schemes, the weighted ordered p-values (WOP) methods have great potential in detecting consistent\nsignal in meta-analysis with heterogeneity.
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