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Abstract:
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Fisher's combination test is an important statistical strategy to combine a group of p-values for testing global hypotheses. For dependent input p-values a critical computational problem is to properly control the type I error rate. Current methods, such as Brown's approximation, tend to be too liberal when alpha < 0.05, which is often a problem for big data analysis. To tackle this problem, we first propose a general family of Fisher type p-value combination statistics, referred as the GFisher, which allows weighted combination of chi-square transformed input p-values with different degrees of freedom (DF). The corresponding omnibus test, the oGFisher, can automatically select weights and DF by adapting to given data. Second, we propose two novel methods to calculate the p-value of GFisher, especially when alpha is small (e.g., 1e-6). The first method is based on higher moments matching. The second method is an efficient analytical solution based on a quadratic approximation of the GFisher. The accuracy of relevant methods are evidenced by extensive simulations. An example of application is illustrated by a gene-based SNP-set genetic association study of osteoporosis.
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