Karl Pearson的Meta分析
Karl Pearson's meta-analysis revisited
摘要：
本文回顾了Pearson [Biometrika 26（1934）425- 442]提出并由David [Biometrika 26（1934）1- 11]首次使用的荟萃分析方法。它被认为是不可接受的超过50年，可以追溯到一个文件Birnbaum [J。Assoc.49（1954）559- 574]。事实证明，伯恩鲍姆分析的方法不是皮尔逊提出的方法。我们证明了皮尔森的提议是可接受的。因为它是可接受的，它在某些替代品上比Fisher [Statistical Methods for Research Workers（1932）Oliver and Boyd]的标准检验具有更好的功效，而在其他替代品上具有更差的功效。皮尔逊方法在所有或大部分非零参数具有相同符号时具有优势。皮尔森检验已被证明在基因组设置中有用，筛选与年龄相关的基因。本文还提出了一种基于FFT的非负随机变量之和CDF的硬上、下界的求取方法。
英文摘要：
This paper revisits a meta-analysis method proposed by Pearson [Biometrika 26 (1934) 425--442] and first used by David [Biometrika 26 (1934) 1--11]. It was thought to be inadmissible for over fifty years, dating back to a paper of Birnbaum [J. Amer. Statist. Assoc. 49 (1954) 559--574]. It turns out that the method Birnbaum analyzed is not the one that Pearson proposed. We show that Pearson's proposal is admissible. Because it is admissible, it has better power than the standard test of Fisher [Statistical Methods for Research Workers (1932) Oliver and Boyd] at some alternatives, and worse power at others. Pearson's method has the advantage when all or most of the nonzero parameters share the same sign. Pearson's test has proved useful in a genomic setting, screening for age-related genes. This paper also presents an FFT-based method for getting hard upper and lower bounds on the CDF of a sum of nonnegative random variables.
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