Karl Pearson’s meta analysis revisited

By Art B. Owen. 2009

108 citations recorded by the source corpus.

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.

Subfields: Experimental and Cognitive Psychology, Molecular Biology, Statistics and Probability

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Citations in the corpus

Transportability of Causal Effects: Completeness Results (2012, unknown): “Although the problem has been discussed in many areas of statistics, economics, and the health sciences, under rubrics such as “external validity” [Campbell and Stanley, 1963; Manski, 2007], “meta-analysis” [Glass, 1976; Hedges and Olkin, 1985; Owen, 2009], “heterogeneity” [Hofler, Gloster, and Hoye”
Combining p-values via averaging (2012, unknown): “A summary of combination methods for p-values can be found in, e.g., Oosterhoff [29] and Cousins [5]; see also the more specialized review Owen [30].”
Comprehensive literature review and statistical considerations for microarray meta-analysis (2012, methodology): “Owen (130) applied a similar Pearson one-sided test adjustment for Fisher’s method and the modiﬁcation can be extended to minP, maxP and other methods.”
Meta-Transportability of Causal Effects: A Formal Approach (2013, unknown): “…sciences, under rubrics such as “external validity” (Campbell and Stanley, 1963, Manski, 2007), “meta-analysis” (Glass, 1976, Hedges and Olkin, 1985, Owen, 2009), “overgeneralization” (Hofler, Gloster, and Hoyer (2010)), “quasi-experiments” (Shadish, Cook, and Campbell (2002), Ch. 3, Adelman…”
Somatic mutation in single human neurons tracks developmental and transcriptional history (2015, methodology): “To test for enrichment across the dataset, p-values were combined (47) and corrected for multiple testing (Bonferroni correction).”