Following the approach of Morris & Pounds, a distribution of P-values can be decomposed as a mixture of two β-distributions, one with shape paramter (α) of 1 - modelling noise under the null-hypothesis - and another with an emperically fit shape parament (α) of a, modelling the signal component. One can view this as modeling P-values as a random mixture process, where P ~ (1-λ)β(a,1) + λβ(1,1).
Fisher's method of combining independent P-values can be used to conduct a meta-analysis across several tests. However, it assumes a null hypothesis of uniformly distributed P-values, which in the presence of signal is manifestly incorrect. This work looks to produce an analagous test against an appropriately specified null-hypothesis that respects the pre-existing signal.
The aim of this work is a short paper for BioArXiv/PeerJ and a small R package.
Yes, the package name is a bad play on the 80's metal band.
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