Choosing Between Methods of Combining p-values
arXiv:1707.06897 · doi:10.1093/biomet/asx076
Abstract
Combining p-values from independent statistical tests is a popular approach to meta-analysis, particularly when the data underlying the tests are either no longer available or are difficult to combine. A diverse range of p-value combination methods appear in the literature, each with different statistical properties. Yet all too often the final choice used in a meta-analysis can appear arbitrary, as if all effort has been expended building the models that gave rise to the p-values. Birnbaum (1954) showed that any reasonable p-value combiner must be optimal against some alternative hypothesis. Starting from this perspective and recasting each method of combining p-values as a likelihood ratio test, we present theoretical results for some of the standard combiners which provide guidance about how a powerful combiner might be chosen in practice.
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