Admissibility of unbiased tests for a composite hypothesis with a restricted alternative

Iwasa, Manabu

doi:10.1007/bf00121645

Cited by 8 publications

(1 citation statement)

References 17 publications

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“…In Section 3.1 we constructed monotone α-admissible p-values for H r/n 0 , we we show that they fail to be admissible if we allow non-monotone tests. For the case n = r = 2, the construction of such counter-examples dates back to Lehmann (1952) and Iwasa (1991).…”

Section: Inadmissibilitymentioning

confidence: 99%

Admissibility in Partial Conjunction Testing

Wang

Owen

2018

Journal of the American Statistical Association

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Meta-analysis combines results from multiple studies aiming to increase power in finding their common effect. It would typically reject the null hypothesis of no effect if any one of the studies shows strong significance. The partial conjunction null hypothesis is rejected only when at least r of n component hypotheses are non-null with r = 1 corresponding to a usual metaanalysis. Compared with meta-analysis, it can encourage replicable findings across studies. A by-product of it when applied to different r values is a confidence interval of r quantifying the proportion of non-null studies. Benjamini and Heller (2008) provided a valid test for the partial conjunction null by ignoring the r − 1 smallest p-values and applying a valid meta-analysis p-value to the remaining n − r + 1 p-values. We provide sufficient and necessary conditions of admissible combined p-value for the partial conjunction hypothesis among monotone tests. Non-monotone tests always dominate monotone tests but are usually too unreasonable to be used in practice. Based on these findings, we propose a generalized form of Benjamini and Heller's test which allows usage of various types of meta-analysis p-values, and apply our method to an example in assessing replicable benefit of new anticoagulants across subgroups of patients for stroke prevention.

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Section: Inadmissibilitymentioning

confidence: 99%