The assessment of replicability using the sum of p-values

Leonhard Held; Samuel Pawel; Charlotte Micheloud

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arXiv · 2401.13615

The assessment of replicability using the sum of p-values

Leonhard Held·Samuel Pawel·Charlotte Micheloud

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Abstract

Statistical significance of both the original and the replication study is a commonly used criterion to assess replication attempts, also known as the two-trials rule in drug development. However, replication studies are sometimes conducted although the original study is non-significant, in which case Type-I error rate control across both studies is no longer guaranteed. We propose an alternative method to assess replicability using the sum of p-values from the two studies. The approach provides a combined p-value and can be calibrated to control the overall Type-I error rate at the same level as the two-trials rule but allows for replication success even if the original study is non-significant. The unweighted version requires a less restrictive level of significance at replication if the original study is already convincing which facilitates sample size reductions of up to 10%. Downweighting the original study accounts for possible bias and requires a more stringent significance level and larger samples sizes at replication. Data from four large-scale replication projects are used to illustrate and compare the proposed method with the two-trials rule, meta-analysis and Fisher's combination method.

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Leonhard Held, Samuel Pawel, Charlotte Micheloud. 2024-05-30. The assessment of replicability using the sum of p-values. https://arxiv.org/abs/2401.13615

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