Reassessing the Statistical Evidence in Clinical Trials with Extended Approximate Objective Bayes Factors

Bayesian hypothesis testing using the Bayes factor is an alternative to hypothesis testing based on the p-Value. They are especially useful if one considers the p-postulate, which suggests that equal p-values, irrespective of sample size, should represent equal evidence against a null hypothesis, false. Bayes factors can, however, be computationally intensive and require a prior distribution. We define an extension of Jeffrey's approximate objective Bayes factor (eJAB) based on a generalization of the unit information prior. Its computation requires nothing more than the p-value and the sample size and it provides a measure of evidence that allows one to interpret the p-value in light of the associated sample size through the lens of an approximate Bayes factor corresponding to an objective prior. We apply eJAB to reexamine the evidence from 71,130 clinical trial findings with particular attention to contradictions between Bayes factors and NHST—i.e., instances of the Jeffreys–Lindley paradox (JLP). Our findings reflect increasing evidence in the literature of problematic clinical trial design and results.

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