Characterization of a credibility index

In recent years, the role of the p-value in applied research has been heavily scrutinized. Several new proposals have been put forward from a Bayesian viewpoint, including the analysis of credibility. By using the reverse Bayes theorem, and reasoning in terms of subverting the significance or the non-significance denoted by the p-value, this analysis provides the credibility, in a Bayesian sense, of an experimental result. We discuss a normalized indicator of credibility, namely (Formula presented.), a variant of the index (Formula presented.) (Quatto et al. J. Biopharm. Stat. 32, 308–329, 2022). This can be used to assess the degree of credibility of experimental results and can also be compared with a fixed threshold. The index is extended to the case of one-sided hypotheses. A simulation study is conducted to empirically assess the behavior of the index (Formula presented.). Two illustrative examples in the contexts of pharmacotherapy for COVID-19 and heart failure are presented. We then propose adopting the credibility index for meta-analyses, in which it can provide a suitable diagnostic value for modeling fixed and random effects.