Some important research questions require the ability to find evidence for two conditions being practically equivalent. This is impossible to accomplish within the traditional frequentist null hypothesis significance testing framework; hence, other methodologies must be utilized. We explain and illustrate three approaches for finding evidence for equivalence: The frequentist two one-sided tests procedure, the Bayesian highest density interval region of practical equivalence procedure, and the Bayes factor interval null procedure. We compare the classification performances of these three approaches for various plausible scenarios. The results indicate that the Bayes factor interval null approach compares favorably to the other two approaches in terms of statistical power. Critically, compared with the Bayes factor interval null procedure, the two one-sided tests and the highest density interval region of practical equivalence procedures have limited discrimination capabilities when the sample size is relatively small: Specifically, in order to be practically useful, these two methods generally require over 250 cases within each condition when rather large equivalence margins of approximately .2 or .3 are used; for smaller equivalence margins even more cases are required. Because of these results, we recommend that researchers rely more on the Bayes factor interval null approach for quantifying evidence for equivalence, especially for studies that are constrained on sample size.

The last 25 years have shown a steady increase in attention for the Bayes factor as a tool for hypothesis evaluation and model selection. The present review highlights the potential of the Bayes factor in psychological research. We discuss six types of applications: Bayesian evaluation of point null, interval, and informative hypotheses, Bayesian evidence synthesis, Bayesian variable selection and model Daniel W. Heck https://orcid.

Some important research questions require the ability to find evidence for two conditions being practically equivalent. This is impossible to accomplish within the traditional frequentist null hypothesis significance testing framework; hence, other methodologies must be utilized. We explain and illustrate three approaches for finding evidence for equivalence: The frequentist two one-sided tests procedure, the Bayesian highest density interval region of practical equivalence procedure, and the Bayes factor interval null procedure. We compare the classification performances of these three approaches for various plausible scenarios. The results indicate that the Bayes factor interval null approach compares favorably to the other two approaches in terms of statistical power. Critically, compared to the Bayes factor interval null procedure, the two one-sided tests and the highest density interval region of practical equivalence procedures have limited discrimination capabilities when the sample size is relatively small: specifically, in order to be practically useful, these two methods generally require over 250 cases within each condition when rather large equivalence margins of approximately 0.2 or 0.3 are used; for smaller equivalence margins even more cases are required. Because of these results, we recommend that researchers rely more on the Bayes factor interval null approach for quantifying evidence for equivalence, especially for studies that are constrained on sample size.

The use of Cox proportional hazards regression to analyze time-to-event data is ubiquitous in biomedical research. Typically, the frequentist framework is used to draw conclusions about whether hazards are different between patients in an experimental and a control condition. We offer a procedure to calculate Bayes factors for simple Cox models, both for the scenario where the full data is available and for the scenario where only summary statistics are available. The procedure is implemented in our "baymedr" R package. The usage of Bayes factors remedies some shortcomings of frequentist inference and has the potential to save scarce resources.

Background Following testing in clinical trials, the use of remdesivir for treatment of COVID-19 has been authorized for use in parts of the world, including the USA and Europe. Early authorizations were largely based on results from two clinical trials. A third study published by Wang et al. was underpowered and deemed inconclusive. Although regulators have shown an interest in interpreting the Wang et al. study, under a frequentist framework it is difficult to determine if the non-significant finding was caused by a lack of power or by the absence of an effect. Bayesian hypothesis testing does allow for quantification of evidence in favor of the absence of an effect. Findings Results of our Bayesian reanalysis of the three trials show ambiguous evidence for the primary outcome of clinical improvement and moderate evidence against the secondary outcome of decreased mortality rate. Additional analyses of three studies published after initial marketing approval support these findings. Conclusions We recommend that regulatory bodies take all available evidence into account for endorsement decisions. A Bayesian approach can be beneficial, in particular in case of statistically non-significant results. This is especially pressing when limited clinical efficacy data is available.