Using Bayesian Methods to Augment the Interpretation of Critical Care Trials An Overview of Theory and Example Reanalysis of the Alveolar Recruitment for Acute Respiratory Distress Syndrome Trial

Most randomized trials are designed and analyzed using frequentist statistical approaches such as null hypothesis testing and P values. Conceptually, P values are cumbersome to understand, as they provide evidence of data incompatibility with a null hypothesis (e.g., no clinical benefit) and not direct evidence of the alternative hypothesis (e.g., clinical benefit). This counterintuitive framework may contribute to the misinterpretation that the absence of evidence is equal to evidence of absence and may cause the discounting of potentially informative data. Bayesian methods provide an alternative, probabilistic interpretation of data. The reanalysis of completed trials using Bayesian methods is becoming increasingly common, particularly for trials with effect estimates that appear clinically significant despite P values above the traditional threshold of 0.05. Statistical inference using Bayesian methods produces a distribution of effect sizes that would be compatible with observed trial data, interpreted in the context of prior assumptions about an intervention (called "priors"). These priors are chosen by investigators to reflect existing beliefs and past empirical evidence regarding the effect of an intervention. By calculating the likelihood of clinical benefit, a Bayesian reanalysis can augment the interpretation of a trial. However, if priors are not defined a priori, there is a legitimate concern that priors could be constructed in a manner that produces biased results. Therefore, some standardization of priors for Bayesian reanalysis of clinical trials may be desirable for the critical care community. In this Critical Care Perspective, we discuss both frequentist and Bayesian approaches to clinical trial analysis, introduce a framework that researchers can use to select priors for a Bayesian reanalysis, and demonstrate how to apply our proposal by conducting a novel Bayesian trial reanalysis.