Bayesian Analytical Methods in Cardiovascular Clinical Trials: Why, When, and How

Abstract

The Bayesian analytical framework is clinically intuitive, characterized by the incorporation of previous evidence into the analysis, and allowing an estimation treatment effects and their associated uncertainties. The application of Bayesian statistical inference is not new to the cardiovascular field, as illustrated by various recent randomized trials that applied a primary Bayesian analysis. Given the guideline-shaping character of trials, a thorough understanding of the concepts and technical details of Bayesian statistical methodology is of utmost importance to the modern practicing cardiovascular physician. Therefore, this Review aims to present a step-by-step guide to interpreting and performing a Bayesian (re-)analysis of cardiovascular clinical trials, while highlighting the main advantages of Bayesian inference for the clinical reader. After an introduction of the concepts of frequentist and Bayesian statistical inference and reasons to apply Bayesian methods, key steps for performing a Bayesian analysis are presented, including: the verification of the clinical appropriateness of the research question, the quality and completeness of the trial design, as well as the adequate elicitation of the prior (i.e., ones belief towards a certain treatment before the current evidence becomes available), identification of the likelihood, and their combination into a posterior distribution. Examination of this posterior distribution offers the possibility of not only determining the probability of treatment superiority, but also the probability of exceeding any chosen minimal clinically important difference. Multiple priors should be transparently prespecified, limiting post-hoc manipulations. Using this guide, three cardiovascular randomized controlled trials are re-analysed, demonstrating the clarity and versatility of Bayesian inference.