Statistical primer: an introduction into the principles of Bayesian statistical analyses in clinical trials

Trials in cardiac surgery are often hampered at the design level by small sample sizes and ethical considerations. The conventional analytical approach, combining frequentist statistics with null hypothesis significance testing, has known limitations and its associated P-values are often misinterpreted, leading to dichotomous conclusions of trial results. The Bayesian statistical framework may overcome these limitations through probabilistic reasoning and is subsequently introduced in this Primer. The Bayesian framework combines prior beliefs and currently obtained data (the likelihood), resulting in updated beliefs, also known as posterior distributions. These distributions subsequently facilitate probabilistic interpretations. Several previous cardiac surgery trials have been performed under a Bayesian framework and this Primer enhances the understanding of their basic concepts by linking results to graphical presentations. Furthermore, contemporary trials that were initially analysed under a frequentist framework, are re-analysed within a Bayesian framework to demonstrate several interpretative advantages.