Bayesian statistics: a primer for perioperative medicine clinicians.

Bayesian methods offer an intuitive and coherent statistical framework for updating probabilistic beliefs by integrating prior knowledge-whether from existing data or expert consensus-with new evidence via likelihood functions to generate posterior probability distributions. This approach yields clinically meaningful outputs, such as credible intervals and probabilities of treatment benefit, and can incorporate thresholds relevant to practice, like the region of practical equivalence (ROPE). Recent advances in computation-including Markov chain Monte Carlo (MCMC) sampling, Hamiltonian Monte Carlo algorithms, and probabilistic programming languages like Stan and JAGS- have made Bayesian approaches feasible even for complex hierarchical models. In perioperative medicine, these methods are particularly valuable for (1) complementing trial results by quantifying clinically important effects in the context of statistically nonsignificant findings or modest probabilities of benefit despite statistical significance, (2) enhancing meta-analyses through coherent integration of heterogeneous studies and sparse data, and (3) enabling adaptive and platform trial designs through continuous evidence synthesis. The ability to incorporate informative priors can complement existing knowledge, especially in small-sample studies, which are common in perioperative medicine, where traditional approaches provide insufficient precision. Although concerns remain regarding subjectivity in prior specification, these are increasingly addressed through structured guidelines, benchmark priors, and comprehensive sensitivity analyses. Altogether, Bayesian methods provide a flexible and powerful alternative for generating actionable insights in complex clinical settings, including in perioperative care.