Bayesian statistics for clinical research

Frequentist and Bayesian statistics represent two differing paradigms for the analysis of data. Frequentism became the dominant mode of statistical thinking in medical practice during the 20th century. The advent of modern computing has made Bayesian analysis increasingly accessible, enabling growing use of Bayesian methods in a range of disciplines, including medical research. Rather than conceiving of probability as the expected frequency of an event (purported to be measurable and objective), Bayesian thinking conceives of probability as a measure of strength of belief (an explicitly subjective concept). Bayesian analysis combines previous information (represented by a mathematical probability distribution, the prior) with information from the study (the likelihood function) to generate an updated probability distribution (the posterior) representing the information available for clinical decision making. Owing to its fundamentally different conception of probability, Bayesian statistics offers an intuitive, flexible, and informative approach that facilitates the design, analysis, and interpretation of clinical trials. In this Review, we provide a brief account of the philosophical and methodological differences between Bayesian and frequentist approaches and survey the use of Bayesian methods for the design and analysis of clinical research.