Introduction to Bayesian Statistics

Background: The analysis of a study with Bayesian statistics makes use of additional information to supplement the new study data. In this review, we explain the principles of the application of this method in clinical research. Methods: The concept of Bayesian statistics is introduced and explained with the aid of an illustrative example from a drug approval study. Its major aspects are discussed. The existing prior knowledge is formulated as a probability distribution of an odds ratio. Multiple scenarios are shown to demonstrate how a suitable prior distribution is determined and how it can affect the final result. Results: Bayesian statistics makes use of prior knowledge, e.g., the findings of earlier clinical trials, and combines the prior probability distribution with the findings of the current study for statistical analysis. The suitability and applicability of the prior knowledge in question must be assessed and the prior knowledge weighted accordingly, and any uncertainties must be taken into account in the analysis. The result that is derived is called the posterior distribution of the parameters of interest and is summarized in terms of point estimators and credibility intervals. In contrast to classical statistics, results of this type permit direct quantitative statements on the probability of parameter values and on the probabilities of the null and alternative hypotheses (in one-sided statistical tests). Conclusion: Combining the current study findings with prior knowledge can enable the more precise estimation of a treatment effect, or else lessen the number of subjects needed for a clinical trial. Central elements of Bayesian statistics are the selection and weighting of prior knowledge; subjective judgements must be made. Bayesian techniques require a precise description of the methods applied, meticulous study of the available literature, and experience in the mathematical representation of the results.