[Bayesian statistics and its applications in medical research]

Bayesian statistics dates back to the 18th century. Its development was once hindered by computational complexity. However, as computing methods and technologies have advanced, Bayesian statistics has demonstrated its advantages across many research scenarios, including small-population studies, information borrowing, complex and innovative designs, and dynamic decision-making. Recently, regulatory authorities in China, the United States, and Europe have issued guidelines, acknowledging the role of Bayesian statistics in new drug research and development. This paper introduced the basic concepts, theoretical foundations, and inference frameworks of Bayesian statistics. Bayesian statistics uses Bayes' theorem to combine prior information with sample data to derive the posterior distribution, which serves as the basis for Bayesian inference and decision-making. Unlike the traditional frequentist approach, which focuses on "analyzing only the data from the current study", the Bayesian approach aims to "integrate and use previous information together with current data," thereby forming a statistical decision-making approach that continuously accumulates and makes dynamic decision-making. The paper also discussed the strengths and weaknesses of the frequentist and the Bayesian, as well as their respective strengths and weaknesses. The authors note that the two inference frameworks will be used in a complementary manner in the future, and Bayesian methods play an invaluable role in advancing innovative medical research.