Bayesian and Frequentist Approaches in Utilizing Historical Data

Incorporating historical data in current studies becomes a crucial method due to the need to increase statistical power and reduce costs. Yet, historical data present challenges such as limited sample sizes and a lack of guidelines for method suitability based on their types. This paper provides a comprehensive review of Bayesian, Frequentist, and empirical Bayes approaches for integrating historical data into research. The Bayesian approach incorporates prior knowledge through formal distributions, offering flexibility but introducing subjectivity. The Frequentist approach treats historical data as additional samples, prioritizing objectivity but requiring larger samples and homogeneity assumptions. Empirical Bayes, serving as a hybrid approach, estimates priors from data to strike a balance between flexibility and objectivity. The review compares these approaches in terms of philosophical foundations, data requirements, flexibility, computational demand, and application domains, concluding that method selection should be guided by data characteristics, prior knowledge availability, and practical constraints. Furthermore, this review proposes practical guidelines for researchers choosing among the three approaches.