Hierarchical Bayes Approach to Estimate the Treatment Effect for Randomized Controlled Trials

One important issue in Bayesian estimation is the determination of an effective informative prior. In hierarchical Bayes models, the uncertainty of hyperparameters in a prior can be further modeled via their own priors, namely, hyper priors. This study introduces a framework to construct hyper priors for both the mean and the variance hyperparameters for estimating the treatment effect in a two-group randomized controlled trial. Assuming a random sample of treatment effect sizes is obtained from past studies, the hyper priors can be constructed based on the sampling distributions of the effect size mean and precision. The performance of the hierarchical Bayes approach was compared with the empirical Bayes approach (hyperparameters are fixed values or point estimates) and the ordinary least squares (OLS) method via simulation. The design factors for data generation included the sample treatment effect size, treatment/control group size ratio, and sample size. Each generated data set was analyzed using the hierarchical Bayes approach with three hyper priors, the empirical Bayes approach with twelve priors (including correct and inaccurate priors), and the OLS method. Results indicated that the proposed hierarchical Bayes approach generally outperformed the empirical Bayes approach and the OLS method, especially with small samples. When more sample effect sizes were available, the treatment effect was estimated more accurately regardless of the sample sizes. Practical implications and future research directions are discussed.