Priors on Between-Study Heterogeneity in Bayesian Meta-Analysis Models: A Simulation Study Using Hamiltonian Monte Carlo Sampling

OBJECTIVES: Meta-analysis (MA) plays a crucial role in health economic and outcomes research. Random effects models in MA allow for heterogeneity in treatment effects between studies. In a Bayesian framework, prior beliefs are assigned to model parameters, including the between-study heterogeneity, often using non-informative priors. Previous studies have explored use of different heterogeneity priors on MA results using Gibbs sampling. Hamiltonian Monte Carlo (HMC) sampling is used increasingly more often in recent years. This study updates previous research by using HMC and an updated set of priors.

METHODS: A case study and a simulation study were utilized to evaluate MA outcomes and model diagnostics. Fourteen priors, varying in distribution and level of information, were tested, along with centred and non-centred parameterizations of the models. One thousand simulated dichotomous outcome datasets, with differing true between-study standard deviation (SD) and number of studies, were evaluated. Results were compared by assessing bias, coverage, Deviance Information Criterion (DIC) and convergence issues.

RESULTS: The case study demonstrated that centred model parameterization and priors with zero density at plausible values may lead to biased results. Among simulation scenarios, random effects models with a gamma prior on precision and an informative prior on variance were most likely to be favoured over fixed effect models (lowest DIC). Convergence issues were more prominent when using the improper uniform prior and the non-informative normal prior on SD, especially in datasets with fewer studies and higher true SD.

CONCLUSIONS: Selection of an appropriate between-study heterogeneity prior is crucial as it impacts the posterior treatment effect, particularly when dealing with limited data. While informative priors are desirable, caution must be exercised to avoid bias. In future studies, adopting non-centred model parameterization as standard practice is advisable over centred parameterization. HMC warnings are helpful and show that priors with zero density at plausible values should be avoided.