A Bayesian dose–response meta-analysis model: A simulations study and application

Dose–response models express the effect of different dose or exposure levels on a specific outcome. In meta-analysis, where aggregated-level data is available, dose–response evidence is synthesized using either one-stage or two-stage models in a frequentist setting. We propose a hierarchical dose–response model implemented in a Bayesian framework. We develop our model assuming normal or binomial likelihood and accounting for exposures grouped in clusters. To allow maximum flexibility, the dose–response association is modelled using restricted cubic splines. We implement these models in R using JAGS and we compare our approach to the one-stage dose–response meta-analysis model in a simulation study. We found that the Bayesian dose–response model with binomial likelihood has lower bias than the Bayesian model with normal likelihood and the frequentist one-stage model when studies have small sample size. When the true underlying shape is log–log or half-sigmoid, the performance of all models depends on choosing an appropriate location for the knots. In all other examined situations, all models perform very well and give practically identical results. We also re-analyze the data from 60 randomized controlled trials (15,984 participants) examining the efficacy (response) of various doses of serotonin-specific reuptake inhibitor (SSRI) antidepressant drugs. All models suggest that the dose–response curve increases between zero dose and 30–40 mg of fluoxetine-equivalent dose, and thereafter shows small decline. We draw the same conclusion when we take into account the fact that five different antidepressants have been studied in the included trials. We show that implementation of the hierarchical model in Bayesian framework has similar performance to, but overcomes some of the limitations of the frequentist approach and offers maximum flexibility to accommodate features of the data.