  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 present the model
with cubic dose-response shapes for a dichotomous outcome and take into account
heterogeneity due to variability in the dose-response shape. We develop our
Bayesian model assuming normal or binomial likelihood and accounting for
exposures grouped in clusters. 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 slightly lower bias than the Bayesian model with the normal
likelihood and the frequentist one-stage model. However, all three 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 antidepressant drugs. All models
suggest that the dose-response curve increases between zero dose and 40 mg of
fluoxetine-equivalent dose, and thereafter is constant. 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
approaches and offers maximum flexibility to accommodate features of the data.
