  Modeling dose-response relationships of drugs is essential to understanding
their effect on patient outcomes under realistic circumstances. While
intention-to-treat analyses of clinical trials provide the effect of assignment
to a particular drug and dose, they do not capture observed exposure after
factoring in non-adherence and dropout. We develop Bayesian methods to flexibly
model dose-response relationships of binary outcomes with continuous treatment,
allowing for treatment effect heterogeneity and a non-linear response surface.
We use a hierarchical framework for meta-analysis with the explicit goal of
combining information from multiple trials while accounting for heterogeneity.
In an application, we examine the risk of excessive weight gain for patients
with schizophrenia treated with the second generation antipsychotics
paliperidone, risperidone, or olanzapine in 14 clinical trials. Averaging over
the sample population, we found that olanzapine contributed to a 15.6% (95%
CrI: 6.7, 27.1) excess risk of weight gain at a 500mg cumulative dose.
Paliperidone conferred a 3.2% (95% CrI: 1.5, 5.2) and risperidone a 14.9% (95%
CrI: 0.0, 38.7) excess risk at 500mg olanzapine equivalent cumulative doses.
Blacks had an additional 6.8% (95% CrI: 1.0, 12.4) risk of weight gain over
non-blacks at 1000mg olanzapine equivalent cumulative doses of paliperidone.
