Multiplicative interaction in network meta-analysis

Meta-analysis of a set of clinical trials is usually conducted using a linear predictor with additive effects representing treatments and trials. Additivity is a strong assumption. In this paper, we consider models for two or more treatments that involve multiplicative terms for interaction between treatment and trial. Multiplicative models provide information on the sensitivity of each treatment effect relative to the trial effect. In developing these models, we make use of a two-way analysis-of-variance approach to meta-analysis and consider fixed or random trial effects. It is shown using two examples that models with multiplicative terms may fit better than purely additive models and provide insight into the nature of the trial effect. We also show how to model inconsistency using multiplicative terms.