Network meta-analysis involves the aggregation of study results in order to contrast the effects of different treatments for a common condition. While standard meta-analysis only summarizes over one pair of treatment contrasts, network meta-analysis can combine a multitude of different treatments.
In this article, we define a nonparametric "effect of interest" in a network meta-analysis over heterogeneous underlying populations. We then develop a set of restrictions that allow for estimation of this effect. We propose several estimators and compare their realistic small-sample performance in a simulation study. Finally, we demonstrate this approach in a real data example to evaluate the relative effectiveness of antibiotics on methicillin-resistant Staphylococcus aureus (MRSA) infection.