Background:
Treatments in network meta-analysis (NMA) can be complex interventions, for example, some treatments may be combinations of others or of common components. In standard NMA, all existing (single or combined) treatments are different nodes in the network.

Objectives:
To develop a model to investigate the effects of treatment combinations as well as single components.

Methods:
We propose a NMA approach that models effects of treatment combinations as additive sums of their components. All parameters are estimated using weighted least-squares regression. The model's fit is compared to that of the standard NMA model using a simple Chi-square test. The model can also be applied to disconnected networks, if the composite treatments in the sub-networks contain at least one common component.

Results:
The model has been implemented in the frequentist R package netmeta. We present a successful application to a NMA of treatments for depression in primary care.

Conclusions:
The additive NMA model is a useful addition to the toolbox of statistical methods for NMA.

Patient or healthcare consumer involvement:
Not applicable.