  Random-effects meta-analyses are very commonly used in medical statistics.
Recent methodological developments include multivariate (multiple outcomes) and
network (multiple treatments) meta-analysis. Here we provide a new model and
corresponding estimation procedure for multivariate network meta-analysis, so
that multiple outcomes and treatments can be included in a single analysis. Our
new multivariate model is a direct extension of a univariate model for network
meta-analysis that has recently been proposed. We allow two types of unknown
variance parameters in our model, which represent between-study heterogeneity
and inconsistency. Inconsistency arises when different forms of direct and
indirect evidence are not in agreement, even having taken between-study
heterogeneity into account. However the consistency assumption is often assumed
in practice and so we also explain how to fit a reduced model which makes this
assumption. Our estimation method extends several other commonly used methods
for meta-analysis, including the method proposed by DerSimonian and Laird
(1986). We investigate the use of our proposed methods in the context of a real
example.
