# A matrix-based method of moments for fitting multivariate network meta-analysis models with multiple outcomes and random inconsistency effects

## TL;DR

This paper introduces a new multivariate network meta-analysis model that incorporates multiple outcomes and treatments, allowing for the estimation of heterogeneity and inconsistency effects within a unified framework.

## Contribution

It extends existing univariate models to a multivariate network setting and provides an estimation procedure accommodating both heterogeneity and inconsistency.

## Key findings

- Effective estimation of heterogeneity and inconsistency parameters.
- Application to real medical data demonstrates model utility.
- Extension of DerSimonian and Laird method to multivariate network meta-analysis.

## Abstract

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.