Network meta-analysis and random walks

Annabel Davies, Tobias Galla, Theodoros Papakonstantinou, Adriani Nikolapoulou, Gerta Ruecker

Research output: Contribution to journalArticlepeer-review


Network meta-analysis (NMA) is a central tool for evidence synthesis in clinical research. The results of an NMA depend critically on the quality of evidence being pooled. In assessing the validity of an NMA, it is therefore important to know the proportion contributions of each direct treatment comparison to each network treatment effect. The construction of proportion contributions is based on the observation that each row of the hat matrix represents a so-called “evidence flow network” for each treatment comparison. However, the existing algorithm used to calculate these values is associated with ambiguity according to the selection of paths. In this article, we present a novel analogy between NMA and random walks. We use this analogy to derive closed-form expressions for the proportion contributions. A random walk on a graph is a stochastic process that describes a succession of random “hops” between vertices which are connected by an edge. The weight of an edge relates to the probability that the walker moves along that edge. We use the graph representation of NMA to construct the transition matrix for a random walk on the network of evidence. We show that the net number of times a walker crosses each edge of the network is related to the evidence flow network. By then defining a random walk on the directed evidence flow network, we derive analytically the matrix of proportion contributions. The random-walk approach has none of the associated ambiguity of the existing algorithm.
Original languageEnglish
Pages (from-to)2091-2114
Number of pages24
JournalStat Med
Issue number12
Early online date16 Mar 2022
Publication statusPublished - 30 May 2022


  • electrical networks
  • evidence flow
  • network meta-analysis
  • proportion contribution
  • random walks
  • statistical mechanics


Dive into the research topics of 'Network meta-analysis and random walks'. Together they form a unique fingerprint.

Cite this