Statistical physics and complex networks in meta-analysis

In medical research, clinical trials are used to compare two or more treatments for a particular condition. By monitoring the health outcomes of participants assigned to the different treatment options, we can work out which are the most effective. Network meta-analysis (NMA) is a statistical method to combine the results of all the trials that have compared different treatments for the same condition. NMA makes use of 'indirect evidence' which is the idea that when two treatments, A and B, have not been compared in any trials, we can work out which is better using information from trials in which these treatments have been compared to some common third treatment, C. Essentially, if we know that A is more effective than C (from trials comparing A and C) and that C is more effective than B (from trials comparing B and C) then it follows that A is more effective than B. By analysing all relevant trials, NMA produces a coherent ranking of all the treatments. This makes efficient use of the data and increases the precision of the treatment effect estimates. NMA is therefore an important method for presenting evidence about competing treatment options.

A network graph is a mathematical structure representing a set of objects and connections between those objects. Typically, they are depicted as a collection of circles (nodes) connected by lines (edges). Networks can be used to represent a variety of systems including transport links, electrical circuits, social interactions, and ecosystems. The study of networks, or `network science', is a key part of many academic disciplines drawing on theories developed in statistical physics (the study of complex networks) and mathematics (graph theory).

In NMA, we can represent the collection of treatments and trials as a graph. Nodes represent treatments and edges are comparisons between treatments in trials. Despite this, there is currently little overlap between NMA research and other areas of network science.

This pioneering project aims to establish new analogies between NMA and other real-world systems studied in network science and statistical physics. It will exploit the wealth of knowledge in these disciplines to address open challenges in NMA. The project will also build collaboration between academics in medical statistics, statistical physics, and mathematics via the organization of a workshop to bring them together.

A particular challenge in NMA involves understanding how confident we can be in the results. This depends on how well the individual trials were conducted and whether they were done on an appropriate group of patients. This project aims to assess the influence of individual trials on the NMA and how robust the results are to trials that have limitations. Similar topics in other areas of network science include identifying critical routes in transport networks and predicting the robustness of electrical power grids to transmission line failures. By drawing similarities with other physical systems, this project will build on methods developed in network science to address questions of NMA robustness and to analyse the importance of individual trials.

Simulated data are widely used in statistics to examine how well statistical methods work. To examine whether NMA models work, we need to simulate NMA networks of treatments and trials. However, NMAs are difficult to simulate, especially when there are lots of treatments. Simulating graphs is an active topic in graph theory and statistical physics. This project will draw on this existing work to develop a method to simulate NMA networks that resemble those observed in real life. This will improve the efficiency of NMA simulations and allow researchers to simulate larger networks.