Assessing the consistency assumption underlying network meta-analysis in systematic reviews


Systematic reviews of trial evidence are often carried out to summarise and compare the effectiveness of treatments for a specific disease. Meta-analysis (MA) is a statistical method used to combine trial results to provide a quantitative measure of treatment effectiveness. Conventional pairwise MA is used to compare two treatments in a single analysis, while network meta-analysis (NMA) is used to compare multiple treatments simultaneously.

The assumption of consistency of direct and indirect evidence underlies NMA. The assumption is satisfied when treatment effects estimated by direct evidence agree with those from indirect evidence. For instance, direct evidence for the treatment effect of treatment B versus treatment A is from trials that allocate both treatments A and B, and indirect evidence could be from trials of A vs treatment C and trials of B vs C. If the consistency assumption is violated, NMA results may be unreliable; however, little is known about when results become unreliable and the extent of the unreliability. Various methods exist to assess the consistency assumption, but these methods are considered to have low power to detect inconsistency, and there is no single well- established method. Further, most methods can only be applied when both direct and indirect evidence exist for the same treatment comparison. Where both direct and indirect evidence does not exist, NMA results are often used inappropriately to draw clinical conclusions.

Aims and Objectives

The aim is to identify and review current practice in terms of consistency assessment in NMAs, evaluate the performance of methods used to detect inconsistency, and to develop guidance.


This is an excellent opportunity for a student to develop strong statistical and quantitative research skills while training with leading experts in evidence synthesis.

The project will be tailored to suit the student’s strengths and interests.

The student will systematically review current practice in terms of use of methods, potential for application of methods, and findings regarding consistency assessments. The methods used to assess consistency will be compared. If appropriate, methods and software will be extended to construct and calculate user-friendly results. User-friendly guidance will be produced and shared with reviewers and healthcare decision makers.


This project will be based in the Department of Health Data Science at the University of Liverpool. To apply for the position, please email attaching a covering letter, CV and details of 2 referees.


Open to students worldwide

Funding information

Self-funded project

This is a self-funded PhD.



  1. Donegan, S., Williamson, P., D'Alessandro, U. and Tudur Smith, C. (2013), Assessing key assumptions of network meta-analysis: a review of methods. Res. Syn. Meth., 4: 291-323.
  2. Donegan S, Williamson P, Gamble C, Tudur-Smith C. Indirect comparisons: a review of reporting and methodological quality. PLoS One. 2010 Nov 10;5(11):e11054. doi: 10.1371/journal.pone.0011054. PMID: 21085712; PMCID: PMC2978085.