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4-year PhD Studentship: Validity of population adjustment methods for disconnected networks of evidence

   Faculty of Health Sciences

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  Dr N Welton, Dr D Phillippo  No more applications being accepted  Self-Funded PhD Students Only

About the Project

Network meta-analysis (NMA) is a method to pool published summary treatment effects from randomised controlled trials (RCTs) to obtain estimates of relative treatment effects between multiple treatments. NMA is routinely used to inform decisions as to which treatments are effective or cost-effective. Covariates can be classified into (i) those that interact with relative treatment effects (Effect Modifiers), and (ii) those that predict outcomes but don’t interact with treatment effects (Prognostic Factors). NMA assumes that, if effect modifiers are present, their distribution is the same, or similar, in all the included trials. However, this may not hold. Recently a multi-level network meta-regression (ML-NMR) method has been developed that relaxes this assumption, as long as individual patient data is available from one or more RCTs. Estimates can be obtained in any population of interest by integrating over the relevant joint distribution of effect modifiers. To date, the method has only been developed for the case where networks of evidence are connected (there is a path of RCT evidence joining any two treatments in the network). However, it is becoming more common that health care policy makers are confronted with disconnected networks of evidence which may include single-arm (non-randomised) studies.

Aims and Objectives

The aim of this project is to extend the ML-NMR method to disconnected networks of evidence for a range of likelihoods, including likelihoods for survival outcomes, and to explore methods to assess the validity of the ML-NMR method in the context of disconnected networks of evidence.


ML-NMR uses copulae to approximate the joint distribution of effect modifiers and quasi-Monte Carlo integration to obtain the aggregate-level likelihood. Population adjustment with disconnected networks of evidence requires that not only the effect modifying covariates are accounted for, but also all prognostic factors since absolute outcomes rather than relative effects are modelled. This project will: (i) formulate extensions to ML-NMR to model absolute outcomes alongside relative effects, whilst minimising bias in the estimated relative treatment effects (ii) assess the performance and properties of such approaches in a simulation study (iii) develop in-sample methods for assessing the validity of assumptions, such as cross-validation to estimate the proportion of variation explained by the model so that any unexplained variation will be largely due to missing prognostic variables or effect modifiers that have not been accounted for; and (iv) develop out-of-sample methods that aim to estimate prediction error by identifying external studies in a given population and comparing the absolute outcomes predicted by ML-NMR in this external population with the observed outcomes. Methods will be developed using the STAN Bayesian statistics package in R, and the methods developed will be incorporated into the R package that performs ML-NMR.


Population adjustment, Bayesian statistics, Evidence synthesis, Health Technology Assessment, Network Meta-Analysis, Indirect Comparisons

How to apply for this project

This project will be based in Bristol Medical School - Population Health Sciences in the Faculty of Health Sciences at the University of Bristol.

Please visit the Faculty of Health Sciences website for details of how to apply

Funding Notes

This project is open for University of Bristol PGR scholarship applications (closing date 25th February 2022)
The University of Bristol PGR scholarship pays tuition fees and a maintenance stipend (at the minimum UKRI rate) for the duration of a PhD (typically three years but can be up to four years).


Phillippo DM, Ades AE, Dias S, Palmer S, Abrams K, Welton NJ. Methods for population-adjusted indirect comparisons in health technology appraisal. Medical Decision Making. 2018. 38:200-211.
Phillippo DM, Dias S, Ades AE, Belger M, Brnabic A, Schacht A, Saure D, Kadziola S, Welton NJ. Multilevel Network Meta-Regression for population-adjusted treatment comparisons. JRSSA 2020. 183:1189-1210
Phillippo DM, Dias S, Ades AE, Welton NJ. Assessing the performance of population adjustment methods for anchored indirect comparisons: A simulation study. Statistics in Medicine. 2020 39: 4885-4911
Dias S, Ades AE, Welton NJ, Jansen JP, Sutton AJ. Network Meta-analysis for Comparative Effectiveness Research. Wiley. 2018.
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