Validity of population adjustment methods for disconnected networks of evidence

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, but requires that the RCT evidence forms a connected network of comparisons (the map of comparisons made in RCTs is a connected network). Covariates such as age, biomarker status, or disease severity 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. ML-NMR fits a model for individual-level treatment effects in studies where there is individual patient data, and then for each of the studies with aggregate-level data integrates the individual-level likelihood over the joint distribution of effect modifiers in each study to obtain an aggregate-level likelihood. This is achieved using copulae to approximate the joint distribution of effect modifiers and quasi-Monte Carlo integration to obtain the aggregate-level likelihood. Estimates can then be obtained in any population of interest (for example, the population represented by one of the included studies, or the UK population) 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. 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. The aim of this project is to extend the ML-NMR method for 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. This will include: (i) formulating extensions to the ML-NMR model for modelling absolute outcomes alongside relative effects, without introducing bias into the estimated relative treatment effects (ii) assessing the performance and properties of such approaches in a simulation study (iii) developing 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) developing 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.

The COMPASS Centre for Doctoral Training will have the following impact.

Doctoral Students Impact.

I1. Recruit and train over 55 students and provide them with a broad and comprehensive education in contemporary Computational Statistics & Data Science, leading to the award of a PhD. The training environment will be built around a set of multilevel cohorts: a variety of group sizes, within and across year cohort activities, within and across disciplinary boundaries with internal and external partners, where statistics and computation are the common focus, but remaining sensitive to disciplinary needs. Our novel doctoral training environment will powerfully impact on students, opening their eyes to not only a range of modern technical benefits and opportunities, but on the power of team-working with people from a range of backgrounds to solve the most important problems of the day. They will learn to apply their skills to achieve impact by collaborative working with internal and external partners, such as via our Rapid Response Teams, Policy Workshops & Statistical Clinics.

I2. As well as advanced training in computational statistics and data science, our students will be impacted by exposure to, and training in, important cognate topics such as ethics, responsible innovation, equality, diversity and inclusion, policy, effective communication and dissemination, enterprise, impact and consultancy skills. It is vital for our students to understand that their training will enable them to have a powerful impact on the wider world, so, e.g., AI algorithms they develop should not be discriminatory, and statistical methodologies should be reproducible, and statistical results accurately and comprehensibly communicated to the general public and policymakers.

I3. The students will gain experience via collaborations with academic partners within the University in cognate disciplines, and a wide range of external industrial & government partners. The students will be impacted by the structured training programmes of the UK Academy of Postgraduate Training in Statistics, the Bristol Doctoral College, the Jean Golding Institute, the Alan Turing Institute and the Heilbronn Institute for Mathematical Sciences, which will be integrated into our programme.

I4. Having received an excellent training, the students will then impact powerfully on the world in their future fruitful careers, spreading excellence.

Impact on our Partners & ourselves.

I5. Direct impacts will be achieved by students engaging with, and working on projects with, our academic partners, with discipline-specific problems arising in engineering, education, medicine, economics, earth sciences, life sciences and geographical sciences, and our external partners Adarga, the Atomic Weapons Establishment, CheckRisk, EDF, GCHQ, GSK, the Office for National Statistics, Sciex, Shell UK, Trainline and the UK Space Agency. The students will demonstrate a wide range of innovation with these partners, will attract engagement from new partners, and often provide attractive future employment matches for students and partners alike.

Wider Societal Impact

I6. COMPASS will greatly benefit the UK by providing over 55 highly trained PhD graduates in an area that is known to be suffering from extreme, well-known, shortages in the people pipeline nationally. COMPASS CDT graduates will be equipped for jobs in sectors of high economic value and national priority, including data science, analytics, pharmaceuticals, security, energy, communications, government, and indeed all research labs that deal with data. Through their training, they will enable these organisations to make well-informed and statistically principled decisions that will allow them to maximise their international competitiveness and contribution to societal well-being. COMPASS will also impact positively on the wider student community, both now and sustainably into the future.