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### Abstract

Standard network meta-analysis (NMA) and indirect comparisons combine aggregate data (AgD) from multiple studies on treatments of interest, assuming that any effect modifiers are balanced across populations. We can relax this assumption if individual patient data (IPD) are available from all studies by fitting an IPD meta-regression. However, in many cases IPD are only available from a subset of the studies.

In the simplest scenario, IPD are available for an AB study but only AgD for an AC study. Methods such as Matching Adjusted Indirect Comparison (MAIC) and Simulated Treatment Comparison (STC) create a population-adjusted indirect comparison between treatments B and C using reweighting or regression adjustment respectively. However, the resulting comparison is only valid in the AC study population unless additional assumptions are made, and the methods cannot be extended beyond pairwise indirect comparisons to larger networks of treatments. Alternatively, approaches based on meta-regression can be used which are readily applicable to larger networks. However, these typically fit the same model at both the individual and aggregate level which incurs aggregation bias when a non-identity link function is used.

We propose a new method, Multilevel Network Meta-Regression, which extends the standard NMA framework. An individual level regression model is defined, and aggregate study data are fitted by integrating this model over the covariate distributions of the respective studies, avoiding aggregation bias. Since closed-form integration is often complex or even intractable, we provide a general numerical approach using Quasi-Monte Carlo integration. Correlation structures between covariates are accounted for using copulae. The method is efficient to compute, and generic code is available. Crucially for decision making, comparisons may be provided in any target population with a given covariate distribution, without the need for additional assumptions.

We illustrate the method using an example and compare the results to those obtained using current methods. Where heterogeneity may be explained by imbalance in effect modifiers between studies we achieve a similar fit to a random effects NMA, but uncertainty is substantially reduced, and the model is more interpretable.

Multilevel Network Meta-Regression is a flexible and general method for synthesising evidence from mixtures of individual and aggregate level data in networks of all sizes. The use of numerical integration allows for easy implementation regardless of model form or complexity. Decision making is aided by the production of effect estimates relevant to the decision target population.

In the simplest scenario, IPD are available for an AB study but only AgD for an AC study. Methods such as Matching Adjusted Indirect Comparison (MAIC) and Simulated Treatment Comparison (STC) create a population-adjusted indirect comparison between treatments B and C using reweighting or regression adjustment respectively. However, the resulting comparison is only valid in the AC study population unless additional assumptions are made, and the methods cannot be extended beyond pairwise indirect comparisons to larger networks of treatments. Alternatively, approaches based on meta-regression can be used which are readily applicable to larger networks. However, these typically fit the same model at both the individual and aggregate level which incurs aggregation bias when a non-identity link function is used.

We propose a new method, Multilevel Network Meta-Regression, which extends the standard NMA framework. An individual level regression model is defined, and aggregate study data are fitted by integrating this model over the covariate distributions of the respective studies, avoiding aggregation bias. Since closed-form integration is often complex or even intractable, we provide a general numerical approach using Quasi-Monte Carlo integration. Correlation structures between covariates are accounted for using copulae. The method is efficient to compute, and generic code is available. Crucially for decision making, comparisons may be provided in any target population with a given covariate distribution, without the need for additional assumptions.

We illustrate the method using an example and compare the results to those obtained using current methods. Where heterogeneity may be explained by imbalance in effect modifiers between studies we achieve a similar fit to a random effects NMA, but uncertainty is substantially reduced, and the model is more interpretable.

Multilevel Network Meta-Regression is a flexible and general method for synthesising evidence from mixtures of individual and aggregate level data in networks of all sizes. The use of numerical integration allows for easy implementation regardless of model form or complexity. Decision making is aided by the production of effect estimates relevant to the decision target population.

Original language | English |
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Publication status | Unpublished - 17 Jul 2018 |

Event | 13th Annual Meeting of the Society for Research Synthesis Methodology - M Shed, Bristol, United Kingdom Duration: 17 Jul 2018 → 19 Jul 2018 https://www.bristol.ac.uk/population-health-sciences/centres/cresyda/the-13th-annual-srsm-conference---bristol-2018/ |

### Conference

Conference | 13th Annual Meeting of the Society for Research Synthesis Methodology |
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Country | United Kingdom |

City | Bristol |

Period | 17/07/18 → 19/07/18 |

Internet address |

## Fingerprint Dive into the research topics of 'Multilevel meta-regression for population adjustment based on individual and aggregate level data'. Together they form a unique fingerprint.

## Projects

- 1 Finished

## No Pfizer: Calibration of multiple treatment comparisons using individual patient data

1/03/17 → 29/02/20

Project: Research

## Student Theses

## Calibration of Treatment Effects in Network Meta-Analysis using Individual Patient Data

Author: Phillippo, D. M., 28 Nov 2019Supervisor: Welton, N. (Supervisor) & Dias, S. (Supervisor)

Student thesis: Doctoral Thesis › Doctor of Philosophy (PhD)

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## Activities

- 1 Participation in conference

## 13th Annual Meeting of the Society for Research Synthesis Methodology

David M Phillippo (Speaker)

17 Jul 2018 → 19 Jul 2018

Activity: Participating in or organising an event types › Participation in conference

## Cite this

Phillippo, D., Dias, S., Ades, T., & Welton, N. (2018).

*Multilevel meta-regression for population adjustment based on individual and aggregate level data*. Abstract from 13th Annual Meeting of the Society for Research Synthesis Methodology, Bristol, United Kingdom.