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Abstract
Standard network metaanalysis (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 metaregression. 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 populationadjusted 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 metaregression 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 nonidentity link function is used.
We propose a new method, Multilevel Network MetaRegression, 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 closedform integration is often complex or even intractable, we provide a general numerical approach using QuasiMonte 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 MetaRegression 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 populationadjusted 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 metaregression 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 nonidentity link function is used.
We propose a new method, Multilevel Network MetaRegression, 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 closedform integration is often complex or even intractable, we provide a general numerical approach using QuasiMonte 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 MetaRegression 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 

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/populationhealthsciences/centres/cresyda/the13thannualsrsmconferencebristol2018/ 
Conference
Conference  13th Annual Meeting of the Society for Research Synthesis Methodology 

Country/Territory  United Kingdom 
City  Bristol 
Period  17/07/18 → 19/07/18 
Internet address 
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Dive into the research topics of 'Multilevel metaregression 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 MetaAnalysis 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 2018Activity: Participating in or organising an event types › Participation in conference