Concept Architecture
Concept
Theoretically, Mixed Treatment Comparison (MTC) is a statistical evidence synthesis method that simultaneously combines direct and indirect evidence to estimate the relative effectiveness of multiple competing interventions. It extends conventional pairwise meta-analysis by analysing an entire network of treatment comparisons rather than isolated pairs of interventions. The method exists to estimate treatment effects for comparisons lacking direct head-to-head trials while improving precision through integration of all available evidence.
Mathematically, mixed treatment comparison is based on a connected treatment network in which relative treatment effects are estimated under consistency assumptions. The statistical framework simultaneously models direct and indirect evidence using either Bayesian or frequentist methods. Treatment effects are estimated relative to a reference intervention while preserving the correlation structure among comparisons within the evidence network.
In practice, mixed treatment comparison is widely used in health technology assessment, comparative effectiveness research and reimbursement evaluation where multiple competing treatments are available. The resulting estimates allow comprehensive comparison and ranking of interventions and frequently provide the clinical effectiveness inputs for health economic models. Modern implementations are generally referred to as network meta-analysis, although mixed treatment comparison remains a recognised methodological term.
Purpose
Used to estimate comparative treatment effects across multiple interventions by combining direct and indirect evidence within a connected treatment network.
Mathematical Formulae
Primary Formula
Relative treatment effect:
dAB = dAC ? dBC
where:
- dAB = treatment effect for A versus B
- dAC = treatment effect for A versus common comparator C
- dBC = treatment effect for B versus common comparator C
Supporting Formulae
Random-effects model:
?? ~ N(d, ��)
Random-effects weight:
w? = 1 / (Var(???) + ��)
Consistency relationship:
dAB = dAC ? dBC
Related Mathematical Methods
- Network Meta-Analysis
- Bayesian Meta-Analysis
- Frequentist Meta-Analysis
- Bucher Adjusted Indirect Comparison
- Random-Effects Meta-Analysis
- Fixed Effect Meta-Analysis
- Consistency Assessment
- Meta-Regression
Example
Five biologic therapies for psoriasis have been compared through 24 randomised controlled trials, although not every pair of treatments has been evaluated directly. A mixed treatment comparison combines all direct and indirect evidence to estimate the relative effectiveness of every intervention. The resulting treatment estimates and ranking probabilities are subsequently used within a cost-effectiveness model to support reimbursement decisions.
Excel Implementation
| Function | Example Formula | Health Economics Application |
|---|---|---|
| SUMPRODUCT | =SUMPRODUCT(B2:B20,C2:C20)/SUM(B2:B20) | Calculate weighted treatment-effect estimates |
| SUM | =SUM(B2:B20) | Calculate total study weights |
| SQRT | =SQRT(A2+B2) | Calculate standard errors for indirect comparisons |
| EXP | =EXP(A2) | Convert pooled log estimates to odds ratios, hazard ratios or risk ratios |
| Solver | Objective: minimise model deviance | Estimate network treatment effects under consistency constraints |
VBA (Optional)
Automate preparation of treatment networks, generation of comparison matrices and export of evidence structures for mixed treatment comparison modelling.
Sources
- Lu G, Ades AE. Combination of Direct and Indirect Evidence in Mixed Treatment Comparisons. Statistics in Medicine. 2004.
- Dias S, Welton NJ, Sutton AJ, Ades AE. NICE Decision Support Unit Technical Support Documents: Evidence Synthesis for Decision Making.
- Caldwell DM, Ades AE, Higgins JPT. Simultaneous Comparison of Multiple Treatments: Combining Direct and Indirect Evidence. BMJ. 2005.
- NICE. Health Technology Evaluation Manual.
- ISPOR Good Practice Task Force Report on Network Meta-Analysis.
Related Concepts (2)
Library
Publications
3
Network Meta-Analysis for Decision Making — Dias, Ades, Welton, Jansen & Sutton, 1st Edition ed., 2018 (John Wiley & Sons)
The definitive text on network meta-analysis (mixed treatment comparisons) for decision making, presenting a coherent Bayesian framework (implemented in WinBUGS) for synthesising evidence across multiple treatments, including inconsistency, bias adjustment, and use in cost-effectiveness models.
BookView source →NICE DSU Technical Support Document 3: Heterogeneity — Subgroups, Meta-Regression, Bias and Bias-Adjustment — Dias, Sutton, Welton & Ades, TSD 3 ed., 2011 (NICE Decision Support Unit (University of Sheffield))
Guidance on handling heterogeneity in evidence synthesis through subgroup analysis and meta-regression, and on detecting and adjusting for bias (including small-study effects) in pairwise and network meta-analysis.
Interpreting Indirect Treatment Comparisons and Network Meta-Analysis for Health-Care Decision Making: ISPOR Task Force on Indirect Treatment Comparisons Good Research Practices, Part 1 — Jansen, Fleurence, Devine, Itzler, Barrett, Hawkins, Lee, Boersma, Annemans & Cappelleri, Vol. 14, No. 4 ed., 2011 (Value in Health)
The ISPOR good-practice guidance on interpreting indirect treatment comparisons, network and mixed treatment comparisons for decision making — terminology, assumptions, validity and how to critically appraise an ITC/NMA when head-to-head trial evidence is unavailable.
Journal ArticleView source →
Media
1
Introduction to Network Meta-Analysis (ISPOR Statistical Methods SIG) — Emma Hawe & Sofia Dias, 2-part webinar ed., 2023 (ISPOR)
A two-part ISPOR Special Interest Group webinar: an introduction to network meta-analysis by Emma Hawe, followed by special topics in NMA by Sofia Dias — core methods for indirect and mixed treatment comparison.
Webinar RecordingView source →
Frequently Asked Questions (6)
What is a mixed treatment comparison?
An earlier term for network meta-analysis, describing the statistical combination of direct and indirect evidence across a connected treatment network.
Source: Lu & Ades 2004
What does the term mixed treatment comparison describe?
Mixed treatment comparison is an earlier name for network meta-analysis, describing the same idea of combining direct and indirect evidence across a connected set of trials comparing several treatments. The word mixed captures its defining feature: it blends the two kinds of evidence, direct results from head-to-head trials and indirect ones inferred through shared comparators, into a single coherent analysis. The label has largely given way to network meta-analysis, but the method it names is the same. Blending both evidence types is what it denotes. Dias and colleagues (2013) describe this.
Source: Dias et al. 2013
How does a mixed treatment comparison work?
A mixed treatment comparison works by synthesising a connected network of trials, combining the direct evidence from head-to-head comparisons with indirect evidence derived through common comparators, within a single statistical model that estimates the relative effects of all the treatments simultaneously and coherently. It relies on the consistency of direct and indirect evidence and the transitivity of the network. So a mixed treatment comparison works by modelling the whole network of comparisons together, mixing direct and indirect evidence to produce a coherent set of relative effect estimates for all the treatments, which is the approach now generally termed network meta-analysis.
Source: Dias et al. 2013
Why is a mixed treatment comparison used?
A mixed treatment comparison is used to compare multiple treatments simultaneously when the evidence comes from a network of trials, many of which do not compare all treatments directly, so that combining direct and indirect evidence is needed to estimate all the relative effects. It allows treatments never compared head-to-head to be compared through the network and provides coherent estimates and rankings. So a mixed treatment comparison is used to synthesise evidence across multiple treatments efficiently, using the full network to compare treatments and inform decisions where direct evidence alone would be insufficient, particularly in health technology assessment.
Source: Lu & Ades 2004
How does a mixed treatment comparison relate to network meta-analysis?
A mixed treatment comparison relates to network meta-analysis as an earlier name for essentially the same method: both combine direct and indirect evidence across a connected network of trials to estimate the relative effects of multiple treatments simultaneously. The term network meta-analysis has become the more common usage, but mixed treatment comparison and network meta-analysis describe the same approach. So the two are largely synonymous, with mixed treatment comparison the older term emphasising the mixing of direct and indirect evidence, and network meta-analysis the now-standard term for synthesising a network of treatment comparisons.
Source: Lu & Ades 2004
What assumptions does a mixed treatment comparison require?
A mixed treatment comparison requires the network to be connected, so that all treatments are linked; the transitivity, or similarity, assumption, that the trials linked in the network are comparable in effect-modifying factors so that indirect evidence is valid; and consistency, that direct and indirect evidence for the same comparisons agree. Violations of transitivity produce inconsistency and unreliable estimates. So a mixed treatment comparison rests on connectivity, transitivity, and consistency, and these assumptions must be considered and checked, since they underpin the validity of combining direct and indirect evidence across the network to estimate the relative effects of the treatments.
Source: Dias et al. 2013
Trust Record
Verified by Dr Darrin Baines
British health economist
Professional identity: darrinbaines.org
Verification date: 3 Dec 2025
Content version: 1.0.0
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- Term code
- HE-ES-ESM-036
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