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Indirect Comparison

A method estimating the relative effect of two treatments never studied against each other directly, using their separate effects versus a shared comparator.

Last reviewedDarrin Baines IP Ltd

Concept Architecture

Concept

Theoretically, Indirect Comparison is a comparative evidence synthesis method used to estimate the relative effectiveness of two interventions that have not been compared directly within the same randomised controlled trial. It relies on a common comparator and the principle of transitivity, whereby treatment effects can be inferred through shared evidence. Indirect comparison exists to support comparative effectiveness assessment when head-to-head evidence is unavailable.

Mathematically, indirect comparison estimates the relative treatment effect by combining effect estimates from studies sharing a common comparator. The most widely recognised approach is the Bucher adjusted indirect comparison, which derives the indirect treatment effect as the difference between treatment effects estimated against the common comparator. Variance is propagated from the contributing comparisons to quantify uncertainty.

In practice, indirect comparison is applied within systematic reviews, health technology assessment and comparative effectiveness research. It forms the foundation of network meta-analysis and is commonly used to estimate relative treatment effects required for economic evaluation when direct comparative trials are lacking. The validity of the results depends on the assumptions of similarity, homogeneity and transitivity across the contributing studies.


Purpose

Used to estimate comparative treatment effects in the absence of direct head-to-head trials by combining evidence from studies with a shared comparator.


Mathematical Formulae

Primary Formula

Bucher adjusted indirect comparison:

??AB = ??AC ? ??BC

where:

  • ??AB = indirect treatment effect for A versus B
  • ??AC = treatment effect for A versus common comparator C
  • ??BC = treatment effect for B versus common comparator C

Supporting Formulae

Variance of indirect estimate:

Var(??AB) = Var(??AC) + Var(??BC)

Standard error:

SE(??AB) = �Var(??AB)

95% confidence interval:

??AB � 1.96 ? SE(??AB)

Related Mathematical Methods

  • Bucher Adjusted Indirect Comparison
  • Network Meta-Analysis
  • Frequentist Meta-Analysis
  • Bayesian Network Meta-Analysis
  • Random-Effects Meta-Analysis
  • Fixed Effect Meta-Analysis

Example

Two biologic therapies for rheumatoid arthritis have each been compared with placebo but not directly with one another. The estimated log odds ratio for Treatment A versus placebo is ?0.62, while the estimate for Treatment B versus placebo is ?0.38. The indirect comparison gives a log odds ratio of ?0.24 for Treatment A versus Treatment B, indicating superior effectiveness for Treatment A, subject to the assumptions underlying indirect comparison.


Excel Implementation

FunctionExample FormulaHealth Economics Application
SUM=A2-B2Calculate the indirect treatment effect using the Bucher method
SQRT=SQRT(C2+D2)Calculate the standard error from component variances
NORM.S.INV=NORM.S.INV(0.975)Obtain the critical value for a 95% confidence interval
EXP=EXP(A2)Convert pooled log estimates into odds ratios, hazard ratios or risk ratios

VBA (Optional)

Automate Bucher indirect comparisons across multiple treatment networks and generate comparative effectiveness estimates with confidence intervals.


Sources

  • Bucher HC, Guyatt GH, Griffith LE, Walter SD. The Results of Direct and Indirect Treatment Comparisons in Meta-Analysis of Randomised Controlled Trials. Journal of Clinical Epidemiology. 1997.
  • Dias S, Welton NJ, Sutton AJ, Ades AE. NICE Decision Support Unit Technical Support Documents: Evidence Synthesis for Decision Making.
  • Higgins JPT, Thomas J, Chandler J, et al. Cochrane Handbook for Systematic Reviews of Interventions.
  • NICE. Health Technology Evaluation Manual.
  • ISPOR Good Practice Reports for Indirect Treatment Comparisons and Network Meta-Analysis.

Library

Publications

1
  • Book

    Introduction to Meta-Analysis — Borenstein, Hedges, Higgins & Rothstein, 2nd Edition ed., 2021 (John Wiley & Sons)

    A clear, applied introduction to meta-analysis — computing effect sizes, fixed- and random-effects models, heterogeneity, subgroup analysis, meta-regression, and publication bias — written for readers across disciplines.

Frequently Asked Questions (6)

  • What is an indirect comparison?

    A method estimating the relative effect of two treatments never studied against each other directly, using their separate effects versus a shared comparator.

    Source: Bucher et al. 1997

  • How does an indirect comparison estimate an effect never trialled directly?

    An indirect comparison estimates the relative effect of two treatments that were never trialled against each other by using their results against a shared comparator. If one treatment beat placebo by a certain margin and another beat the same placebo by a different margin, the gap between those margins gives an estimate of how the two would compare directly. This works only if the trials are similar enough that the shared comparator behaves the same way in each. Bridging through a common reference is its logic. Dias and colleagues (2013) describe this method.

    Source: Dias et al. 2013

  • How does an indirect comparison work?

    An indirect comparison works by using the results of trials that share a common comparator: the effect of treatment A versus the comparator and the effect of treatment B versus the comparator are combined, preserving the randomisation within each trial, to estimate the relative effect of A versus B. The Bucher method does this for a single common comparator. The estimate relies on the trials being similar enough that the comparison is valid. So an indirect comparison combines the effects of two treatments against a shared comparator to infer their relative effect, using the common comparator as the link between the otherwise unconnected treatments.

    Source: Bucher et al. 1997

  • When is an indirect comparison used?

    An indirect comparison is used when direct head-to-head evidence between two treatments is unavailable but each has been compared with a common comparator, which is common because treatments are often tested against placebo or standard care rather than against each other. It allows their relative effectiveness to be estimated to inform decisions between them. Indirect comparison also underlies network meta-analysis. So an indirect comparison is applied to fill the frequent gap left by the absence of head-to-head trials, providing an estimate of the relative effect of two treatments through their shared comparator when direct evidence is lacking.

    Source: Dias et al. 2013

  • What assumptions does an indirect comparison require?

    An indirect comparison requires the assumption of similarity, or transitivity: that the trials linked through the common comparator are sufficiently alike in their populations, methods, and the behaviour of the comparator, so that the indirect comparison validly reflects the true relative effect. If the trials differ in factors that modify the treatment effect, the comparison can be biased. So the validity of an indirect comparison depends on the linked trials being comparable, particularly in effect-modifying characteristics, and this assumption must be considered when interpreting the results, since violations of it can distort the estimated relative effect derived through the shared comparator.

    Source: Bucher et al. 1997

  • What are the limitations of an indirect comparison?

    The limitations of an indirect comparison arise because it depends on the assumption that the linked trials are comparable, and differences between them in effect-modifying factors can bias the estimate; it provides weaker, less certain evidence than a direct head-to-head trial; and errors can arise if the similarity assumption fails. Population-adjustment methods can address some differences but rely on further assumptions. So an indirect comparison is interpreted cautiously, with attention to the comparability of the trials and the greater uncertainty inherent in comparing treatments without direct evidence, and direct evidence is preferred where available.

    Source: Bucher et al. 1997

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Verified by Dr Darrin Baines

British health economist

Professional identity: darrinbaines.org

Verification date: 2 Dec 2025

Content version: 1.0.0

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