Indirect Treatment Comparison: The Bucher Method and Its Assumptions

The Bucher method is the simplest form of indirect treatment comparison: when one trial compares Treatment A vs. Treatment B and a separate trial compares Treatment A vs. Treatment C, but B and C have never been tested head-to-head, it combines the two trials through their shared comparator (A) to estimate the B-vs-C effect indirectly. It is the two-treatment special case of what network meta-analysis generalizes to entire networks of interventions — understanding Bucher’s method first makes the logic of full network meta-analysis much easier to follow, because the underlying arithmetic is the same, just scaled up.

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The problem it solves: no head-to-head trial exists

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In evidence synthesis and health technology assessment (HTA), a reviewer is routinely asked to compare two treatments that were never enrolled in the same trial against each other — a newer agent tested only against placebo or an older standard of care, compared with a competitor tested against that same standard in a different trial program. A direct randomized comparison of the two treatments a decision-maker actually needs to choose between simply may not exist, and running a new head-to-head trial is often infeasible on the review’s timeline.

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Bucher HC, Guyatt GH, Griffith LE, and Walter SD formalized the fix in their 1997 paper “The results of direct and indirect treatment comparisons in meta-analysis of randomized controlled trials” (Journal of Clinical Epidemiology, 1997;50(6):683–691): use the trials that already exist, both of which share a common comparator, to construct an adjusted indirect comparison rather than treating the missing head-to-head trial as a dead end.

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How the calculation works

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The mechanics are deliberately simple, which is part of why the method is still widely taught and used. Working on the scale where treatment effects are approximately normally distributed — the log scale for a ratio measure like an odds ratio or relative risk, the natural scale for a mean difference — the indirect estimate of B vs. C is just the difference between the two existing direct estimates:

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Effect(B vs. C) = Effect(A vs. B) − Effect(A vs. C)

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The variance of that indirect estimate is the sum of the two trials’ individual variances:

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Var(B vs. C) = Var(A vs. B) + Var(A vs. C)

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That variance-addition step is the mechanically important part. Because the two trials were run independently — no patient appears in both — their sampling errors are uncorrelated, so the variances simply add rather than partially canceling. A confidence interval built from that summed variance is, almost without exception, wider than either input trial’s own confidence interval. That is the price of borrowing evidence indirectly instead of measuring it directly, and it is true even when the underlying trials themselves are large and precise.

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The assumption the whole method depends on: similarity (transitivity)

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The arithmetic above is valid only if a specific condition holds: the A-vs-B trial and the A-vs-C trial have to be similar enough, in everything besides the treatment being tested, that treatment A can act as a valid common yardstick across both. This is usually called the similarity or transitivity assumption, and it means comparable patient populations, disease severity, dosing, background care, follow-up duration, and outcome definitions across the two trials — not identical, but not systematically different in a way that would itself change how well A performs.

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Transitivity is not something a statistical test can confirm from the summary data alone; the Cochrane Handbook’s chapter on network meta-analysis (Chapter 11) frames it as a question that has to be reasoned through clinically and epidemiologically before the numbers are trusted — are the trial populations, in aggregate, similar enough that A’s effect would be expected to transfer across both contexts? If the A-vs-B trial enrolled a much sicker population, used a different dose of A, or ran a decade earlier under a different standard of background care than the A-vs-C trial, the indirect B-vs-C estimate inherits that imbalance with no warning sign visible in the point estimate itself.

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How this relates to full network meta-analysis

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Bucher’s method is the special case of network meta-analysis (NMA) with exactly three treatments and exactly one indirect comparison to make. NMA generalizes the same underlying idea — borrowing strength through shared comparators — to networks with many treatments and many trials, combining direct and indirect evidence for every pairwise comparison simultaneously within one statistical model, whether estimated in a Bayesian (typically Markov chain Monte Carlo) or frequentist framework. See Bayesian vs. frequentist network meta-analysis for how those two estimation approaches differ once a network is large enough to need one.

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Two things a full NMA can do that the two-trial Bucher calculation cannot: first, when a network has closed loops — more than one independent evidentiary path between two treatments — NMA can formally check consistency between direct and indirect evidence for the same comparison, something a single Bucher calculation has no second path to check itself against. Second, once a network is estimated jointly, every treatment can be given a single relative ranking across the whole set, which is exactly what a metric like SUCRA summarizes. A two-treatment Bucher comparison has nothing to rank; ranking is a network-scale question.

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Limitations to weigh before relying on it

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• Wider confidence intervals than a direct trial would give. Variance addition (above) means an indirect estimate is inherently less precise than a genuine head-to-head trial of the same size would have been — sometimes wide enough that a result which looks clinically meaningful on the point estimate is statistically inconclusive once the full interval is reported.

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• No protection if transitivity is violated. Unlike random allocation within a single trial, which protects a direct comparison against confounding, an indirect comparison has no analogous safeguard. If the two contributing trials differ in an effect modifier, the resulting bias does not announce itself in the output — it has to be assessed by reasoning about the trials’ populations and designs before the calculation is trusted, not caught afterward by inspecting the number.

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• Only handles one shared comparator at a time. If evidence exists via more than one common comparator, or via a longer indirect chain (A→B known, B→C known, A→C wanted, plus other partial evidence), the single-comparator Bucher formula doesn’t combine everything at once — that is the scenario a full network meta-analysis is built to handle instead.

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When the Bucher method is the right tool

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The Bucher calculation remains a reasonable, transparent choice when the evidence base genuinely is just two trials sharing one comparator — a sparse network too small to justify the added modeling complexity of a full NMA, or a case where a fast, auditable adjusted indirect comparison is needed for an early-stage evidence review before a larger network model is built. It is also useful as a sanity check: many HTA submissions report a simple Bucher-style comparison alongside a full NMA result for the same pair of treatments, precisely because the closed-form calculation is easy for a reviewer to independently verify by hand, which a multi-parameter NMA model is not. Once more than three treatments or more than one indirect path are in play, though, a full network meta-analysis is the appropriate method, not repeated pairwise Bucher calculations stitched together informally.

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Frequently asked questions

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Is the Bucher method the same as network meta-analysis?

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No — it’s the two-treatment, single-comparator special case. Network meta-analysis is the general method; the Bucher calculation is what NMA reduces to when there are only three treatments in total and only one indirect path between the two that lack a direct trial.

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Can I just subtract the two trials’ results without adjusting for anything?

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That’s essentially what the Bucher formula does on the appropriate scale (log scale for ratio measures), but “adjusted” in “adjusted indirect comparison” refers to the fact that both trials’ effects are expressed relative to the same common comparator (A) before being combined — an unadjusted comparison of B’s and C’s outcomes against a mismatched or absent common reference is not a valid comparison at all.

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What happens if the two trials aren’t similar enough?

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The transitivity assumption is violated, and the indirect estimate is at risk of bias that the calculation itself cannot reveal. This is a judgment call made by examining the trials’ populations, interventions, and designs — not something the resulting confidence interval will visibly flag.

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Is the Bucher method Bayesian or frequentist?

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Frequentist and closed-form — it’s a direct algebraic calculation (subtract the effects, sum the variances), not a simulation-based or model-fitting approach. Full network meta-analysis can be run either way; see Bayesian vs. frequentist network meta-analysis.

What if I only have individual patient data for one of the two trials?

The Bucher method assumes aggregate data are available for both trials. When you have individual patient data (IPD) for your own trial but only published aggregate results for the comparator, a matching-adjusted indirect comparison (MAIC) is the appropriate method instead — it reweights your IPD to match the comparator trial’s reported baseline characteristics before comparing outcomes.

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