Cross-gap contrasts are absent from the randomized likelihood
Source note. This entry derives in part from a source document whose inline citations were ChatGPT interface tokens rather than references, and so resolve to nothing. Claims below are attributed to that document and were checked independently where possible; anything that could not be independently sourced is marked in the verification trail.
Statement
In a connected network the relative effect between two treatments is identified through a path of randomized contrasts; when no such path exists the cross-subnetwork contrast lies outside the row space of the design and is absent from the randomized likelihood, so no amount of additional within-component data supplies it. Any finite estimate of that contrast comes from structure the analyst imposes: a proper prior, an equality restriction, a component or class model, external evidence, or a bridging trial. Goring et al. 2016 describe the setting and the standard fix of inserting a distribution for the unknown contrast, and Pedder et al. 2021 state that comparisons between disconnected treatments are not possible without strong assumptions. Unanchored MAIC and STC sit in this class; their requirement is conditional exchangeability of absolute potential outcomes across studies together with positivity, consistency, and correct outcome modeling, which Phillippo et al. 2018 describe as much stronger assumptions widely regarded as infeasible.
Why it is open
The missing quantity is a structural property of the evidence graph rather than a sampling limitation: the cross-component contrast lies in a null direction of the design, so within-component precision can grow without ever touching it. Removing the anchor removes the structure that made cross-trial differences cancel, so the analysis must reconstruct an absolute-outcome comparison from studies never designed to be compared. Once any linking structure is added, Bayesian and frequentist software returns a finite estimate with an interval that reads to a decision maker exactly like an identified result, and posterior connectedness is not likelihood identification. Reporting guidance for population-adjusted comparisons now exists (Ishak et al. 2025), so this is not a total absence of standards, but that framework is scoped to population adjustment and does not require a disconnected-network result to name the structure that supplied the cross-gap contrast.
What has been tried
| Work | What it contributes |
|---|---|
| Goring et al. 2016 | canonical description of disconnected networks with neither direct evidence nor an indirect route between certain treatments, and of the recommended fix of inserting a distribution for the unknown contrast |
| Pedder et al. 2021 | states that comparisons between disconnected treatments are not possible without making strong assumptions, and demonstrates a dose-response bridge that supplies them |
| Phillippo et al. 2018 | sources the claim that unanchored comparisons make much stronger assumptions, which are widely regarded as infeasible |
| Ishak et al. 2025 | publishes a reporting and risk-of-bias framework for population-adjusted indirect comparisons; it does not require a disconnected-network analysis to declare the structure that identifies the cross-gap contrast |
Probable solution or research direction
Precede every disconnected-network result with an explicit statement that the randomized evidence identifies effects only within each connected component and that the cross-component comparison is identified only after imposing the stated bridge assumptions. Report the linking structure as part of the estimand definition rather than as a modeling footnote, and extend the existing population-adjustment reporting framework so it covers which parameter carries a disconnected gap. Drop the goal of a single algorithm combining five named linking devices: that combination is unbuilt only because nobody has proposed it, and the useful work is making whichever bridge is used auditable.
Verification
Verdict. Confirmed open. Auditors agreed the problem is open and no counterevidence surfaced.
The source said. “In a connected network the relative effect between two treatments is identified through a path of randomized contrasts; when no such path exists the cross-subnetwork contrast is not merely imprecise but absent from the randomized likelihood. Any finite estimate of that contrast is supplied entirely by structure the analyst imposes, which is why unanchored MAIC and STC and other disconnected-network methods inherit strong no-unmeasured-confounding assumptions.”
What was wrong with it. The source asserted the identification claim without attribution; the literature auditor supplied the canonical sources, doi:10.1002/jrsm.1204 (Goring et al. 2016), doi:10.1177/0272989X20983315 (Pedder et al. 2021), and doi:10.1177/0272989X17725740 (Phillippo et al. 2018), so the claim is now sourced. GPT-5.6 Sol replaced the loose no-unmeasured-confounding wording with the assumption unanchored comparisons actually require, and neither auditor could establish the entry’s further claims that disconnected aggregate-data methods are still niche or that no algorithm combines five named linking devices, so both are dropped.
- Literature and prior-art check
- open / supported-with-caveat. prior_work is empty, so I retrieved the canonical sources myself. Goring et al. 2016 (Res Synth Methods) frames disconnected networks exactly as the entry does and states the standard fix is to insert a distribution for the unknown contrast. Pedder et al. 2021 states outright that comparisons between disconnected treatments are not possible without strong assumptions. Phillippo et al. 2018 supplies the unanchored-MAIC/STC claim verbatim. The structural non-identification claim is correct and cannot be solved by any paper, so open is right. Caveats: two claims are absence claims I cannot verify by finding nothing, namely that disconnected aggregate-data methods are ‘still niche in practice’ and that ‘no network-connecting algorithm currently combines’ five named devices. The second is trivially true only because nobody has proposed that particular five-way combination; it should not be read as a research gap of consequence. The entry should cite Goring 2016, which is the reference a disconnected-networks reader will expect first. Cites 10.1002/jrsm.1204: Sources the unsourced identification claims and is the canonical missing citation for this entry. Cites 10.1177/0272989X17725740: Sources the claim that unanchored MAIC and STC inherit much stronger (no-unmeasured-confounding style) assumptions. Cites 10.1177/0272989X20983315: Sources the claim that a cross-gap contrast requires structure beyond the randomized evidence.
- GPT-5.6 Sol, technical and source-code lens
- open / supported-with-caveat. C2-C6 are correct for a standard contrast-based NMA after fixing a common estimand and the usual consistency and transport assumptions. With an edge-incidence design, a disconnected graph has component-specific shift directions that leave the randomized likelihood unchanged; a cross-component contrast is outside the design row space. Additional within-component data cannot remove that null direction. A proper prior, equality restriction, component or class model, external evidence, or bridging trial can produce a finite estimate, but posterior connectedness is not likelihood identification. C7 is directionally correct, although the precise requirement for unanchored MAIC or STC is conditional exchangeability of absolute potential outcomes across studies, together with positivity, consistency, and correct modeling, rather than generic treatment-confounding language. C8-C9 and C1 are practice, universal-absence, or sourcing claims that cannot be established under this technical-only audit. Identification disclosure is decision-critical; the proposed five-way algorithm is a roadmap item.
- Decision path
-
R5:default-open → R11:caveated(n=2)
How the evidence falls in time
26 papers in the reviewed corpus bear on this problem, published 2013 to 2026. Every paper found here asserts the problem is open; none reports progress.
This problem is recurrent: three or more papers spanning at least eight years assert it independently. Sustained restatement by authors who mostly do not cite each other is the strongest evidence this reading can offer that a gap is real rather than one group’s framing.
| Year | Says | Paper |
|---|---|---|
| 2013 | confirms it is open | Evidence synthesis for decision making 1: introduction |
| 2013 | confirms it is open | Evidence synthesis for decision making 7: a reviewer’s checklist |
| 2014 | confirms it is open | Network meta-analysis of multiple outcome measures accounting for borrowing of information across outcomes |
| 2017 | confirms it is open | Interventions for hereditary haemochromatosis: an attempted network meta-analysis |
| 2018 | confirms it is open | Automated methods to test connectedness and quantify indirectness of evidence in network meta-analysis |
| 2018 | confirms it is open | Borrowing of strength from indirect evidence in 40 network meta-analyses |
| 2018 | confirms it is open | Network meta-analysis explained |
| 2018 | confirms it is open | Quantifying and presenting overall evidence in network meta-analysis |
| 2018 | confirms it is open | The use of single armed observational data to closing the gap in otherwise disconnected evidence networks: a network meta-analysis in multiple myeloma |
| 2019 | confirms it is open | Network meta-analysis of multicomponent interventions |
| 2019 | confirms it is open | A systematic literature review and network meta-analysis feasibility study to assess the comparative efficacy and comparative effectiveness of pneumococcal conjugate vaccines |
| 2021 | confirms it is open | Component network meta-analysis compared to a matching method in a disconnected network: A case study |
| 2021 | confirms it is open | Supplementary appendix to Furukawa et al., Dismantling, optimising, and personalising internet cognitive behavioural therapy for depression: a systematic review and component network meta-analysis using individual participant data |
| 2022 | confirms it is open | Comparative effectiveness of medical treatment vs. metabolic surgery for histologically proven non-alcoholic steatohepatitis and fibrosis: a matched network meta-analysis |
| 2022 | confirms it is open | Evaluation of Information Theoretic Network Meta-analysis to Rank First-Line Anticancer Regimens for Hormone Receptor-Positive, ERBB2-Negative Metastatic Breast Cancer |
| 2022 | confirms it is open | Network Meta-analysis on Disconnected Evidence Networks When Only Aggregate Data Are Available: Modified Methods to Include Disconnected Trials and Single-Arm Studies while Minimizing Bias |
| 2022 | confirms it is open | Treatment of unruptured middle cerebral artery aneurysms: Systematic review in an attempt to perform a network meta-analysis |
| 2023 | confirms it is open | Model selection for component network meta-analysis in connected and disconnected networks: a simulation study |
| 2023 | confirms it is open | Network meta-interpolation: Effect modification adjustment in network meta-analysis using subgroup analyses (Harari, Soltanifar, Cappelleri, Verhoek, Ouwens, Daly, Heeg; Research Synthesis Methods 2023;14(2):211-233) |
| 2023 | confirms it is open | Bayesian hierarchical model-based network meta-analysis to overcome survival extrapolation challenges caused by data immaturity |
| 2024 | confirms it is open | Feasibility of Indirect Treatment Comparisons Between Niraparib Plus Abiraterone Acetate and Other First-Line Poly ADP-Ribose Polymerase Inhibitor Treatment Regimens for Patients with BRCA1/2 Mutation-Positive Metastatic Castration-Resistant Prostate Cancer |
| 2025 | confirms it is open | Dismantling behavioural weight management interventions: component network meta-analysis of randomised controlled trials and real-world services |
| 2025 | confirms it is open | Two-stage Bayesian network meta-analysis of individualized treatment rules for multiple treatments with siloed data |
| 2026 | confirms it is open | Creating Treatment and Component Hierarchies in Component Network Meta-Analysis |
| 2026 | confirms it is open | Reframing Population-Adjusted Indirect Comparisons as a Transportability Problem: An Estimand-Based Perspective and Implications for Health Technology Assessment (Chandler & Ishak; arXiv:2602.17041v3). The batch file points at media/media/Table_1_v2.pdf; the full LaTeX source Transportability_PAIC.tex sits in the same arXiv package and was read. |
| 2026 | confirms it is open | Anchors Away: Navigating Unanchored Indirect Comparisons with Multilevel Unanchored Meta-Regression (ML-UMR) (Chandler & Ishak; arXiv:2606.20341v1). The batch file points at media/media/Table1.pdf; the full LaTeX source mlumr.tex sits in the same arXiv package and was read. |
Source
Derived from A:L48, A:L49, A:L62, C:L52, C:L1078-1086 of the reviewed corpus.