No standard ledger names the parameter carrying the gap
Statement
A bridge ledger should name, for each bridge in use, the identifiable cross-gap functional carrying the information, the identifying assumptions, and a prespecified sensitivity parameter appropriate to that model. Shared baselines, shared component effects, component-by-modifier interactions, class deviations, dose-response transport deviations, and external-control bias functions are defensible examples; the literature auditor checked those rows against Beliveau et al. 2017 and Thom et al. 2022 for baselines, Petropoulou et al. 2023 for additivity, Perren et al. 2026 for class effects, Pedder et al. 2021 for dose-response transport, and Hussein et al. 2023 for the external-control bias parameter. The sensitivity parameters are analysis-specific rather than canonical: a baseline heterogeneity standard deviation estimated from the data is not automatically a sensitivity parameter, and systematic subnetwork nonexchangeability is better represented by a location shift or bias function. In rank-deficient component models the carrying object may be an identifiable row-space functional rather than any individual shared coefficient.
Why it is open
Bridge assumptions are distributed across model code, prior specifications, and prose, so a reader cannot reconstruct from the published output which parameter produced the cross-gap answer. There is no agreed vocabulary pairing each bridge with its untestable component and a model-appropriate sensitivity parameter, and the reporting guidance that does exist is scoped to population-adjusted comparisons rather than to disconnected-network bridges. The consequence is that disconnected analyses are published with one narrow interval and no bridge sensitivity, and the fact that the software connected the network is mistaken for evidence of identification.
What has been tried
| Work | What it contributes |
|---|---|
| Beliveau et al. 2017 | supports the baseline-synthesis ledger row: the baseline effect is the carrying parameter and baseline exchangeability the untestable part |
| Thom et al. 2022 | supports the baseline row and quantifies the residual bias and undercoverage that the sensitivity parameter would have to cover |
| Petropoulou et al. 2023 | supports the component-additivity row: constancy of the shared component effect across subnetworks is the untestable part across a gap |
| Perren et al. 2026 | supports the class-effect row; the class-outlier probability proposed as its sensitivity parameter is the catalog’s coinage and appears nowhere in this paper |
| Pedder et al. 2021 | supports the dose-response row: transport of the dose-response curve across populations is the untestable part |
| Hussein et al. 2023 | supports the external-control row by formulating residual design bias as an explicit bias parameter in a hierarchical synthesis model |
| Ishak et al. 2025 | publishes a reporting and risk-of-bias framework for population-adjusted indirect comparisons, so a reporting standard does exist; it does not supply a per-bridge ledger naming the parameter that carries a disconnected-network gap |
Probable solution or research direction
Develop the ledger as a reporting object with one row per bridge, naming the identifiable functional that carries the gap, its identifying assumptions, and a sensitivity parameter chosen for that model rather than taken from a fixed menu. Extend the existing population-adjustment reporting framework to cover it instead of proposing a parallel standard, and use the PRISMA-NMA update as the route into general network meta-analysis reporting. Pair each declared sensitivity parameter with an actual fragility or drift analysis rather than leaving it nominal, and make the ledger machine-readable so it can be checked rather than merely read.
Verification
Verdict. Partially addressed. Auditors agreed the problem is open and no counterevidence surfaced. Reopened by the full-text reading: 3 findings from 3 papers survived both the reader and an independent second reviewer, so the verdict moves from confirmed-open to partially-addressed.
The source said. “Every disconnected analysis should include a bridge ledger listing, for each bridge used, the parameter carrying information across the gap, the empirical evidence supporting it, the untestable part, the sensitivity parameter, and the impact on the target contrast. The report supplies a six-row template covering baseline synthesis, component additivity, component effect modification, class effects, dose response, and external controls; no such object is currently required.”
What was wrong with it. The source presented a fixed six-row ledger with canonical sensitivity parameters; GPT-5.6 Sol found the mapping is not uniquely determined, that a baseline-drift standard deviation is the wrong canonical choice, and that class-outlier probability is underdefined without an outlier distribution and magnitude. The literature auditor confirmed the ledger content against the primary literature but flagged class-outlier probability as the catalog’s own coinage, absent from Perren et al., and treated the claim that no reporting standard requires naming the carrying parameter as unproven rather than established: a reporting and risk-of-bias framework for population-adjusted comparisons does exist (Ishak et al. 2025, doi:10.1007/s40273-025-01503-1), and the PRISMA-NMA update is at scoping-review and Delphi stage.
Revised by the full-text reading. Applied 2026-07-26 full-text reading of the consolidated library (687 papers).
- Verdict changed
- confirmed-open -> partially-addressed 3 surviving findings from: Anchors Away: Navigating Unanchored Indirect Comparisons wit; Evidence contributions in component network meta-analysis fr; Network meta-analysis of multiple outcome measures accountin. New citations: 10.1186/1471-2288-14-92, 10.1186/s12874-026-02766-8
- Literature and prior-art check
- open / supported-with-caveat. I checked each of the six ledger rows against the primary literature rather than the report. Baseline synthesis: the carrying parameter is the baseline effect and the untestable part is baseline exchangeability, consistent with Beliveau 2017 and Thom 2022. Additivity across a gap: consistent with Petropoulou 2023. Class: consistent with Perren 2026, though ‘class-outlier probability’ as the sensitivity parameter is the entry’s coinage and appears nowhere in Perren. Dose-response transport: consistent with Pedder 2021. External control residual confounding with a bias function: consistent with the bias-parameter formulation in Hussein et al. 2023. So the ledger content is technically sound. The final claim, that no reporting standard requires naming the parameter that carries the gap, is an absence claim; I confirmed PRISMA-NMA has no such item and that its update is only now at scoping-review and Delphi stage for early 2026, but absence of a requirement cannot be positively verified, so treat it as unproven rather than established.
- GPT-5.6 Sol, technical and source-code lens
- open / overstated. C2, C3, C5, and C6 are reasonable ledger examples, not uniquely determined mappings. C1 incorrectly treats a baseline-drift standard deviation as canonical: an estimated baseline heterogeneity SD is not necessarily a sensitivity parameter, and systematic subnetwork nonexchangeability is more directly represented by a location shift or bias function. C4’s class-outlier probability is underdefined without an outlier distribution and magnitude and is only one possible parameterization. In rank-deficient component models the carrying object may be an identifiable row-space functional rather than an individual shared coefficient. C7 is an unverified reporting-standard absence claim. Explicit disclosure is important for decision-grade work, but mandating this exact ledger is a reporting roadmap rather than a mathematical solution.
- Decision path
-
R5:default-open → R9:substantiated-single-overstatement:codex
How the evidence falls in time
7 papers in the reviewed corpus bear on this problem, published 2014 to 2026. The most recent paper to touch this reports progress on it, and every paper calling it open is older.
It is also being closed in pieces: partial results come from more than one paper in more than one year, each covering a different part.
Does the later work answer the earlier work? Put to an independent reviewer with the older and newer claims side by side, it judged that the later work answers a component of it, leaving a named part (high confidence). The later work provides substantive ledger entries for particular bridge families: contribution flows for component NMA and an assumption-plus-delta sensitivity formulation for unanchored meta-regression. It does not establish the general ledger or make its use a standard reporting requirement across bridge types. What remains: A cross-family reporting standard that requires every bridge analysis to name its carrying functional, identifying assumptions, and prespecified sensitivity parameter.
| Year | Says | Paper |
|---|---|---|
| 2014 | partly addresses it | Network meta-analysis of multiple outcome measures accounting for borrowing of information across outcomes |
| 2019 | confirms it is open | Creating historical controls using data from a previous line of treatment - two non-standard approaches |
| 2021 | confirms it is open | Component network meta-analysis compared to a matching method in a disconnected network: A case study |
| 2025 | confirms it is open | A leave-one-out algorithm for contribution analysis in component network meta-analysis |
| 2025 | confirms it is open | Risk of Bias in Network Meta-Analysis (RoB NMA) tool |
| 2026 | partly addresses it | Evidence contributions in component network meta-analysis from the shortest-path approach |
| 2026 | partly addresses it | 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 C:L52, C:L1167-1179, C:L2476, C:L2513 of the reviewed corpus.