Strict component additivity may be clinically false

Strict component additivity can be clinically false, and interaction CNMA already relaxes it: Rucker et al. 2020 define interaction CNMA models and implement them in netmeta by adding interaction columns to the combination matrix. What is not solved is the disconnected and sparse case, where Petropoulou et al. 2023 found that forward selection of interaction CNMAs performs poorly and recommended separate subnetwork analyses, and where the number of possible component interactions grows combinatorially while the number of observed combinations does not. No method bounds how far an omitted component interaction could move a target cross-gap contrast, and no heredity-constrained sparse selection with subnetwork drift blocks has been implemented for component PAIC. Additivity is also what makes a never-administered combination estimable, and that reporting consequence is unaddressed. Under strict additivity a de novo regimen lies inside the row space, so every estimability screen returns estimable for exactly the extrapolations that are most assumption-driven, and its estimate, interval and rank are printed like those of a randomized regimen; applied reviews then recommend such regimens by name, one estimating 27 daratumumab-based regimens, stating that some have never been reported, and recommending a never-reported one in its abstract. What is missing is a defined provenance quantity, for example the fraction of a regimen’s predicted effect carried by component pairs never co-administered in any arm, and a convention requiring it beside the estimate.

CMP-03 Partially addressed Very high priority Emerging

ImportantA study has been run against this problem

No. At a synergy of 0.2 (twice a contrast’s SE), 15 of 32 never-administered regimen results that the additive model reported as estimable had 95% coverage below 0.90, down to 0.11. Synergy on a never co-administered pair went wholly into the regimens containing it and was undetectable; synergy on a co-administered pair was absorbed into the component effects and biased regimens without that pair by -0.125, including a never-administered one. Modeling co-administered pairs’ interactions removed the leakage. The share of a regimen’s pairs never co-administered did not flag the failures (AUROC 0.37). Read the study below.

Statement

Strict component additivity can be clinically false, and interaction CNMA already relaxes it: Rucker et al. 2020 define interaction CNMA models and implement them in netmeta by adding interaction columns to the combination matrix. What is not solved is the disconnected and sparse case, where Petropoulou et al. 2023 found that forward selection of interaction CNMAs performs poorly and recommended separate subnetwork analyses, and where the number of possible component interactions grows combinatorially while the number of observed combinations does not. No method bounds how far an omitted component interaction could move a target cross-gap contrast, and no heredity-constrained sparse selection with subnetwork drift blocks has been implemented for component PAIC. Additivity is also what makes a never-administered combination estimable, and that reporting consequence is unaddressed. Under strict additivity a de novo regimen lies inside the row space, so every estimability screen returns estimable for exactly the extrapolations that are most assumption-driven, and its estimate, interval and rank are printed like those of a randomized regimen; applied reviews then recommend such regimens by name, one estimating 27 daratumumab-based regimens, stating that some have never been reported, and recommending a never-reported one in its abstract. What is missing is a defined provenance quantity, for example the fraction of a regimen’s predicted effect carried by component pairs never co-administered in any arm, and a convention requiring it beside the estimate.

Why it is open

Additivity is what reconnects a disconnected network, so adding interaction terms consumes the degrees of freedom the bridge depends on, and the contrasts that would discriminate between candidate interaction structures are the ones spanning the gap. Petropoulou et al. 2023 measured the consequence: data-driven selection of interaction structures recovers the right model rarely in disconnected networks and tends to fall back on sparse additive models even when additivity is violated. The proposed global-plus-drift decomposition also needs reference or zero-mean constraints to separate beta from u_s, eta from v_s, and Gamma from Lambda_s, and no bound currently exists for how far unmodeled synergy could move the target contrast.

What has been tried

Work	What it contributes
Rucker et al. 2020	defines and implements additive and interaction CNMA in the frequentist netmeta framework, so strict additivity is not the only available model form
Petropoulou et al. 2023	simulates mild and strong additivity violations and shows forward selection of interaction CNMA models does not work well for disconnected networks
Veroniki et al. 2026	documents that synergy and antagonism motivate interaction CNMA and that additivity cannot be assessed statistically in disconnected networks
netmeta	supplies the frequentist component NMA engine, including the interaction CNMA models
cpaic 0.1.0 (development version, choxos/cpaic@9d150e9)	unreleased development R package on GitHub, not on CRAN; fits additive component bridges with total and nested additivity lack-of-fit diagnostics, and implements no component-by-component interaction or subnetwork drift model
Nunns et al. 2025, Journal of Medical Internet Research	Component network meta-analysis of digital weight-loss interventions that reports and recommends a specific three-component package while stating that no trial arms used this specific combination of components.
Huang et al. 2025, Systematic Reviews	Estimates the effects of 27 daratumumab-based regimens in newly diagnosed multiple myeloma, states that some of them have never been reported, and recommends one of the never-reported regimens in its conclusion and abstract.
Efthimiou et al. 2022, Statistics in Medicine	Presents the ability to estimate a combination previously not tested in any trial as a distinctive feature of component models, usable for designing new treatments. The estimate for such a regimen rests on the zero-interaction constraint, whose column is identically zero for any pair of components never co-administered.
Freeman et al. 2023, BMC Medical Research Methodology	Develops the CNMA-circle plot, which marks in gray the links whose differing component combination is not delivered in any single trial arm. The closest existing support marker, and it sits beside the analysis: the forest plot, the league table and the ranking still treat de novo and observed regimens identically.
Yang et al. 2026, BMC Medical Research Methodology	Decomposes a component effect into study-level contributions through pseudo-paths and flow allocation, the first machinery capable of supporting a component-level provenance measure. It attributes evidence to component parameters rather than to a requested combination, so the fraction of a de novo regimen’s predicted effect carried by never-co-administered component pairs is still not computed anywhere.

Probable solution or research direction

Build on interaction CNMA rather than reinventing it: prespecify the interactions that are estimable given the observed combinations, and use sparse or hierarchical priors with an explicit heredity or mechanistic rationale rather than data-driven forward selection, which is already known to fail across a disconnection. Derive omitted-interaction bounds that quantify how far a target cross-gap contrast could move under unmodeled synergy, since that is the part with no existing method. Report for each cross-gap contrast how much of the result depends on shrinkage rather than on likelihood information, and state which drift and interaction directions the design can identify.

Our study

An omitted component interaction biases never-administered regimens and leaks into regimens that do not contain it

The question put to it. When additivity makes a never-administered combination estimable, how far can an omitted component interaction move its predicted effect, and does it contaminate other regimens?

What it found. No. At a synergy of 0.2 (twice a contrast’s SE), 15 of 32 never-administered regimen results that the additive model reported as estimable had 95% coverage below 0.90, down to 0.11. Synergy on a never co-administered pair went wholly into the regimens containing it and was undetectable; synergy on a co-administered pair was absorbed into the component effects and biased regimens without that pair by -0.125, including a never-administered one. Modeling co-administered pairs’ interactions removed the leakage. The share of a regimen’s pairs never co-administered did not flag the failures (AUROC 0.37).

Results.

• Synergy on C+D (never co-administered): regimens containing C+D biased by 0.2, coverage 0.63 to 0.71; all others exact.
• Synergy on A+B (co-administered): B+C and B+D biased by -0.125 (coverage 0.73 and 0.81) though neither contains A+B.
• Interaction model for the co-administered pairs: unbiased when the synergy is on a co-administered pair, no help for C+D.

Design.

Estimand

Effect of each two- to four-component regimen against placebo

Methods compared

additive component network meta-analysis, component model with interactions for co-administered pairs

Data-generating mechanism

Exact calculation on an eight-trial component network with three co-administered and three never co-administered component pairs; synergy of three magnitudes placed on one pair, both kinds, or all pairs; additive and prespecified-interaction models.

Replicates

Exact calculation: 4 synergy locations x 3 magnitudes x 2 models x 11 regimens

What this does not answer. One connected network, continuous outcome, fixed effect; no disconnection, covariate adjustment, selection procedures or formal synergy bound. Peer review has not been done.

Peer review. Not yet done. The result stands on the study alone until it is.

Read it: PDF · Markdown · OpenDocument · Code and data: studies/CMP-03-estimable-by-assumption · Protocol: registered before the run

Verification

Verdict. Partially addressed. Part of this problem is addressed by existing work; the entry names which part.

The source said. “The additive component model assumes a combination’s effect equals the sum of its component effects, but synergy and antagonism can be precisely what defines the value of a combination therapy, and omitted interaction terms are assumed negligible by default. The proposed replacement writes theta_{t,s}(x) = C_t’(beta + u_s) + Z_t’(eta + v_s) + C_t’(Gamma + Lambda_s)x, adding candidate interactions Z_t and subnetwork-specific drift blocks with shrinkage priors.”

What was wrong with it. The source presented relaxing additivity as an unbuilt research direction; interaction CNMA has existed since Rucker et al. 2020 and ships in netmeta, and Petropoulou et al. 2023 already simulated mild and strong additivity violations. Both the literature auditor and Grok 4.5 supplied those locators, and GPT-5.6 Sol corrected the claim that the drift-and-interaction model is estimable only through its priors: sufficiently rich replicated designs can identify some of those contrasts through the likelihood.

Dissent. literature dissented (open): Retrieved Rucker et al. 2020: interaction CNMA already exists (‘Interaction CNMA models also allow interactions between the components’), and Petropoulou et al. 2023 simulated exactly this, with mild and strong additivity violations (exp(lambda) = 1.5 and 2). So the ‘additivity may be false’ half is settled published fact, not an open problem; what is open is the heredity-constrained sparse selection, the drift-block parameterisation, and omitted-interaction bounds. Petropoulou et al. supply the nearest thing to a source asserting the software absence the entry claims: ‘More advanced methods penalizing the size of the estimated interaction parameters like the LASSO could in principle also be used to select interaction CNMA models, however, this would not be possible using our R scripts.’ Caveat: the entry cites only ‘cpaic 0.1.0’ and ‘netmeta’ for a claim whose real evidence base is the Rucker/Petropoulou line of work; the netmeta citation is functionally decorative because the substantive content sits in the papers, not the package. I found no bounds for omitted component synergy.

Revised by the full-text reading. Applied full-text reading.

merged-in

absorbed a proposal the reading raised separately: No provenance or extrapolation marker for never-administered component regimens 5 citation(s) added. The drafter disagreed with placing it here: Two of the three readers had this accepted as a distinct problem and the reviewer’s merge reason corrects a genuine overreach, since related combinations can inform an interaction even when the exact regimen has no direct evidence. That correction does not make the two the same object: CMP-03 asks whether additivity is true and how far an omitted interaction could move a cross-gap contrast, while this asks for a support and provenance label on a specific reported package inside a connected network where additivity may well hold. The clinical-deliverability half, whether a recommended package respects a total-dose ceiling, a contact-time budget or mutually exclusive delivery formats, has no counterpart in CMP-03 at all. It is recorded as a merge as directed.

Literature and prior-art check

open / supported-with-caveat. Retrieved Rucker et al. 2020: interaction CNMA already exists (‘Interaction CNMA models also allow interactions between the components’), and Petropoulou et al. 2023 simulated exactly this, with mild and strong additivity violations (exp(lambda) = 1.5 and 2). So the ‘additivity may be false’ half is settled published fact, not an open problem; what is open is the heredity-constrained sparse selection, the drift-block parameterisation, and omitted-interaction bounds. Petropoulou et al. supply the nearest thing to a source asserting the software absence the entry claims: ‘More advanced methods penalizing the size of the estimated interaction parameters like the LASSO could in principle also be used to select interaction CNMA models, however, this would not be possible using our R scripts.’ Caveat: the entry cites only ‘cpaic 0.1.0’ and ‘netmeta’ for a claim whose real evidence base is the Rucker/Petropoulou line of work; the netmeta citation is functionally decorative because the substantive content sits in the papers, not the package. I found no bounds for omitted component synergy. Cites doi:10.1002/bimj.201800167: Partially covers the ‘relax additivity’ direction: interaction CNMA models are already defined and implemented; the open part is principled sparse/heredity-constrained selection and bounding of omitted interactions..

GPT-5.6 Sol, technical and source-code lens

open / overstated. C1-C3 are correct for cpaic: cnma_bridge() uses theta=C beta, and cmlnmr() adds component-by-covariate interactions but no component-by-component synergy terms. No exported function or fitted parameter block implements the proposed Z, u_s, v_s, or Lambda_s structure, supporting C14. C8 and C9 correctly describe interaction CNMA and the proposed blocks. C4 and C6 are software- or literature-wide nonexistence claims that this audit does not adjudicate. C5 is mathematically possible only after a credible bound set for omitted interactions is specified. C7 and C10-C12 are defensible modeling choices, not general statistical requirements: heredity can be weak or strong, qualitative interactions can violate heredity, and shrinkage strength should follow scientific scale information rather than automatically being stronger for every interaction. The proposed global-plus-drift decomposition also needs reference or zero-mean constraints to distinguish beta from u_s, eta from v_s, and Gamma from Lambda_s. Interactions and drift contrasts are not necessarily identified only by priors; sufficiently rich replicated designs can identify some or all of them through the likelihood. The issue is decision-critical when plausible synergy loads the requested cross-gap contrast, but a high-dimensional heredity-and-drift model is otherwise a roadmap item rather than a universally required replacement.

Grok 4.5, recency lens

partially-solved / supported-with-caveat. Clinical falsehood of strict additivity and the existence of interaction CNMA are already in the literature: Rücker et al. 2020 implement pairwise (and higher) interaction CNMA in netmeta; Welton et al. 2009 introduce interaction models; Veroniki et al. 2026 state that interaction CNMA is used when synergy or antagonism violates additivity and warn that power to detect interactions is limited by observed combinations. Petropoulou et al. 2023 evaluate forward selection of interactions and show poor performance for disconnected reconnection. That partially answers the claim that analysts must assume pure additivity, but does not resolve the problem as stated for sparse/disconnected component PAIC: omitted-interaction bounds on the target contrast, heredity-constrained sparse selection with subnetwork drift blocks, and quantification of how much a cross-gap contrast depends on shrinkage toward zero drift were not found in software or published methods. Searches for omitted-interaction bounds, heredity priors in CNMA/PAIC, and drift-plus-interaction models returned no resolving implementation. cpaic is not on CRAN. So the clinical and modeling recognition is partly covered by interaction CNMA; the bound-and-shrinkage agenda remains open. Caveat on support: C3–C4, C6, C14 about current software gaps are supported by absence of public tools; C5, C7, C10–C13 are proposals, not established solutions. Cites 10.1002/bimj.201800167: Defines and implements additive and interaction CNMA in the frequentist netmeta framework, so strict additivity is not the only model form when interactions are included as extra combination-matrix columns.. Cites 10.1136/bmj-2024-083075: States that synergy/antagonism motivates interaction CNMA and that additivity cannot be assessed statistically in disconnected networks, documenting the clinical and identification tension the problem describes.. Cites 10.1186/s12874-023-01959-9: Evaluates forward selection of interaction terms that relax additivity; shows selection does not perform well for disconnected networks, so relaxing additivity via data-driven interactions is not a solved reconnection strategy..

Decision path

R3:partially-solved(n=1) → R9:substantiated-single-overstatement:codex

How the evidence falls in time

58 papers in the reviewed corpus bear on this problem, published 2018 to 2026. Partial progress is on the record, and later work still calls this open. Both belong in view.

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.

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.

Year	Says	Paper
2018	confirms it is open	Dismantling cognitive-behaviour therapy for panic disorder: a systematic review and component network meta-analysis
2018	confirms it is open	Component network meta-analysis identifies the most effective components of psychological preparation for adults undergoing surgery under general anesthesia
2019	confirms it is open	Network meta-analysis of multicomponent interventions
2019	confirms it is open	Dismantling, personalising and optimising internet cognitive-behavioural therapy for depression: a study protocol for individual participant data component network meta-analysis
2019	confirms it is open	Perspective: Network Meta-analysis Reaches Nutrition Research: Current Status, Scientific Concepts, and Future Directions
2020	confirms it is open	Supporting information (Bayesian analysis) to Ruecker, Petropoulou and Schwarzer, Network meta-analysis of multicomponent interventions
2020	confirms it is open	Interventions for adults with a history of complex traumatic events: the INCiTE mixed-methods systematic review
2020	confirms it is open	Psychological and pharmacological interventions for posttraumatic stress disorder and comorbid mental health problems following complex traumatic events: Systematic review and component network meta-analysis
2021	partly addresses it	Relative effectiveness of non-surgical interventions for pain management in knee osteoarthritis: a protocol for a component network meta-analysis of randomised controlled trials
2021	confirms it is open	Cognitive effects and acceptability of non-invasive brain stimulation on Alzheimer’s disease and mild cognitive impairment: a component network meta-analysis (online supplementary data and main article)
2021	confirms it is open	Behavioural interventions for smoking cessation: an overview and network meta-analysis
2021	confirms it is open	Non-pharmacological interventions for preventing delirium in hospitalised non-ICU patients
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	Optimal perioperative nutrition therapy for patients undergoing pancreaticoduodenectomy: a systematic review with a component network meta-analysis
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
2021	confirms it is open	A review of the quantitative effectiveness evidence synthesis methods used in public health intervention guidelines
2022	confirms it is open	Low FODMAP Diet and Probiotics in Irritable Bowel Syndrome: A Systematic Review With Network Meta-analysis
2022	confirms it is open	Identifying relative efficacy of components of prehabilitation in adult surgical patients: protocol for a systematic review and component network meta-analysis
2022	confirms it is open	Combination of antiplatelet and anticoagulant therapy, component network meta-analysis of randomized controlled trials
2022	confirms it is open	Psychological interventions for inflammatory bowel disease: a systematic review and component network meta-analysis protocol
2022	confirms it is open	Meta-Research: Methods and Protocols (Evangelou E, Veroniki AA, eds), Methods in Molecular Biology vol. 2345
2022	confirms it is open	Pharmacological and non-pharmacological treatments for restless legs syndrome in end-stage kidney disease: a systematic review and component network meta-analysis (supplementary file and main article)
2022	confirms it is open	Bayesian unanchored additive models for component network meta-analysis
2023	confirms it is open	The efficacy and adverse events of arsenic trioxide for the patients with myelodysplastic syndrome: a systematic review and component network meta-analysis
2023	confirms it is open	Impact of pharmacological interventions on intrapulmonary shunt during one-lung ventilation in adult thoracic surgery: a systematic review and component network meta-analysis
2023	confirms it is open	Understanding the effectiveness of different exercise training programme designs on VO2peak in COPD: a component network meta-analysis
2023	confirms it is open	Physical Prehabilitation in Patients who Underwent Major Abdominal Surgery: A Comprehensive Systematic Review and Component Network Meta-Analysis Using GRADE and CINeMA Approach
2023	confirms it is open	Immunonutrition in patients who underwent major abdominal surgery: A comprehensive systematic review and component network metanalysis using GRADE and CINeMA approaches
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	Data visualisation approaches for component network meta-analysis: visualising the data structure
2023	confirms it is open	netmeta: An R Package for Network Meta-Analysis Using Frequentist Methods
2024	partly addresses it	When does the placebo effect have an impact on network meta-analysis results?
2024	confirms it is open	Adherence-enhancing interventions for pharmacological and oxygen therapy in patients with COPD: a systematic review and component network meta-analyses
2024	confirms it is open	Exploring the Effectiveness of Self-Management Interventions in Type 2 Diabetes: A Systematic Review and Network Meta-Analysis
2024	confirms it is open	Components and Delivery Formats of Cognitive Behavioral Therapy for Chronic Insomnia in Adults: A Systematic Review and Component Network Meta-Analysis
2024	confirms it is open	Interventions to prevent the onset of frailty in adults aged 60 and older (PRAE-Frail): a systematic review and network meta-analysis
2024	confirms it is open	Lipid lowering for prevention of venous thromboembolism: a network meta-analysis (supplementary material)
2024	confirms it is open	Network meta-analysis examining efficacy of components of cognitive behavioural therapy for insomnia
2024	confirms it is open	Comparing interventions for early psychosis: a systematic review and component network meta-analysis
2024	confirms it is open	Pharmacological Treatments in Heart Failure With Mildly Reduced and Preserved Ejection Fraction: Systematic Review and Network Meta-Analysis
2024	confirms it is open	Effects of non-pharmacological interventions for adults with subjective cognitive decline: a network meta-analysis and component network meta-analysis
2025	confirms it is open	Disentangling preventive effects of differential exercise types on tension-type headache: a component network meta-analysis of randomized controlled trials
2025	confirms it is open	Pain science education and exercise interventions for people with knee or hip osteoarthritis: a systematic review, content and meta-analysis
2025	confirms it is open	Understanding the effectiveness and underlying mechanisms of lifestyle modification interventions in adults with learning disabilities: a mixed-methods systematic review
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	Evaluation of the Aspects of Digital Interventions That Successfully Support Weight Loss: Systematic Review With Component Network Meta-Analysis
2025	confirms it is open	Efficacy of pharmacological and non-pharmacological interventions for the treatment of anorexia nervosa in adolescents and adults (EfaNosa): protocol for a network meta-analysis
2025	confirms it is open	Regional anaesthesia modalities for primary total hip arthroplasty: a systematic review and component network meta-analysis
2025	confirms it is open	Impact of pulmonary rehabilitation programme design on effectiveness in COPD: a systematic review and component network meta-analysis
2025	confirms it is open	Comparative efficacy and adverse effects of beta3-agonists and antimuscarinics in overactive bladder: a network and component network meta-analysis
2025	confirms it is open	Optimal daratumumab-based regimen for patients with newly diagnosed and previously untreated multiple myeloma: systematic review and component network meta-analysis
2026	confirms it is open	Components of cognitive-behavioral interventions to prevent the onset of depression among the high-risk population: a systematic review and component network meta-analysis
2026	confirms it is open	Effectiveness of interventions to increase vaccine uptake: component network meta-analysis
2026	confirms it is open	Components and Delivery Formats of Cognitive Behavioral Therapy for Chronic Fatigue Syndrome/Myalgic Encephalomyelitis: A Systematic Review and Component Network Meta-Analysis
2026	confirms it is open	Cognitive Behavioral Interventions for Children and Adolescents With Overweight or Obesity: A Systematic Review and Component Network Meta-Analysis
2026	confirms it is open	Comparative Effectiveness of Inspiratory Muscle Training Approaches Within Intensive Care Unit-Acquired Weakness Prevention and Rehabilitation Strategies: A Systematic Review and Component Network Meta-Analysis
2026	confirms it is open	BEhavioural Weight Management: COMponents of Effectiveness (BE:COME) Synopsis
2026	confirms it is open	Analysing complex interventions using component network meta-analysis

Related problems

• ADJ-03 — Efficient influence-function transport estimators for ITC networks
• ADJ-19 — Shapley attribution of regimen effects to treatment components
• CMP-27 — Component models cannot represent delivery order or sequencing
• CMP-28 — Component NMA has no dose-response dimension
• CMP-29 — No component-level transitivity and coherence assessment
• CMP-30 — No diagnostic for anchor choice in additive component models
• DEC-15 — No certainty-of-evidence framework rates component effects
• DIA-15 — Coding-error bias, rank reversal and drift calibration go unscored
• DIS-06 — Component additivity across a gap cannot be checked from the data
• HET-15 — Composite comparator nodes are collapsed rather than modeled as reported mixtures

Source

Derived from C:L1357, C:L1235-1237, C:L214-215, C:L240, C:L1416-1445, scope:field-level (component NMA/CNMA generally; inherited by cpaic), scope:field-level model proposal; not implemented in cpaic of the reviewed corpus.