What a component network meta-analysis does
Complex interventions have several parts. A program to improve a chronic condition may combine education, exercise, counselling and follow-up calls, and different trials use different mixtures. A conventional network meta-analysis treats each mixture as a distinct node. With many combinations, the network becomes sparse and the nodes poorly connected, and it tells nothing about which element is responsible for the effect.
A component network meta-analysis, introduced by Welton and colleagues in 2009 and developed since, models the effect of a combination as a function of the effects of its components. It estimates the contribution of each component, and from these it can predict the effect of combinations that no trial has tested. It is closely related to network meta-regression, with a binary indicator for each component as a covariate.
The models
The additive model. The simplest assumption is that components add up on the chosen scale, such as the log risk ratio. The effect of E plus X relative to usual care is the effect of E plus the effect of X. This is parsimonious, with one parameter per component, and allows predictions for any combination of the components. Its drawback is the strong assumption that components do not interact.
Interaction models. To relax additivity, the model can include interaction terms, so that the effect of a pair of components may differ from the sum. Each interaction adds a parameter, and the data seldom support many. Models may allow a limited number of interactions chosen on theory, or use regularization that shrinks interaction terms toward zero.
Choosing between them. Compare the fit of the additive model with that of the standard network model, which treats each combination as a separate node and is the most flexible. If the two fit equally well, the additive model is supported, and if the standard model fits much better, there is evidence of interaction. The comparison can use statistical tests, information criteria or the heterogeneity and inconsistency statistics. Like other tests of fit in networks, these have low power.
A worked example
A simulated network compares complex programs for a chronic condition with usual care. There are three components: education (E), exercise (X) and counselling (C). Four program types were tested against usual care, with log risk ratios (negative values favor the program).
| Program | Log RR | SE | Fitted by additive model |
|---|---|---|---|
| Education alone (E) | -0.10 | 0.08 | -0.11 |
| Exercise alone (X) | -0.25 | 0.09 | -0.26 |
| Education + exercise (E+X) | -0.40 | 0.12 | -0.38 |
| Education + counselling (E+C) | -0.30 | 0.10 | -0.30 |
The additive model, fitted by weighted least squares, estimates the effects of the three components as follows.
| Component | Effect (log RR) | SE | Risk ratio |
|---|---|---|---|
| Education (E) | -0.11 | 0.07 | 0.89 |
| Exercise (X) | -0.26 | 0.08 | 0.77 |
| Counselling (C) | -0.19 | 0.12 | 0.83 |
The fitted values agree closely with the observations. The largest gap is for education plus exercise, observed at -0.40 and fitted at -0.38, which is well within its standard error of 0.12. That fits an additive pattern. No trial tested exercise plus counselling, but the model predicts a log risk ratio of -0.45 (standard error 0.16), a risk ratio of about 0.64, as the sum of the two component effects. The interval is wide, because the prediction combines two uncertain estimates. The numbers are simulated.
The example shows both the strength and the risk. The model allowed the estimation of an untested combination and of the contribution of counselling, which appeared only in one program. But the prediction is only as good as the assumption of additivity. If counselling works only in combination with education, then the prediction for exercise plus counselling would be wrong, and there is no way to find that out from this network.
Identifiability and network structure
For component effects to be estimated separately, the components must be varied independently across the network. If every program that includes exercise also includes education, the two effects cannot be separated. Mathematically, the design matrix that links components to observed comparisons must have full rank. It is easy to check, and software warns when components are confounded. Networks in which components appear in several different combinations, and in which some trials compare the combination with the same combination minus one component, are the most informative. Such component-dropping or component-adding trials are the strongest evidence.
Networks can also be disconnected in the standard sense and still connected through components. For instance, if two groups of trials share no treatment but share a component, the additive model can link them, which standard network meta-analysis cannot. This is a benefit, but it relies entirely on additivity, and the results should be flagged as dependent on the model.
Defining the components
The difficult part of a component analysis is often the definition of components, not the statistics. Complex interventions are described inconsistently, and the same label can cover different content. The process normally has these stages.
- Develop a taxonomy. From the literature and expert input, list the distinct components, such as the content of education, the type, intensity and supervision of exercise, and who delivered counselling.
- Code each intervention arm. Two coders should independently record which components each arm contained, resolving disagreements, and a coding manual should be written.
- Decide on granularity. Too fine a division creates components that are always present together, which cannot be separated, and too coarse a division hides differences.
- Consider dose and delivery. A component present at low intensity is not the same as at high intensity, and the binary coding may need extension to allow for dose.
- Report the coding. The table of components by arm is part of the results.
Guidance such as the TIDieR checklist for describing interventions helps to extract consistent information from trial reports, and the poor reporting of many interventions limits what can be coded.
Assumptions to check and report
- Additivity on the chosen scale, and the sensitivity of results to interactions.
- Transitivity, as in standard network meta-analysis: the trials should be similar in effect modifiers apart from the components being compared.
- Consistency, and its assessment by comparing the additive model with the standard one.
- Component definitions that are valid and applied consistently.
- Absence of important confounding between components and trial characteristics, such as the population or the setting, since a component may stand in for something else.
Estimates for components that are rarely tested, or tested only in combination, should be reported with their uncertainty and flagged as dependent on the model. CINeMA and GRADE for networks can be adapted for rating certainty, though the guidance is still developing.
Software and reporting
The netmeta package in R includes functions for component network meta-analysis in the frequentist framework (netcomb, discomb), and Bayesian implementations can be written in JAGS or Stan, or with the multinma package. Reporting follows PRISMA for network meta-analyses, with added items: the taxonomy of components, the coding of each arm, the models fitted, the comparison with the standard model, the estimated component effects with their intervals, any predictions for combinations that were not tested, and a discussion of the assumption of additivity. Present a table of the components in each arm, a network graph that can show combinations, and a plot of component effects.
Common mistakes and how to read the results
The first common mistake is defining components after seeing the results. A component list that is fixed in the protocol, with written rules for how each intervention arm is coded, protects the analysis from choices that favour a pleasing story. The coding should be done by two people working independently, and disagreements should be recorded and resolved before any model is fitted. The TIDieR checklist helps here because it forces a description of what was delivered, by whom, how often and for how long, which is the information needed to decide whether two arms share a component.
The second mistake is reading a component effect as a causal statement without checking the design. The estimate of a component's effect is conditional on the other components in the model and on the additive assumption. If a component is almost always delivered together with another one, the estimate is formally identifiable but very imprecise, and its confidence interval should be shown, not hidden behind a point estimate.
The third mistake is presenting predictions for untested combinations as if they were trial results. A prediction for a combination that no trial has studied should be labelled as a model-based prediction, shown with its interval, and accompanied by the comparison of the additive model with the standard network model. When the additive model fits much worse, the combination predictions should not be used.
A useful report has four parts. It gives a table of components and their coding, a network graph in which nodes are combinations and edges are comparisons, a table of component effects with intervals and heterogeneity, and a statement about which questions the data can and cannot answer. The reader should be able to see which components were varied independently and which were not.
Finally, the certainty of the estimates should be judged. Component effects inherit the risk of bias, indirectness and imprecision of the trials that inform them, and the additive assumption is an additional source of indirectness. Reviewers should state this explicitly and should avoid ranking components with a precision the data do not support.
Limitations
Component analysis rests on strong assumptions, and its predictions for untested combinations cannot be checked by the data. It needs a network with adequate variation of components, which many fields lack, and the quality of the coding limits it. Components are not independent of context, so the effect of a component in one setting may not carry over. Estimates of component effects from observational comparisons across trials are subject to confounding. The results suggest which elements are worth testing, and do not replace trials that test them directly. They do not provide advice for individual patients.
Component estimates inform the design and evaluation of programs. They are not recommendations for the care of an individual.
How we can help
Support for component network meta-analysis
The method can be supported at different depths. Choose what you need, and the scope is agreed in writing before work begins.
Feasibility check
A review of your studies and data to confirm that the method is suitable and which approach fits.
Analysis and figures
The analysis run to a prespecified plan, with forest plots and the other figures.
Methods and results text
Written for the manuscript and aligned with PRISMA 2020 or the relevant extension.
Manuscript and submission
Optional: the full paper, the reporting checklist and the submission materials.
Frequently asked questions
What is a component network meta-analysis?
A network meta-analysis that estimates the effect of each component of complex interventions, instead of treating every combination as a separate treatment.
What is the additive model?
The assumption that the effect of a combination of components is the sum of the effects of its components on the chosen scale.
Can it predict combinations that were never tested?
Yes, under the additive or another specified model, but the prediction depends on the assumption and has wide uncertainty.
When can component effects be separated?
When components are varied independently across the network, so the design matrix has full rank. If two components always appear together, their effects cannot be separated.
How do I check for interactions?
Compare the additive model with the standard network model, and consider interaction terms chosen on theory. These tests have low power.
Which software supports it?
The netmeta package in R, with netcomb and discomb, and Bayesian implementations in JAGS, Stan or multinma.
References
- Welton NJ, Caldwell DM, Adamopoulos E, Vedhara K. Mixed treatment comparison meta-analysis of complex interventions: psychological interventions in coronary heart disease. Am J Epidemiol. 2009;169(9):1158-1165.
- Rucker G, Petropoulou M, Schwarzer G. Network meta-analysis of multicomponent interventions. Biom J. 2020;62(3):808-821.
- Freeman SC, Scott NW, Powell R, Johnston M, Sutton AJ, Cooper NJ. Component network meta-analysis identifies the most effective components of psychological preparation for adults undergoing surgery under general anesthesia. J Clin Epidemiol. 2018;98:105-116.
- Pompoli A, Furukawa TA, Efthimiou O, Imai H, Tajika A, Salanti G. Dismantling cognitive-behaviour therapy for panic disorder: a systematic review and component network meta-analysis. Psychol Med. 2018;48(12):1945-1953.
- Hoffmann TC, Glasziou PP, Boutron I, et al. Better reporting of interventions: template for intervention description and replication (TIDieR) checklist and guide. BMJ. 2014;348:g1687.
- Hutton B, Salanti G, Caldwell DM, et al. The PRISMA extension statement for reporting of systematic reviews incorporating network meta-analyses of health care interventions: checklist and explanations. Ann Intern Med. 2015;162(11):777-784.