**Network meta-analysis for components of complex interventions**

Nicky Welton*University of Bristol, UK*

Meta-analysis is used to combine results from studies identified in a systematic review comparing specific interventions for a given patient population. However, the validity of the pooled estimate from a meta-analysis relies on the study results being similar enough to pool (homogeneity). Heterogeneity in study results can arise for various reasons, including differences in intervention definitions between studies. Network-meta-analysis (NMA) is an extension of meta-analysis that can combine results from studies to estimate relative effects between multiple (2 or more) interventions, where each study compares some (2 or more) of the interventions of interest. NMA can reduce heterogeneity by treating each intervention definition as a distinct intervention. However, if there are many distinct interventions then evidence networks may be sparse or disconnected so that relative effect estimates are imprecise or not possible to estimate at all. Interventions can sometimes be considered to be made up of component parts, such as some complex interventions or combination therapies.

Component network meta-analysis has been proposed for the synthesis of complex interventions that can be considered a sum of component parts. Component NMA is a form of network meta-regression that estimates the effect of the presence of particular components of an intervention. We discuss methods for categorisation of intervention components, before going on to introduce statistical models for the analysis of the relative efficacy of specific components or combinations of components. The methods respect the randomisation in the included trials and allow the analyst to explore whether the component effects are additive, or if there are interactions between them. The full interaction model corresponds to a standard NMA model.

We illustrate the methods with a range of examples including CBT for depression, electronic interventions for smoking cessation, school-based interventions for anxiety and depression, and psychological interventions for patients with coronary heart disease. We discuss the benefits of component NMA for increasing precision and connecting networks of evidence, the data requirements to fit the models, and make recommendations for the design and reporting of future randomised controlled trials of complex interventions that comprise component parts.

**Model selection for component network meta-analysis in disconnected networks: a case study**

Maria Petropoulou, Guido Schwarzer, Gerta Rücker*Institute of Medical Biometry and Statistics, Faculty of Medicine and Medical Center – University of Freiburg, Germany*

Standard network meta-analysis (NMA) synthesizes direct and indirect evidence of randomized controlled trials (RCTs), estimating the effects of several competing interventions. Many healthcare interventions are complex, consisting of multiple, possibly interacting, components. In such cases, more general models, the component network meta-analysis (CNMA) models, allow estimating the effects of components of interventions.

Standard network meta-analysis requires a connected network. However, sometimes a disconnected network (two or more subnetworks) can occur when synthesizing evidence from RCTs. Bridging the gap between subnetworks is a challenging issue. CNMA models allow to “reconnect” a network with multi-component interventions if there are common components in subnetworks. Forward model selection for CNMA models, which has recently been developed, starts with a sparse CNMA model and, by adding interaction terms, ends up with a rich CNMA. By model selection, the best CNMA model is chosen based on a trade-off between goodness of fit (minimizing Cochran’s Q statistic) and connectivity.

Our aim is to check whether CNMA models for disconnected networks can validly re-estimate the results of a standard NMA for a connected network (benchmark). We applied the methods to a case study comparing 27 interventions for any adverse event of postoperative nausea and vomiting. Starting with the connected network, we artificially constructed disconnected networks in a systematic way without dropping interventions, such that the network keeps its size. We ended up with nine disconnected networks differing in network geometry, the number of included studies, and pairwise comparisons. The forward strategy for selecting appropriate CNMA models was implemented and the best CNMA model was identified for each disconnected network.

We compared the results of the best CNMA model for each disconnected network to the corresponding results for the connected network with respect to bias and standard error. We found that the results of the best CNMA models from each disconnected network are comparable with the benchmark. Based on our findings, we conclude that CNMA models, which are entirely based on RCT evidence, are a promising tool to deal with disconnected networks if some treatments have common components in different subnetworks. Additional analyses are planned to be conducted to simulated data under several scenarios for the generalization of results.

**Uncertainty in treatment hierarchy in network meta-analysis: making ranking relevant**

Theodoros Papakonstantinou^{1,2}, Georgia Salanti^{1}, Dimitris Mavridis^{3,4}, Gerta Rücker^{2}, Guido Schwarzer^{2}, Adriani Nikolakopoulou^{1,2}^{1}Institute of Social and Preventive Medicine, University of Bern, Switzerland; ^{2}Institute of Medical Biometry and Statistics, University of Freiburg, Germany; ^{3}Department of Primary Education, University of Ioannina, Ioannina, Greece; ^{4}Faculty of Medicine, Paris Descartes University, Paris, France

Network meta-analysis estimates all relative effects between competing treatments and can produce a treatment hierarchy from the least to the most desirable option. While about half of the published network meta-analyses report a ranking metric for the primary outcome, methodologists debate several issues underpinning the derivation of a treatment hierarchy. Criticisms include that ranking metrics are not accompanied by a measure of uncertainty or do not answer a clinically relevant question.

We will present a series of research questions related to network meta-analysis. For each of them, we will derive hierarchies that satisfy the set of constraints that constitute the research question and define the uncertainty of these hierarchies. We have developed an R package to calculate the treatment hierarchies.

Assuming a network of T treatments, we start by deriving the most probable hierarchies along with their probabilities. We derive the probabilities of each possible treatment hierarchy (T! permutations in total) by sampling from a multivariate normal distribution with relative treatment effects as means and corresponding variance-covariance matrix. Having the frequencies for each treatment hierarchy to arise, we define complex clinical questions: probability that (1) a specific hierarchy occurs, (2) a given order is retained in the network (e.g. A is better than B and B is better than C), (3) a specific triplet of quadruple of interventions is the most efficacious, (4) a treatment is in at a specific hierarchy position and (5) a treatment is in a specific or higher position in the hierarchy. These criteria can also be combined so that any number of them simultaneously holds, either of them holds or exactly one of them holds. For each defined question, we derive the hierarchies that satisfy the set criteria along with their probability. The sum of probabilities of all hierarchies that fulfill the criterion gives the probability of the criterion to hold. We extend the procedure to compare relative treatment effects against a clinically important value instead of the null effect.

We exemplify the method and its implementation using a network of four treatments for chronic obstructive pulmonary disease where the outcome of interest is mortality and is measured using odds ratio. The most probable hierarchy has a probability of 28%.

The developed methods extend the decision-making arsenal of evidence-based health care with tools that support clinicians, policy makers and patients to make better decisions about the best treatments for a given condition.