# Network meta-analysis framework

### Why does Kiuse network meta-analysis?

Meta-analytic methods provide comparative effectiveness research for interventions of the same condition. By utilizing the meta-analysis methods, the synthesis of numerous studies can provide precise estimates and inform clinical practice for the promotion of healthy growth. Network meta-analysis is a subset of meta-analysis that leverages data from direct evidence to estimate indirect comparisons between two comparators that are not directly compared.

### WHAT ARE META-ANALYSIS AND NETWORK META-ANALYSIS?

Traditional meta-analysis is a pairwise approach to consolidate effect estimates between a single intervention and control. This approach calculates a weighted average effect across multiple studies.

Network meta-analysis allows comparisons of multiple interventions for the same health condition by using indirect and direct comparisons.[1, 2]

Network diagrams include nodes (specific interventions) and lines that connect the nodes (which represent a randomized clinical trial [RCT]) to visualize the direct estimates (Figure 1). ###### FIGURE 1. Indirect and direct evidence

Direct evidence, also referred to as head-to-head evidence, is the estimate reported from an RCT between two nodes. (2) Indirect comparisons are conducted by identifying a common comparator between two different interventions and calculating an indirect estimate of the effect (Figure 2).

An example of an indirect estimate is between treatment B and C (no line connecting the two nodes). In this example, treatment B has an estimated effect that is significantly lower effect than treatment C, although they were never directly compared. ### Statistical methods

There are two primary approaches to statistical analysis of NMA: Frequentist and Bayesian.

• Frequentist analyses utilize population probability distributions to assess the probability of the observed data.
• Bayesian analyses (which is the more commonly used analysis for NMA) define the probability distribution based on the observed data and external information about the parameters. For example, if there is a known logarithmic growth shape for caloric intake as a predictor on malnutrition as a response variable, then the Bayesian approach would utilize this predetermined relationship to inform the model.

Local or global approaches test the model for inconsistency.

The local approach determines the presence of inconsistency in a specific head-to-head comparison in the network (i.e. if two trials of the same intervention have different outcomes, then the test for local approach consistency is violated). The global approach evaluates inconsistency across the entire network (i.e. when comparing indirect trials and there are different outcomes, then the test for global approach consistency is violated).

NMA requires at least 3 comparators. The availability of multiple trials for each comparator is advantageous.

• Studies included in NMA assume Congruence.
• Congruence requires inclusion of similar studies to ensure their effect measures are combinable, which includes study and patient characteristics.
• NMA assumes Homogeneity of trial results for the same head to head pair comparisons.
• NMA assumes Transitivity, or equal distribution of effect modifiers, to ensure direct and indirect estimates are consistent.

Example: A valid indirect estimate can be calculated between intervention A and intervention B, if a direct estimate of intervention A versus placebo A and a direct estimate of intervention B versus placebo A were obtained among participants with similar baseline comorbidities, treatment doses, and of similar study quality. ###### FIGURE 3. Network diagram of micronutrient supplementation and deworming for children from Rally 4B. The numbers are the number of direct comparisons from RCTs for each connecting line.

NMA improves the precision of estimates (reduces the confidence interval) by combination of multiple study results and calculating a relative treatment effect for all treatment interventions.

Graphical representation of the network helps describe the evidence. Nodes or edges can be proportional to the amount of data available from direct comparisons (Figure 3).

• Depending on the number of comparators, there may be a complex set of outputs.
• Assumed homogeneity can be difficult when including several comparators.
• Effect modifiers are frequently underreported, making the transitivity assumption untestable.
• The statistical modeling is complex, and lack of interpretability prevents utilization from other researchers using simpler methods.