Equation (12.1) from before, which allows us to estimate indirect evidence from direct comparisons, only holds if a crucial pre-requisite is met: the assumption of transitivity. We can have a much higher confidence in effect sizes which were estimated from observed data, compared to results which had to be inferred mathematically. This means that effect sizes estimated from indirect evidence will always have a greater variance, and thus a lower precision, than the ones based on direct evidence ( Dias et al. To calculate the variance of the indirect comparison, we add up the variances of the direct comparisons. We can describe the relationship between A and B in terms of the effect size \(\hat\theta_ \right) In our case, the interpretation of the line is quite easy. The edge represents how A and B relate to each other. The second component is the line connecting these two nodes.
#Transitivity network analysis definition trial
The first one are two circles (so-called nodes), which represent the two conditions A and B in trial \(i\). Graphs are structures used to model how different objects relate to each other, and there is an entire sub-field of mathematics, graph theory, which is devoted to this topic. This visual representation of a treatment comparison is called a graph. We will therefore go through the essential details in small steps, in order to get a better understanding of this method. The underpinnings of network meta-analysis can be a little abstract at times. Therefore, it is important to first discuss the core components and assumptions of network meta-analysis models. However, this method also comes with additional challenges and pitfalls, particularly with respect to heterogeneity and so-called network inconsistency ( Salanti et al. In the last decade, it has been increasingly picked up by applied researchers in the bio-medical field, and other disciplines. Network meta-analysis is a “hot” research topic. This is because it integrates multiple direct and indirect treatment comparisons into one model, which can be formalized as a “network” of comparisons. Network meta-analysis is also known as mixed-treatment comparison meta-analysis ( Valkenhoef et al. Network meta-analysis can be used to incorporate such indirect comparisons, and thus allows us to compare the effects of several interventions simultaneously ( Dias et al. For example, it is possible that two medications were never compared directly, but that the effect of both medications compared to a pill placebo has been studied extensively. Different treatments may have been evaluated in separate trials, but all of these trials may have used the same control group. However, while direct comparisons between two or more treatments may not exist, indirect evidence is typically available. This often means that traditional meta-analyses can not be used to establish solid evidence on the relative effectiveness of several treatments. In many research fields, it is common to find that only few–if any–trials have compared the effects of two treatments directly, in lieu of “weaker” control groups. To assess the comparative effectiveness of several treatments in a conventional meta-analysis, sufficient head-to-head comparisons between two treatments need to be available. Instead, we want to find out which treatment is the most effective for some specific indication. Especially in “matured” research fields, it is often less relevant to show that some kind of treatment is beneficial. Migraine, for example, can be treated with various kinds of medications, and non-pharmaceutical therapy options also exist. Yet, in many research areas, there is not only one “definitive” type of treatment–there are several ones. All else being equal, this allows to assess if a specific type of treatment is effective. We include studies in which the same type of intervention was compared to similar control groups, for example a placebo. Hen we perform meta-analyses of clinical trials or other types of intervention studies, we usually estimate the true effect size of one specific treatment.