Three's a Crowd: How to Deal with More than Two Arms in a Meta-Analysis

It is not uncommon to come across the following scenario: when conducting a meta-analysis between two arms (e.g., an active therapy vs. a placebo), the meta-analyst includes a study that actually included two active arms (e.g., two different doses of the same experimental drug vs. placebo, two different routes of administration, etc.) Let's say that both of these arms were relevant to the clinical question. How should meta-analysis be undertaken in this case? A new tutorial article published in Cochrane Evidence Synthesis and Methods gives a primer on how to approach this common conundrum. 

Including the study twice in the forest plot – for instance, with one dose versus placebo and the other versus the same placebo group – is statistically problematic. It leads to a "unit of analysis" error by essentially "double-counting" the participants in the control group and violating the assumption that every individual participant is only counted twice. (Aside: this is also a common error in meta-analyses combining multiple similar outcomes – e.g., including the handgrip strength of both the dominant and non-dominant hand in the same forest plot – and risks committing the same violation unless advanced multi-level statistical techniques are used to account for this). 

This leaves two basic options for including the data from more than two study arms into the same forest plot: combining interventions that are similar, and splitting the control group in half. For instance, if the three groups in question are as such (assuming a dichotomous outcome):

• Experimental group A: 50 participants, 45 of whom had the event.
• Experimental group B: 50 participants, 41 of whom had the event.
• Control group: 50 participants, 22 of whom had the event.

These two experimental groups can either be combined (100 participants, 89 of whom had the event) and compared to the control group as-is, or they can be split out and compared (on separate lines of the forest plot) to half of the control group on each line:

• Experimental group A (45 out of 50) versus control (11 out of 25)
• Experimental group B (41 out of 50) versus control (11 out of 25).

Both approaches will yield very similar pooled results.

In the case of a continuous outcome, the same general approaches can be applied. However, if pooling two or more arms together, a pooled mean and SD will need to be calculated using the following equations from the Cochrane Handbook:

Reference: Axon, E., Dwan, K., & Richardson, R. (2023) Multiarm studies and how to handle them in a meta-analysis: A tutorial. Cochrane Evidence Synthesis and Methods. Available at publisher's website here.