One trial has three treatment arms and one control. How do I extract it for my meta-analysis in CMA?

Of course. It is a small problem and easy to solve.

A study with A1, A2, A3 and a control is called a multi-arm study. For data extraction there are two approaches, and this is how Cochrane puts it. I list below the reference you can cite in your Materials and Methods.

To include a study with more than two intervention groups in a meta-analysis, a recommended approach is (i) to omit groups that are not relevant to the comparison being made, and (ii) to combine multiple groups that are eligible as the experimental or comparator intervention to create a single pair-wise comparison.

• Higgins JPT, Eldridge S, Li T. Chapter 23: Including variants on randomized trials (last updated October 2019). In: Cochrane Handbook for Systematic Reviews of Interventions, version 6.5. Cochrane, 2024. https://www.cochrane.org/authors/handbooks-and-manuals/handbook/current/chapter-23

Let me explain with an example. Suppose the drug is A, and A1, A2 and A3 are doses of 1 mg, 2 mg and 3 mg.

The first approach is to drop the groups that are not relevant. For example, if all your other studies compare 3 mg of A with control, that is, A3 versus control, simply ignore A1 and A2 and use only A3 versus control.

The second approach is to combine the three groups. For example, if your other studies include A1 versus control and also A2 versus control, and your meta-analysis only asks whether A works regardless of dose, you can combine A1, A2 and A3 in this study into a single A group and treat it as one A versus control comparison.

To combine the three groups you need to handle three numbers: N, mean and SD. N is simple: add the three groups. The mean is a weighted average, which you could still manage with a calculator, but the SD is a bit tricky. The Cochrane Handbook gives the formula in Table 6.5.a (Section 6.5.2.10). It combines two groups at a time, so combine A1 and A2 first, then combine that result with A3.

For this I recommend an online calculator. This is the one I use: enter N, mean and SD for each group, and it calculates the combined values for you. The page shows more than one formula for the combined SD. Choose the one with N − 1 in it, which is the same as the Cochrane formula; the other one divides by N and gives a slightly different result.

• Combined mean and standard deviation calculator (AtoZmath): https://atozmath.com/CONM/Ch2_CombinedSD.aspx
• Higgins JPT, Li T, Deeks JJ (editors). Chapter 6: Choosing effect measures and computing estimates of effect (last updated August 2023), Section 6.5.2.10 and Table 6.5.a. In: Cochrane Handbook for Systematic Reviews of Interventions, version 6.5. Cochrane, 2024. https://www.cochrane.org/authors/handbooks-and-manuals/handbook/current/chapter-06#section-6-5-2-10