# How to perform a meta-analysis with combination of single and multiple groups

I am intending to perform a meta-analysis to analyze efficacy and safety profile of particular intervention. However, out of 9 studies included, some of them consists of a single group (experimental only), and the other consists of 2 groups (experimental and control).

I was wondering, can I perform meta-analysis with these data or do I have to exclude some of them? If I can, is there any guideline or example of how it's done? Another question will be, what software can I utilize to perform the meta-analysis?

Thank you very much

• Very general questions -> very general answers. Be more specific. – user2974951 Jan 17 at 7:31
• A perfect choice would be mvmeta, which can encompass missingness. – Joe_74 Jan 19 at 17:52

Secondly, one of the more obvious approaches is to use a generalized linear mixed effects model (GLMM). The very simplest form would be $$g(E Y_{ij}) = \beta_i + \gamma_j + \delta_{ij},$$ where $$Y_{ij}$$ is the outcome in arm $$j$$ of trial $$i$$, $$g()$$ is the link function, $$\beta_i$$ is the main effect for trial $$i$$, $$\gamma_j$$ is the (fixed) main effect for treatment $$j$$ and $$\delta_{ij}$$ is the deviation from effect off treatment $$j$$ in trial $$i$$ (treatment by trial interaction). Crucially, $$\beta_i$$ and $$\delta_{ij}$$ are random effects (which makes this model identifiable) that e.g. follow $$N(0, \tau_\beta)$$ and $$N(0, \tau_\delta)$$ distributions. If you do a frequentist analysis this does not matter, but I believe one would usually use a sum to zero constraint on the treatment main effects for a Bayesian analysis.