# Multilevel Meta-analysis with several treatments

I have data on a number of studies comparing response rates to various treatments of a disorder. There are six different treatments, and some studies only test a single treatment. For each treatment in each study, I have the response rate and the sample size (plus some other variables).

Normally, if there were only two treatments, and each study compared the two, I might use something like $$D_i=\beta_0+\beta_1\cdot SS_i+u_i+\epsilon_i$$ where $D_i$ is the difference between the logits of the response rates in study $i$, $\epsilon_i$ is the corresponding sampling error, $SS_i$ is the sample size of study $i$, and $u_i$ is the residual error term.

Is it possible to sensibly analyze my data in a similar way? Are there keywords / references I should be aware of?

For example, I'd like to use something like $${\rm logit}(RR_{ij})=\beta_0+\beta_1\cdot SS_{ij}+\beta_2\cdot T_j+u_i+\epsilon_{ij}$$ where $i$ is the study and $j$ is the treatment (1 to 6), $T_j$ is an indicator variable for the treatment (alternatively, could be turned into a second random effect), and $u_i$ and $\epsilon_{ij}$ are as above.