I would suggest you calculate  weighted means of frequencies  from all studies in each cell population, the weights being inverse variance (w =1/SE 2). Then compare the two weighted means. The SE of the weighted mean would be estimated as 1/(sigma w)1/2

Hi James,

Thank you for your notes. I would let you know that we aim to consider tumorigenicity potential in two groups of cancer cell population A and B by meta-analysis. So, we assumed that it can be affected by the frequency of cancer stem cells (CSCf) in group A and B. Therefore, we calculate the tumorgenicity potential (Tp) parameter for each study as below:

Tp=CSCfA/CSCfB

Tp: tumorgenicity potential

CSCfA: frequency of stem cells in group A

CSCfB: frequency of stem cells in group B

For calculating the CSCf in each group we included studies that inject different number of cells in NOD mice and have calculated the tumor incidence in each group A and B. Using tumor incidence data, we calculate the CSCf and CI 95% by means of Extreme Limiting Dilutions Analysis (ELDA) online  software (http://bioinf.wehi.edu.au/software/elda/).

The point is how can I perform a meta-analysis between different studies while we are considering Tp? (I guess "mean difference" doesn't make sense in this case for comparison of two groups). What is the "mean of frequency" in this example? and  what is the sample size exactly?

Attached please find a sample data from two independent study:

without knowing how your ELDA software works, i would suggest either (1)  pool all the raw data from all studies (if comparable enough biologically and method wise) and get a pooled CSCfA and a pooled CSCfB and use the ratio  of these pooled esimates as your meta Tp   or (2) using the CSCfA and CSCfB  (with SEs) do a weighted mean CSCfA  and a weighted mean CSCfB (as discussed before) and use the ratio of these weighted means as your meta Tp.

I note order of magnitude differences in your sample data and not sure if this is typical data.