Hi everyone,

I want to do meta-analysis based on some previous meta analyses study, and also some older independent studies on GWAS data. For example, I combine independent study X, independent study Y, meta-analysis study on X, Y, plus their own data set called Z, and so on. The software that I use utilize Stouffer's Z method to combine the Z-score from each study. However, I am not convinced whether it is an acceptable method for doing second order meta analysis, because I can clearly see that some studies will be counted twice or more during the second order meta analysis. If it's acceptable or even the right way to do it, may you guide me through the mathematical derivation on why it is the correct way. If not, is there any other alternative method that you know is more reliable than Stouffer's Z method. Or if I better need to clean my data, which data should I remove or retained?

Thank you!