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I do not have any experience doing statistics with data from a meta-analysis. However, I am working on a research project at the moment where I must look for a significant difference between groups in the meta-analysis. But my project advisor is off at the moment and I would like to begin this part of the project before he returns. So, I was wondering if someone with experience doing meta-analyses can help me?

There are 3 groups in this meta-analysis (group A,B and C). Each group has a different population and different number of people in each group. Each study in the meta-analysis gives me a proportion of individuals with Thyroid cancer for each group (A,B and C). I would like to find if there is a significant difference in prevalence of Thyroid cancer between the 3 groups. I am a bit confused about how to do this? Do I use a T-test to find the sig. difference in each individual study? Do I find the weighted average of the proportions in each group (ie averaging out the proportions for each study in each of the 3 groups) and then do the t-test? Would it be best to use another statistical test?

@mdewey I have about 50 studies in the meta-analysis. Not all of them use the exact same 3 groups. Some only use one of the groups and others use all 3 (none of them use 2 groups). I have the proportions for each study and group in the study. For example, if a study has 3 groups, then I will have a proportion for each of the groups. I would like to find out if there's an overall significant difference in proportions between the 3 groups.

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    $\begingroup$ Do you mean you have a number of primary studies each of which used exactly the same three groups? Do you have just the proportions or do you have numerator and denominator? $\endgroup$ – mdewey Feb 25 '17 at 16:47
  • $\begingroup$ @mdeweyI have about 50 studies in the meta-analysis. Not all of them use the exact same 3 groups. Some only use one of the groups and others use all 3 (none of them use 2 groups). I have the proportions for each study and group in the study. For example, if a study has 3 groups, then I will have a proportion for each of the groups. I would like to find out if there's an overall significant difference in proportions between the 3 groups. $\endgroup$ – aspire94 Feb 25 '17 at 17:16
  • $\begingroup$ In a meta-analysis, you pick one hypothesis - that's comparing two groups. Then you find the estimate of the difference between the groups (possibly standardized) and its standard error. You don't do a t-test. $\endgroup$ – Jeremy Miles Feb 25 '17 at 19:01
  • $\begingroup$ @JeremyMiles But how does that tell you if there is a significant difference? $\endgroup$ – aspire94 Feb 25 '17 at 20:45
  • $\begingroup$ Your comment which someone has kindly edited into the question for you does not answer all my question. Do you have the absolute frequencies or just proportions? $\endgroup$ – mdewey Feb 26 '17 at 12:40
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The most straightforward way to do this would be to set up your data-set with a row for each group within each study so you would have about 150 rows if all studies had all three groups. The fit a meta-analystic model with a random effect for study and a moderator variable with three levels for group. You would need to decide on which transformation to use for the proportions, options would include: raw proportions, log, logit, Freeman-Tukey and perhaps others. The advantage of this analysis would be that you would be able to incorporate all the studies even those with only one group. The disadvantage of that would be that you are then comparing between as well as within studies since if all the studies which just use group A are fundamentally different in some way that will confound your results.

There are examples of how to do this on Wolfgang Viechtbauer's pages about his metafor package http://www.metafor-project.org/doku.php/analyses

Having said all that you are studying thyroid cancer and although this has a good prognosis none the less human lives may be at stake here and I think you should consider getting expert help locally as if you thought that a $t$-test might work here you may need some more help than we can give you on a question and answer site.

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