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I would like to work on a meta analysis project, I have kept 8 studies that satisfy my criteria and I'd like to continue with these. Their results are formed as odds ratios (OR) and confidence intervals (CI).

I read that I should convert them into log values and estimate the standard errors. I did this, but I don't know how to continue since all examples that I have seen are about trials and provide the accurate numbers of outcomes (i.e. before treatment, after treatment, or death/alive, etc) while I have only ORs and CIs.

Could anyone help me please? Please propose also a free software, capable of analyzing ORs and CIs. Many thanks!

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  • $\begingroup$ Not a meta analysis person, but the 8 papers must have reported the frequency and described the samples. You'll need them to weight each of the studies. Just OR and CI alone will only work if they are of equal weight, which is quite unlikely. $\endgroup$ – Penguin_Knight Feb 23 '15 at 19:42
  • $\begingroup$ I have the sample of each study, but you say me that I also have to find the frequency of each case? I mean that I know the OR of children of single parents with headache for example, and I have to find how many are these children? Did I understand the right thing? $\endgroup$ – user26400 Feb 23 '15 at 19:54
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    $\begingroup$ I think you will find this useful: stats.stackexchange.com/q/13705/1934 $\endgroup$ – Wolfgang Feb 23 '15 at 21:04
  • $\begingroup$ @Penguin_Knight Actually the weighting for a meta-analysis is often based on inverse variance for a study (which is discoverable from the above information) although usual practice is to report numbers with/without outcome for each group for each study. $\endgroup$ – James Stanley Feb 23 '15 at 23:28
  • $\begingroup$ @JamesStanley, thanks for the tips! Meta analysis is a fascinating thing. :) $\endgroup$ – Penguin_Knight Feb 24 '15 at 3:41
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Although I'm not strictly answering your question, I assume you want to calculate a mean effect size. Assuming you are using comparable studies you'll need the odds ratios, which you have, and their variances, which you can recover using the post above. The mean effect size is simply a weighted mean of individual effect sizes: $ES_{mean}=\frac{\sum\limits_{i=1}^kw_{i}ES_{i}}{ \sum{w_{i}^{n=k}}}$ where $ES_{i}$ and $w_{i}$ are the effect size and effect size weight for study i. The weight of each effect size is simply the inverse of the estimate's variance, or $w_{i}=\frac{1}{\sigma^{2}_{i}}$, hence the more precise the estimate, the more weight it carries. There are several R packages to conduct meta-analysis; a simple search should provide what you need.

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  • $\begingroup$ This answer is slightly contradictory on the need for transformation: The answer at (stats.stackexchange.com/a/13708/16974) explains how to do the transformation from the odds ratios (with confidence intervals) back to the log(OR) and associated standard error (which is also on the log scale.) You then do meta-analysis (as per this answer) on the log-scale estimates, and then would exponentiate the result of this from the log scale back into an odds ratio for reporting. $\endgroup$ – James Stanley Feb 24 '15 at 0:45
  • $\begingroup$ The comment above is correct. The statement regarding the need to forgo transformation is incorrect. I'll edit the answer and remove the error. $\endgroup$ – user2472377 Feb 24 '15 at 1:27
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For a 'free' program, you can use Review Manager from the Cochrane Collaboration. You will input the log(OR) and SE for each study into the analysis using the Generic Inverse Function. This can also be done in R and many other 'free' meta-analytic software packages depending on your comfort level with using these programs.

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