# Meta-analysis of odds ratios

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? Also, please propose a free software capable of analyzing ORs and CIs.

• 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. Feb 23 '15 at 19:42
• 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? Feb 23 '15 at 19:54
• I think you will find this useful: stats.stackexchange.com/q/13705/1934 Feb 23 '15 at 21:04
• @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. Feb 23 '15 at 23:28
• @JamesStanley, thanks for the tips! Meta analysis is a fascinating thing. :) Feb 24 '15 at 3:41

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.