# Combining two Odds ratios with the same control group

I am doing a meta-analysis of observational studies. As the disease I am working on has different stages, some of the studies reported ORs (95%CI) for each stage separately in comparison to a single (shared) control population. I wonder if we can combine these two ORs (and their 95%CI) given that they reflect two case groups but a single control group. Some other info:

• The sample size for each case group is different.
• We have the sample size for each of the groups but not the frequency of exposure (otherwise we could use just the raw data).
• Please note that I have no problem combining the ORs, but simply combining two ORs without taking into account that they both have the same control group will cause narrowing of the 95%CI and overweighting of the study in the analysis.

Any ideas?

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If you work with R, you may find the metafor package useful. On the metafor package website, you can find code that will reproduce the methods described in the Gleser and Olkin chapter: http://www.metafor-project.org/doku.php/analyses:gleser2009. That should help to get you started.