# Meta Analysis for Binary Outcome, Two Groups, Pre and Post

This seems like a straight-forward problem, but I can't seem to wrap my head around it.

I have a binary outcome (Presence/Absence of a condition for a patient), and an intervention (educational training for the physician).

For each of the four papers included, I have the number of patients studied at baseline and follow-up, and the percentage that experienced the event, before and after the intervention was administered. Exact data below:

         Paper intervention n.base rate.base n.follow rate.follow
1       Paper1      control     72     0.514       72       0.639
2       Paper1          int     74     0.527       74       0.554
3       Paper2      control    176     0.324      159       0.252
4       Paper2          int    183     0.355      174       0.092
5       Paper3      control    192     0.443      192       0.318
6       Paper3          int    190     0.432      189       0.037
7       Paper4      control    173     0.624      173       0.613
8       Paper4          int    211     0.668      211       0.436


What is the best way to study this data? I thought about looking at the change in rates pre vs post, and then those differences, but I can't figure out what the SD would be in that case, or the appropriate sample size. Any advice would be greatly appreciated.

For measuring change in a design where the outcome is binary use is usually made of those poepl who changed between baseline and follow-up as the ones who remain constant are usually seen as uninformative for the hypothesis. From the data presented it is not clear whether this information is available since it cannot be derived from the proportion before and after directly. If it is then there are nw four frequencies from each study, not eight, and so an odds ratio can be computed.

You will be happy to learn that your problem is easy to solve !

You will have to calculate the odds ratio for each of your studies (the odds for the event to happen). I could explain it to you, but a lot of far better experts than I already did it. Quickly, I found those good links:

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2938757/

http://handbook.cochrane.org/chapter_9/9_2_2_2_measures_of_relative_effect_the_risk_ratio_and_odds.htm

Usually, odds ratio are transformed into log odds ratio for computations. See Borenstein, M., L. V. Hedges, J. P. T. Higgins et H. R. Rothstein (2009). Introduction to meta-analysis. Chichester, UK, John Wiley & Sons, Ltd. for details (excellent book)

Finally, note that there are equations to calculate variance for the odd ratio. Good reading !

Edit: Ok, as I've tried calculating the odds ratio, I realize you are right, you have two odds ratio.

I would calculate the odds ratio for the control and for the intervention and use "treatment" (intervention or control) as a moderator in your meta-analysis. That would be really easy and you could evaluate the effect of the intervention on the outcome. If that is your goal...

• The problem is that the study doesn't have a single odds ratio, it has two, there's an odds ratio for improvement for both the intervention and the control groups. Both of your links explain ORs as the single outcome, not a comparison of ORs – slammaster Jul 20 '15 at 14:32
• I've re-checked the links, and I think you are wrong. The odd ratio effect size compare the odds between an experiment and a control. I'll try to improve my answer by doing an example with the data you gave. – Emilie Jul 20 '15 at 15:37
• I was wrong, and I updated my answer. I hope it can help you ! – Emilie Jul 20 '15 at 15:43