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I would like to compare 3 different treatments (no one treatment is considered the placebo, and these are not randomized control trials) from multiple studies in a meta-analysis. I am using the software called "Review Manager" from the Cochrane society, and I am wondering if what I am doing is correct or not:

Say A, B, and C are the different treatments. I make the direct comparisons A vs. B, A vs. C, and B and C to obtain the odds ratios, confidence intervals, Z scores, p values, etc. Then I use the results from A vs. B and A vs. C to calculate the indirect comparison for B vs. C, obtaining the odds ratio and SE.

A vs. BA vs. B Ignore where it says risk ratio, the studies that I will be looking at are all retrospective.

A vs. CA vs. B Ignore where it says risk ratio, the studies that I will be looking at are all retrospective.

I make another analysis with both direct and indirect B vs. C on Review Manager to obtain the odds ratio and statistics for this.

Direct and Indirect B vs. C Results of the analysis Ignore where it says risk ratio, the studies that I will be looking at are all retrospective.

Indirect B vs. C was determined using: Indirect calculations

L or l = log

Please tell me if I am doing this correctly, and whether if this is valid.

If so, how would I report the results from the analysis between the direct and indirect B vs. C? This would be telling me whether if the difference between B and C is significant?

How would I report the overall findings comparing the 3 different treatments?

Thanks for the help!

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    $\begingroup$ are you trying to perform a network meta-analysis? bmj.com/content/346/bmj.f2914 $\endgroup$ – charles Mar 10 '14 at 14:25
  • $\begingroup$ In your third figure, how did you come up with RR=0.42 for the indirect comparison of B vs C? $\endgroup$ – Wolfgang Mar 11 '14 at 9:21
  • $\begingroup$ @charles Yes, I am trying to perform a network meta-analysis. $\endgroup$ – JC22 Mar 11 '14 at 15:14
  • $\begingroup$ @Wolfgang I've added the calculations above for indirect B vs C $\endgroup$ – JC22 Mar 11 '14 at 15:17
  • $\begingroup$ What you are doing is correct but I haven't recalculated them to check your math. This is called the 'Bucher Method' or 'adjusted indirect comparison'. It can be done in a network meta-analysis (or multiple treatment comparison), but also as you have done using GIV to pool the direct and indirect estimates. $\endgroup$ – abousetta Mar 11 '14 at 16:15
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Since this one was effectively answered in the comments this answer just brings it together for the benefit of future readers. Any intellectual credit goes to @abousetta and @wolfgang not to me.

The method outlined is known as Bucher's method after the first author of this paper in J Clin Epid entitled "The results of direct and indirect comparisons in meta--analysis of randomized controlled trials". It is also discussed in the Cochrane handbook. The indirect effect is obtained by subtraction of the log risks for the comparison of the two conditions with a common comparator. The method of network meta-analysis would be appropriate and might have advantages since techniques exist for exploring inconsistency and software for network meta-analysis usually provides interesting graphical display options.

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