# How to carry out adjusted indirect comparison or 'Bucher method' meta-analysis

I have carried out a pairwise meta-analysis of Drug 1 vs. placebo and a pairwise meta-analysis of Drug 2 vs. placebo (I have used RevMan software to do this). From each meta-analyses I have an overall estimate of the log of the risk ratio, accompanied by a standard error.

I want to use the 'Bucher method', or adjusted indirect comparison to get a difference between the two overall estimates (estimate the risk ratio for Drug 2 vs. Drug 1) and obtain an estimate of its variance by adding the variances of the two overall estimates.

However I am not sure how to do this. Essentially all I want to do is for a given outcome determine which drug is better, but I am stuck on having done the pair-wise meta-analysis and don't know how to proceed.

Any help would be greatly appreciated!

Assuming the two groups of studies are independent then http://www.metafor-project.org/doku.php/tips:comp_two_independent_estimates shows you how to do this in R but I think it should be portable to other software although possibly not to RevMan (which I have never used).

Adjusted indirect comparisons are a special case of network meta-analyses, where there is no closed loop in the evidence network. For further details, You can refer to several useful websites, books, and articles, as compiled by Google Scholar. For instance, the website from the Cochrane Collaboration is very complete, and this article by Greco et al is also a useful summary.

Focusing on the Bucher method, the idea behind it is quite simple: if you have trials comparing A vs B and providing an effect estimate of such comparison (e.g. such as log risk ratio [logRR] with corresponding variance [var]), and then trials comparing C vs B (e.g. also providing logRR and var), then the indirect comparison effect estimate of A vs C will be the difference between the two effect estimates above (i.e. logRR of A vs C will be yielded b the difference of logRR of A vs B minus logRR of C vs B). The variance will be instead the sum (not the difference!) of the two variances. From the variance you can easily obtain the standard error (SE) as var=SE^2, and the other way around. Finally, from logRR and SE you can get p values and confidence intervals.

Focusing more on your case, you could use simply Excel and a few formulas, for instance using this Excel sheet which was built mainly for educational purposes. However, for consistency and style I recommend you use Stata or R, especially if you want to publish your findings in a scholarly venue.

Given that you may get several ancillary analyses, including evidence networks and funnel plots, the best option in my opinion is to rely on mvmeta (as well as network graphs) in Stata, or netmeta in R. They are both frequentist and almost correspond to the Bucher method when only indirect comparisons are envisioned.

I cannot run it, so I cannot recommend it to you, but Stata should also have a specific command for this, indirect, by Miladinovic et al.

• Thanks for your reply. Stata or R sounds really complicated. I am an undergraduate student doing a systematic review (dissertation) on 2 drugs to determine which, (if any) is more efficacious. I have looked into network meta-analysis however unfortunately it is quite above my scope to comprehend it, so I thought to follow Bucher's method indirect comparison. Do you know if there is a simple way of differentiating between 2 different risk ratios (Drug 1 vs placebo, Drug 2 vs placebo to get and idea of Drug 1 vs Drug 2)? thanks! – Harose Mar 23 '16 at 17:20
• I have edited my reply providing some suggestions for beginners. Note though that if you want to submit it for a scholarly publication you will need to do it proficiently. – Joe_74 Mar 23 '16 at 20:28
• Dear Guiseppe, thank you very much! May I ask, when obtaining risk ratio from Revman, is given as logRR? for e.g. I have got 1.54 [0.98, 2.42] M-H. Would I need to log1.54? or is it already in the log format? Thank you in advance. – Harose Mar 23 '16 at 21:44
• RevMan provides you RR, not logRR. You thus need to log-transform it (natural logarith). If the SE is not reported, you can back calculate it from the 95% confidence interval, which is indeed built as: exp ( logRR +/- 1.96 * SE ). – Joe_74 Mar 23 '16 at 21:58
• Dear @guiseppe , the Excel sheet you provided looks at Odds Ratio, I have risk ratio for the two drugs, could you tell me how I can use it for risk ratios please. I do apologise, I have very little experience in using computer programs and in meta-analytical methods. Many thanks – Harose Apr 16 '16 at 10:46