[R-meta] Ratio of Means

Viechtbauer Wolfgang (SP) wolfgang.viechtbauer at maastrichtuniversity.nl
Thu Jul 20 10:08:06 CEST 2017

As for using the control group value as a moderator in a meta-regression model: The same concerns apply (actually, most of the papers on that issue were concerned with binomial outcomes and measures like the risk difference/ratio and the odds ratio, but the same concerns apply whether we are dealing with those types of measures or things like mean differences or response ratios).

A relatively straightforward way of examining the relationship between the control and treatment group value is the bivariate model. See, for example:

van Houwelingen, H. C., Arends, L. R., & Stijnen, T. (2002). Advanced methods in meta-analysis: Multivariate approach and meta-regression. Statistics in Medicine, 21(4), 589-624.

The analyses from that paper are also reproduced here:


I do not go into the 'baseline risk' part of the analysis on that page, but once you have fitted the bivariate model, the rest is easy:


### bivariate model
res <- rma.mv(yi, vi, mods = ~ group - 1, random = ~ group | trial, struct="UN", data=dat.long, method="ML")

### var-cov matrix of the random effects

### slope of regression of the underlying true log odds in treatment groups on the log odds in control groups
with(res, G["EXP","CON"] / G["CON","CON"]) ### ~ 0.730 (see page 605 in article)

### standard error of the slope (not given in paper)
r <- with(res, G["EXP","CON"] / sqrt(G["EXP","EXP"] * G["CON","CON"]))
sqrt(with(res, G["EXP","EXP"]/G["CON","CON"] * (1-r^2) / (res$g.levels.comb.k - 2)))

So that relationship is highly significant here.

One can do the same with response ratios. So, for the bivariate model, you analyze the log(m1i) and log(m2i). You will find that (since version 2.0-0) escalc() has measure="MNLN" (log transformed mean) for exactly that purpose.


Wolfgang Viechtbauer, Ph.D., Statistician | Department of Psychiatry and    
Neuropsychology | Maastricht University | P.O. Box 616 (VIJV1) | 6200 MD    
Maastricht, The Netherlands | +31 (43) 388-4170 | http://www.wvbauer.com    

-----Original Message-----
From: James Pustejovsky [mailto:jepusto at gmail.com] 
Sent: Thursday, July 20, 2017 00:19
To: Nathan Pace
Cc: Viechtbauer Wolfgang (SP); r-sig-meta-analysis at r-project.org
Subject: Re: [R-meta] Ratio of Means


I don't know the answer to your question exactly, but I would offer two suggestions that might help you find a good approach for meta-analysis:

First, many clinical studies are woefully sloppy about distinguishing between sample standard deviations versus standard errors (which might be reported if the sample means are estimated with adjustment for baseline covariates). If you have not already done so, it might be worth double checking that your data are truly the raw sample standard deviations. If some of them are actually SEs, then the effect size variances will be under-estimated by a substantial factor, and this in turn might account for the high degree of observed heterogeneity. 

Second, are the outcomes (average drug doses) on a scale that is directly comparable across studies? If so, either an unstandardized mean difference or a response ratio could be an appropriate effect size metric. To determine which metric to use, you might try creating a scatterplot with control group means on the x axis and treatment group means on the y axis. If the scatter resembles a 45-degree line that does not intercept the origin, then the unstandardized mean difference might be a better summary. If the scatter resembles a line (with higher or lower slope) through the origin, then the response ratio might be a better summary.


On Wed, Jul 19, 2017 at 5:05 PM, Nathan Pace <n.l.pace at utah.edu> wrote:
The outcomes in my example are average drug doses under an experimental and a control condition, so ratio scale measurements.

In a RoM meta analysis there is very high heterogeneity (I2 = 94%).

There is interest in whether a control group mean value as a moderator will improve the model and reduce the heterogeneity.

Adding this moderator does not improve the model or reduce heterogeneity.

It is generally recommended to not use a control group value as a moderator in meta regression of the mean difference (various papers by Sharp, etc).

Does this recommendation still apply when the study values have been transformed into the RoM and not using the mean difference?

Does this require a different model or a Bayesian meta regression?

Your insights are much appreciated.


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