[R-meta] Ratio of Means

Hi,

Thanks for the pointers and links.

Next problem is using the measure = ?MNLN? in escalc.

I created the 2k data frame.

arm.df

              study group  mean    sd   n
1        Arici 2009   Exp 35.73  5.24  27
2        Arici 2009   Ctl 62.93  8.67  27
3       Arslan 2011   Exp  4.25  2.03  20
4       Arslan 2011   Ctl 11.25  5.03  20
5       Arslan 2013   Exp  5.15  4.29 100
6       Arslan 2013   Ctl   9.1  4.68 100
7      Aydogan 2008   Exp  0.27  0.08  40
8      Aydogan 2008   Ctl  0.35  0.09  40
9        Cakan 2008   Exp    11     2  20
10       Cakan 2008   Ctl    12     2  20
11       Cobby 1999   Exp    35  20.4  24
12       Cobby 1999   Ctl  54.9  28.3  21
13        Dahl 1997   Exp  21.2  7.88  22
14        Dahl 1997   Ctl  18.7   5.9  21
15      Dilmen 2010   Exp  18.1 13.93  20
16      Dilmen 2010   Ctl    30 11.32  19
17      Durmus 2007   Exp  30.5 11.55  25
18      Durmus 2007   Ctl 42.74 12.33  25
19        Emir 2010   Exp  7.65  0.78  30
20        Emir 2010   Ctl  13.8  2.26  30
21       Fayaz 2004   Exp    12     6  17
22       Fayaz 2004   Ctl    22    13  17
23      Jokela 2010   Exp 38.85  16.8  40
24      Jokela 2010   Ctl 45.15  18.9  40
25     Khalili 2013   Exp     3  2.28  25
26     Khalili 2013   Ctl   4.2  1.57  25
27  Kilieaslan 2010   Exp 20.56   0.4  25
28  Kilieaslan 2010   Ctl  28.6  0.35  25
29     Koppert 2006   Exp    17    22  25
30     Koppert 2006   Ctl    38    22  25
31    Kvalsvik 2003   Exp    16     5  30
32    Kvalsvik 2003   Ctl    20     6  30
33  Montgomery 1996   Exp  27.1    27  19
34  Montgomery 1996   Ctl  34.5  15.1  20
35        Moon 2011   Exp   8.7   5.4  36
36        Moon 2011   Ctl  12.6   6.9  35
37 Munishankar 2008   Exp  33.8  23.8  25
38 Munishankar 2008   Ctl  44.1  24.4  25
39     Sinatra 2005   Exp  38.3  35.1  49
40     Sinatra 2005   Ctl  57.4  52.3  52
41        Syal 2010   Exp  9.53  1.88  30
42        Syal 2010   Ctl 10.19  2.08  30
43      Toygar 2008   Exp  16.5  11.1  30
44      Toygar 2008   Ctl  34.3  11.8  30
45      Yalcin 2012   Exp 48.53  12.4  26
46      Yalcin 2012   Ctl 73.03 22.41  27

The call to escalc returned an error:

arm.df <- escalc(measure = 'MNLN', mi = mean, sdi = sd, ni = n)

Error in sdi < 0 :
  comparison (3) is possible only for atomic and list types

?????


Nathan


-----Original Message-----
From: "Viechtbauer Wolfgang (SP)" <wolfgang.viechtbauer at maastrichtuniversity.nl>
Date: Thursday, July 20, 2017 at 02:08
To: "r-sig-meta-analysis at r-project.org" <r-sig-meta-analysis at r-project.org>
Cc: James Pustejovsky <jepusto at gmail.com>, Nathan L Pace <n.l.pace at utah.edu>
Subject: RE: [R-meta] Ratio of Means

    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:

    http://www.metafor-project.org/doku.php/analyses:vanhouwelingen2002

    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")
    res

    ### var-cov matrix of the random effects
    res$G

    ### 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.

    Best,
    Wolfgang

    --
    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

    Nathan,

    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.

    James

    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.

    Nathan