[R-meta] inner-outer-grouping-factor-structure for multiple treatment studies

Dear Vivien,

This can be thought of as a network meta-analysis, so indeed, the 
dat.hasselblad1998 and dat.senn2013 datasets and the corresponding code 
in the example section of the corresponding help files are quite relevant.

The dataset as given is in the format for a 'contrast-based' analysis. 
And when you have studies where the same group is being reused for 
computing the outcomes, then this results in dependency in the sampling 
errors of those outcomes. You may want to study carefully:

http://www.metafor-project.org/doku.php/analyses:gleser2009

You are dealing with multiple treatment studies. The code given there 
illustrates the computation of the covariance of outcomes that share a 
common group. I do not cover measure="ROM" there, but the covariance is:

sd^2/(n*mean^2)

from the group whose data is being re-used. So, if you want to compute 
this programmatically, you will have to do some coding to make that work 
(and it's a bit more complex in your case, since sometimes the first and 
sometimes the second group appears to be the 'reference' group). But the 
idea is that you need to build the entire V matrix.

And indeed, that will capture the higher dependency in such studies.

Then you need to go back to help(dat.hasselblad1998) and 
help(dat.senn2013) to see how the modeling is done there using a 
contrast-based model. It is shown there, so I rather not repeat all of 
that here.

A final note:

escalc() does not have a 'method' argument, so the 'method = "REML"' 
part of your call to escalc() doesn't do anything.

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

Hi,
I would need help about the way to model mutliple treatment studies.
I have been posting a question on
https://stats.stackexchange.com/questions/300425/metafor-rma-mv-function-inner-outer-grouping-factor-structure
and was told to write to this list :

I would like to know how to use the inner/outer grouping factor structure
when my data set present some multiple treatment studies (e.g., when
multiple treatment groups are compared with a common control/reference
group, such that the data from the control/reference group is used multiple
times to compute the effect sizes or outcomes)? I have been practicing the
metafor examples "dat.hasselblad1998" and "dat.senn2013" where such
multiple treatment studies exist but I could not understood exactly how the
reference group was designated.

I'm performing a meta-analysis on the impact of reforestation/forest cover
change on the soil organic matter content. Here is the dataset I'm using
(sep=";") :

     1.
   
article;Land_use_change;forest_N;forest_mean;forest_sd;ref_N;ref_mean;ref_sd;inner_group_struct
     2. Hes;Forestation ? native forest;5;2,5;0,6;5;8,5;3,1;1
     3. Hes;Forestation ? native forest;5;9,1;1,2;5;22,4;3,2;2
     4. Hes;Forestation ? native forest;5;9,9;1,2;5;13,0;2,7;3
     5. Hes;Afforestation ? ungrazed grassland;5;0,6;0,2;5;0,6;0,0;4
     6. Hes;Afforestation ? ungrazed grassland;5;1,6;0,4;5;2,8;1,2;5
     7. Henr;Afforestation ? ungrazed grassland;3;6,0;0,5;3;7,0;0,4;6
     8. Henr;Afforestation ? grazed grassland;3;6,0;0,5;3;5,9;1,0;6
     9. Henr;Afforestation ? grazed grassland;3;5,9;3,2;3;5,6;4,8;7
     10. Konin;Regrowth ? grazed grassland;8;6,7;2,0;8;4,2;1,1;8
     11. Konin;Regrowth ? grazed grassland;8;9,0;3,3;8;6,4;1,7;9
     12. Konin;Regrowth ? grazed grassland;8;8,0;0,8;8;8,6;3,0;10
     13. Konin;Regrowth ? grazed grassland;8;6,3;1,6;8;5,3;0,9;11
     14. Konin;Regrowth ? grazed grassland;8;6,8;1,5;8;5,3;2,3;12
     15. Dub;Afforestation ? native forest;6;7,6;1,0;6;10,6;1,1;13
     16. Dub;Afforestation ? grazed grassland;6;7,6;1,0;6;13,5;0,8;13
     17. Chaco;Afforestation ? native forest;6;36,6;12,1;6;40,7;17,9;14
     18. Chaco;Afforestation ? grazed grassland;6;40,5;7,7;6;40,3;7,7;15
     19. Rhoade;Forestation ? native forest;10;9,2;4,1;10;11,3;2,5;16
     20. Rhoade;Forestation ? native forest;10;12,9;4,1;10;11,3;3,5;16
     21. Rhoade;Regrowth ? grazed grassland;10;9,2;4,1;10;9,3;2,7;16
     22. Rhoade;Regrowth ? grazed grassland;10;12,9;4,1;10;9,3;2,7;16
     23. Schlatte;Forestation ? native forest;10;14,3;3,1;12;12,6;2,9;17
     24. Farle;Afforestation ? ungrazed grassland;10;5,7;1,6;30;7,2;1,9;18
     25. Farle;Afforestation ? ungrazed grassland;30;6,0;0,9;30;7,2;1,9;18
     26. Farle;Afforestation ? ungrazed grassland;30;4,7;1,1;30;7,2;1,9;18
     27. Nosett;Afforestation ? ungrazed grassland;5;8,6;6,9;3;8,8;7,0;19
     28. Nosett;Afforestation ? grazed grassland;5;8,6;6,9;5;9,0;7,0;19
     29. ManN;Afforestation ? grazed grassland;24;7,5;0,8;24;5,7;1,0;20
     30. Breme;Afforestation ? grazed grassland;60;45,1;3,4;66;39,7;5,4;21

article refers to the study where the data are extracted, Land-use change
is the fixed effect I'm interested in. In each row, I'm comparing a
forestation situation with the referent situation and I've used escalc to
compute the effect size= log ratio of the means

ma.grass=escalc(m1 = forest_mean, m2 = ref_mean,
              sd1 = forest_sd, sd2 = ref_sd,
              n1 = forest_N, n2 = ref_N,
              method = "REML", measure = "ROM",slab=article,
              )

The articles "Dub", "Rhoade", "Farle" and "Nosett" are multiple treatment
studies. For example in "Farle", the the soil matter content of 3 different
pine plantations are compared to a single control. In the same time, an
article like "Hes" gives 5 contrasts from 5 paired-site measurement. Indeed
those 5 contrasts are not independent (same methodology, they come from the
same region, etc...) but I believe the correlations between the contrast
are less strong than between contrasts calculated from the same reference
group as in the above multiple treatment studies. How can I model correctly
these *a prior* different type of correlations within studies? My guess is
I need to use article as the outer factor but I don't know what to write in
the inner factor. I have been trying many different inner group factors but
in any cases the results were satisfying. For example, like in
"dat.hasselblad1998" and "dat.senn2013", I used :

metamodel1=rma.mv
(yi,vi,data=ma.grass,mods=~Land_use_change-1,random=~factor(id)|article,method="REML")

but the results were not satisfying to me since the Land use change
"Afforestation - ungrazed grassland" should be significantly <0

I then created a "inner_group_struct"

metamodel3=rma.mv(yi,vi,data=ma.grass,mods=~Land_use_change-1,random=~factor(inner_group_struct)|article,struct="UN",method="REML")

but it is still not satysfing : the Land.use_change "Forestation - native
forest" is estimated to be >0 while almost all the raw Effect Size from
this treatment apart 1 are negative.

any help will be much appreciated for modeling the inner group structure.
Kind regards

Vivien BONNESOEUR
Docteur en biologie foresti?re

Dear Wolfgang
first of all, thank you very much for your quick and kind answer. I'm new
in this community and I find your work very useful. I'm sure I will manage
to perform this analysis with your help but for the moment I still have a
few difficulties.

I've been changing the way I'm computing the effect size and I have been
using the standardised mean difference instead of the log ratio of the mean
to be able to use the code from "gleser 2009".  In this code, the
covariance is :
matrix <http://stat.ethz.ch/R-manual/R-devel/library/base/html/matrix.html>(
1/x$n2i[1] + outer
<http://stat.ethz.ch/R-manual/R-devel/library/base/html/outer.html>(x$yi,
x$yi, "*")/(2*x$Ni[1]), nrow
<http://stat.ethz.ch/R-manual/R-devel/library/base/html/nrow.html>=nrow
<http://stat.ethz.ch/R-manual/R-devel/library/base/html/nrow.html>(x), ncol
<http://stat.ethz.ch/R-manual/R-devel/library/base/html/ncol.html>=nrow
<http://stat.ethz.ch/R-manual/R-devel/library/base/html/nrow.html>(x))
where n2i is the control group reused. I used this code because N was equal
for the treatment and reference group. There is only the study from Rhoade
where I'm not sure of the application of this formula because in this case
the treatment and the reference are reused once.
I was able to get the variance-covariance V matrix and I used the
metamodel3 <- rma.mv(yi, ], mods = ~ Land_use_change - 1, random = ~
factor(trial) | article, rho=1/2, data=ma.grass) to fit the model and I get
the error message :







*Error in .ll.rma.mv <http://ll.rma.mv>(opt.res$par, reml = reml, Y = Y, M
= V, A = A, X.fit = X,  :   Final variance-covariance matrix not positive
definite.De plus : Warning messages:1: In rma.mv <http://rma.mv>(yi, V[k,
k], mods = ~Luchange - 1, random = ~factor(trial) |  :  'V' appears to be
not positive definite.2: In rma.mv <http://rma.mv>(yi, V[k, k], mods =
~Luchange - 1, random = ~factor(trial) |  :  Redundant predictors dropped
from the model.*

after some tests restricting the matrix to individual studies, it appears
that the sub-matrix from the study Farle is not positive definite.
Could you give a little more help to solve this problem and to confirm that
the code I used was appropriate?
I would like not dropping this study which is quite important in the
meta-analysis.

Thanks in advance
Vivien


On Thu, Aug 31, 2017 at 2:18 PM, Wolfgang Viechtbauer <

Dear Vivien,

This can be thought of as a network meta-analysis, so indeed, the
dat.hasselblad1998 and dat.senn2013 datasets and the corresponding code in
the example section of the corresponding help files are quite relevant.

The dataset as given is in the format for a 'contrast-based' analysis. And
when you have studies where the same group is being reused for computing
the outcomes, then this results in dependency in the sampling errors of
those outcomes. You may want to study carefully:

http://www.metafor-project.org/doku.php/analyses:gleser2009

You are dealing with multiple treatment studies. The code given there
illustrates the computation of the covariance of outcomes that share a
common group. I do not cover measure="ROM" there, but the covariance is:

sd^2/(n*mean^2)

from the group whose data is being re-used. So, if you want to compute
this programmatically, you will have to do some coding to make that work
(and it's a bit more complex in your case, since sometimes the first and
sometimes the second group appears to be the 'reference' group). But the
idea is that you need to build the entire V matrix.

And indeed, that will capture the higher dependency in such studies.

Then you need to go back to help(dat.hasselblad1998) and
help(dat.senn2013) to see how the modeling is done there using a
contrast-based model. It is shown there, so I rather not repeat all of that
here.

A final note:

escalc() does not have a 'method' argument, so the 'method = "REML"' part
of your call to escalc() doesn't do anything.

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

On 08/31/2017 05:07 PM, Vivien Bonnesoeur wrote:
Hi,
I would need help about the way to model mutliple treatment studies.
I have been posting a question on
https://stats.stackexchange.com/questions/300425/metafor-rma
-mv-function-inner-outer-grouping-factor-structure
and was told to write to this list :

I would like to know how to use the inner/outer grouping factor structure
when my data set present some multiple treatment studies (e.g., when
multiple treatment groups are compared with a common control/reference
group, such that the data from the control/reference group is used multiple
times to compute the effect sizes or outcomes)? I have been practicing the
metafor examples "dat.hasselblad1998" and "dat.senn2013" where such
multiple treatment studies exist but I could not understood exactly how the
reference group was designated.

I'm performing a meta-analysis on the impact of reforestation/forest cover
change on the soil organic matter content. Here is the dataset I'm using
(sep=";") :

    1.
  article;Land_use_change;forest_N;forest_mean;forest_sd;ref_
N;ref_mean;ref_sd;inner_group_struct
    2. Hes;Forestation ? native forest;5;2,5;0,6;5;8,5;3,1;1
    3. Hes;Forestation ? native forest;5;9,1;1,2;5;22,4;3,2;2
    4. Hes;Forestation ? native forest;5;9,9;1,2;5;13,0;2,7;3
    5. Hes;Afforestation ? ungrazed grassland;5;0,6;0,2;5;0,6;0,0;4
    6. Hes;Afforestation ? ungrazed grassland;5;1,6;0,4;5;2,8;1,2;5
    7. Henr;Afforestation ? ungrazed grassland;3;6,0;0,5;3;7,0;0,4;6
    8. Henr;Afforestation ? grazed grassland;3;6,0;0,5;3;5,9;1,0;6
    9. Henr;Afforestation ? grazed grassland;3;5,9;3,2;3;5,6;4,8;7
    10. Konin;Regrowth ? grazed grassland;8;6,7;2,0;8;4,2;1,1;8
    11. Konin;Regrowth ? grazed grassland;8;9,0;3,3;8;6,4;1,7;9
    12. Konin;Regrowth ? grazed grassland;8;8,0;0,8;8;8,6;3,0;10
    13. Konin;Regrowth ? grazed grassland;8;6,3;1,6;8;5,3;0,9;11
    14. Konin;Regrowth ? grazed grassland;8;6,8;1,5;8;5,3;2,3;12
    15. Dub;Afforestation ? native forest;6;7,6;1,0;6;10,6;1,1;13
    16. Dub;Afforestation ? grazed grassland;6;7,6;1,0;6;13,5;0,8;13
    17. Chaco;Afforestation ? native forest;6;36,6;12,1;6;40,7;17,9;14
    18. Chaco;Afforestation ? grazed grassland;6;40,5;7,7;6;40,3;7,7;15
    19. Rhoade;Forestation ? native forest;10;9,2;4,1;10;11,3;2,5;16
    20. Rhoade;Forestation ? native forest;10;12,9;4,1;10;11,3;3,5;16
    21. Rhoade;Regrowth ? grazed grassland;10;9,2;4,1;10;9,3;2,7;16
    22. Rhoade;Regrowth ? grazed grassland;10;12,9;4,1;10;9,3;2,7;16
    23. Schlatte;Forestation ? native forest;10;14,3;3,1;12;12,6;2,9;17
    24. Farle;Afforestation ? ungrazed grassland;10;5,7;1,6;30;7,2;1,9;18
    25. Farle;Afforestation ? ungrazed grassland;30;6,0;0,9;30;7,2;1,9;18
    26. Farle;Afforestation ? ungrazed grassland;30;4,7;1,1;30;7,2;1,9;18
    27. Nosett;Afforestation ? ungrazed grassland;5;8,6;6,9;3;8,8;7,0;19
    28. Nosett;Afforestation ? grazed grassland;5;8,6;6,9;5;9,0;7,0;19
    29. ManN;Afforestation ? grazed grassland;24;7,5;0,8;24;5,7;1,0;20
    30. Breme;Afforestation ? grazed grassland;60;45,1;3,4;66;39,7;5,4;21

article refers to the study where the data are extracted, Land-use change
is the fixed effect I'm interested in. In each row, I'm comparing a
forestation situation with the referent situation and I've used escalc to
compute the effect size= log ratio of the means

ma.grass=escalc(m1 = forest_mean, m2 = ref_mean,
             sd1 = forest_sd, sd2 = ref_sd,
             n1 = forest_N, n2 = ref_N,
             method = "REML", measure = "ROM",slab=article,
             )

The articles "Dub", "Rhoade", "Farle" and "Nosett" are multiple treatment
studies. For example in "Farle", the the soil matter content of 3 different
pine plantations are compared to a single control. In the same time, an
article like "Hes" gives 5 contrasts from 5 paired-site measurement. Indeed
those 5 contrasts are not independent (same methodology, they come from the
same region, etc...) but I believe the correlations between the contrast
are less strong than between contrasts calculated from the same reference
group as in the above multiple treatment studies. How can I model correctly
these *a prior* different type of correlations within studies? My guess is

I need to use article as the outer factor but I don't know what to write in
the inner factor. I have been trying many different inner group factors but
in any cases the results were satisfying. For example, like in
"dat.hasselblad1998" and "dat.senn2013", I used :

metamodel1=rma.mv
(yi,vi,data=ma.grass,mods=~Land_use_change-1,random=~factor(
id)|article,method="REML")

but the results were not satisfying to me since the Land use change
"Afforestation - ungrazed grassland" should be significantly <0

I then created a "inner_group_struct"

metamodel3=rma.mv(yi,vi,data=ma.grass,mods=~Land_use_change-
1,random=~factor(inner_group_struct)|article,struct="UN",method="REML")

but it is still not satysfing : the Land.use_change "Forestation - native
forest" is estimated to be >0 while almost all the raw Effect Size from
this treatment apart 1 are negative.

any help will be much appreciated for modeling the inner group structure.
Kind regards

--
Vivien BONNESOEUR
Docteur en biologie foresti?re

Vivien BONNESOEUR
Docteur en biologie foresti?re

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