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

[Vivien Bonnesoeur]

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 forestière

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