[R-meta] Weighting studies combining inverse variance and quality score in multiple treatment studies

[Vivien Bonnesoeur]

Dear all,
I would need some advice in the way to combine quality score and inverse
variance for weighting studies.
I'm contrasting the infiltration rate between tree plantation and grassland
and also tree plantation and native forest (effect size = Log ROM) to know
if tree plantation on grassland can increase the infiltration and recover
to level of infiltration of native forest.

here is the raw data :
article;trial;Land-use_change;Plantation_N;Plantation_mean;Plantation_sd;Control_N;Control_mean;Control_sd;yi;vi;quality_score
Gaitan2016;1;Plantation-grassland;32;36;41;32;11;7;1.186;0.053;1
Gonzalez2015;2;Plantation-grassland;9;76.6;17.6;2;76.6;37.5;0.000;0.126;0.8
Hoyos2005;3;Plantation-grassland;3;101.3;66;23;2.5;1.6;3.702;0.159;0.5
Hoyos2005;4;Plantation-Native_forest;3;101.3;66;3;225;271;-0.798;0.625;0.5
Moreno2012;5;Plantation-grassland;10;8064;7092;10;5004;7092;0.477;0.278;0.3
Moreno2012;6;Plantation-Native_forest;10;8064;7092;10;34092;7092;-1.442;0.082;0.3
Sadeghian2001;7;Plantation-grassland;12;210;120;16;30;27;1.946;0.078;1
Sadeghian2001;8;Plantation-Native_forest;12;210;120;16;760;439;-1.286;0.048;1
Zimmerman2007;9;Plantation-grassland;30;514;137;30;3;4;5.144;0.062;0.8
Zimmerman2007;10;Plantation-Native_forest;30;514;137;30;135;51;1.337;0.007;0.6

If I just used the inverse variance-covariance weighting (to account for
dependency between the reuse of some plantations) :

model1 = rma.mv
(yi,V,mods=~Land-use_change-1,method="REML",slab=article,random=~factor(trial)|article,data=ma.infilt)

I end with a lot of weight to the studies where there is a reuse of the
plantation. Actually, those weight are really different from the inverse
vi. For example
Gaitan2016 : weight(model1) = 2.98%  ;  weight from inverse vi = 7.8%
Hoyos2005.1 :weight(model1) = 9.01%  ;  weight from inverse vi = 2.6%
Hoyos2005.2 :weight(model1) = 7.67%  ;  weight from inverse vi = 0.66%
Zimmerman2007.1 :weight(model1) = 13.6%  ;  weight from inverse vi = 6.7%
Zimmerman2007.2 :weight(model1) = 13.9%  ;  weight from inverse vi = 58%

Here I have a first question :
-is there a way to reduce the weight of studies where the plantation is
reused for contrasting with 2 different control? It seems to be an
artificial over-weighting decision to me?

Besides, some studies with a low quality score have stronger weights than
studies with high quality score. To combine the quality score and the
inverse variance in study weighting, my try is to use the weight from the
model1 and to multiply it with the quality score in this way :

model2=rma.mv
(yi,V,mods=~Land-use_change-1,W=(ma.infilt$quality_score*weights(model1))/sum(ma.infilt$quality_score*weights(model1)),method="REML",slab=article,random=~factor(trial)|article,data=ma.infilt)

It gives more satisfactory weigths since the studies with very low quality
score have now a small contribution to the grand mean.
I would like to know however if this way of combining the quality and
inverse variance weighting is sound theoretically and won't be rejected by
reviewer as a "critical flaw"

Best regards



-- 
Vivien BONNESOEUR


*Merci de m'écrire à ma nouvelle adresse mail, *
*bonnesoeur.vivien at protonmail.com <bonnesoeur.vivien at protonmail.com>*

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