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

Gerta Ruecker ruecker at imbi.uni-freiburg.de
Fri Jan 19 18:17:47 CET 2018

Dear Vivien,

My response is only to the second question (weighting using quality scores):

This is strongly discouraged at least by Cochrane. It is a matter of the 
difference between the multidimensional concept of quality and the 
unidimensional concept of bias (which we want to avoid). Not every item 
of quality leads to bias, and if it does, the direction of bias might be 
unclear. Biases may cancel out. Moreover, to downweight a biased study 
still leads to bias, thus you might as well throw the study out.

See the Cochrane Handbook http://handbook-5-1.cochrane.org/ , particularly

8.3  Tools for assessing quality and risk of bias
8.3.1 Types of tools
8.3.2 Reporting versus conduct
8.3.3 Quality scales and Cochrane reviews
8.3.4 Collecting information for assessments of risk of bias
8.15.2  Assessing risk of bias from other sources


Sander Greenland and Keith O'Rourke, "On the bias produced by quality 
scores in meta-analysis, and a hierarchical view of proposed solutions", 
Biostatistics., vol. 2, pp. 463-471, 2001.

Peter Jüni, Douglas G. Altman, and Matthias Egger, "Assessing the 
quality of controlled clinical trials", Brit. Med. J., vol. 323, pp. 
42-46, 2001.

A. R. Jadad, D. J. Cook, A. Jones, T. P. Klassen, P. Tugwell, M. Moher, 
and D. Moher, "Methodology and reports of systematic reviews and 
meta-analyses: A comparison of Cochrane reviews with articles published 
in paper-based journals.", J. Amer. Med. Assoc., vol. 280, pp. 278-80, 1998.

Emerson JD, Burdick E, Hoaglin DC, Mosteller F, Chalmers TC. An 
empirical study of the possible relation of treatment differences to 
quality scores in controlled randomized clinical trials. Controlled 
Clinical Trials 1990; 11: 339-352.

Schulz KF, Chalmers I, Hayes RJ, Altman DG. Empirical evidence of bias. 
Dimensions of methodological quality associated with estimates of 
treatment effects in controlled trials. JAMA 1995; 273: 408-412.



Am 19.01.2018 um 18:04 schrieb 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


Dr. rer. nat. Gerta Rücker, Dipl.-Math.

Institute of Medical Biometry and Statistics,
Faculty of Medicine and Medical Center - University of Freiburg

Stefan-Meier-Str. 26, D-79104 Freiburg, Germany

Phone:    +49/761/203-6673
Fax:      +49/761/203-6680
Mail:     ruecker at imbi.uni-freiburg.de
Homepage: https://portal.uni-freiburg.de/imbi/persons/ruecker?set_language=en

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