[R-meta] Covariance-variance matrix when studies share multiple treatment x control comparison
Ju Lee
juhyung2 @end|ng |rom @t@n|ord@edu
Thu Sep 19 01:24:18 CEST 2019
Dear Wolfgang and all,
Please ignore my previous e-mail, and refer to this one instead:
Thank you very much for your response. I am using Hedges' d and I assumed this code applies to all SMD type of ES including Hedges' d?
I am still little baffled how I can apply this to more complex combinations. Below table looks busy, but I would appreciate if you can answer the following two questions. FYI, C_ID1 is the shared group ID.
1) In study 1, treatment 0.84 is shared in 3th and 4th response. To account for this inter-dependence, should I use "nt" instead of "nc" for calculating cov.d matrix?
2) I am not sure how to proceed if treatments and controls are shared in fashion as study 2. Clearly, 1st/2nd response shares treatment (1.00) and 2nd/3rd shares control (2.00), but 1st and 3rd do not share any experimental unit. I've categorized 2nd and 3rd with same C_ID1 because they share control, but am unclear if I should assign 1st response the same ID as 2nd and 3rd (c3) since it is still technically not independent from 2nd response (shared control) OR do I assign it a complete different control ID?
Study mt mc nt nc C_ID1 hedges.d var
1 0.92 0.68 6 6 c1 0.937 0.370
1 0.69 0.68 9 6 c1 0.038 0.278
1 0.84 0.69 9 9 c2 0.659 0.234
1 0.84 0.92 9 6 c2 -0.623 0.291
2 1.00 0.32 10 20 c? 0.760 0.056
2 1.00 2.00 10 5 c3 0.885 0.070
2 0.61 2.00 15 5 c3 0.209 0.052
I hope I am not asking too much of your time, but if you can answer this specific question, it will clarify all the doubts I have with this stage of analysis.
Thank you very much, and I hope to hear from you.
Best wishes,
JU
________________________________
From: R-sig-meta-analysis <r-sig-meta-analysis-bounces using r-project.org> on behalf of Ju Lee <juhyung2 using stanford.edu>
Sent: Wednesday, September 18, 2019 3:32 PM
To: Viechtbauer, Wolfgang (SP) <wolfgang.viechtbauer using maastrichtuniversity.nl>; r-sig-meta-analysis using r-project.org <r-sig-meta-analysis using r-project.org>
Subject: Re: [R-meta] Covariance-variance matrix when studies share multiple treatment x control comparison
Dear Wolfgang,
Thank you very much for your response. I am using Hedges' d and I assumed this code applies to all SMD type of ES including Hedges' d?
I am still little baffled how I can apply this to more complex combinations. Below table looks busy, but I would appreciate if you can answer the following two questions. FYI, C_ID1 is the shared group ID.
1) In study 1, treatment 0.84 is shared in 3th and 4th response. To account for this inter-dependence, should I use "nt" instead of "nc" for calculating cov.d matrix?
2) According to your feedback, does my C_ID1 (sharing group common ID) appropriately specified in study for constructing cov. matrix? I initially thought all 6 responses should have same control ID, as they are all inter-related with either shared t or c group (except for 5th response of study 2 which has treatment 0.7 that is not shared by others)
Study mt mc nt nc C_ID1 hedges.d var
1 0.92 0.68 6 6 c1 0.937 0.370
1 0.69 0.68 9 6 c1 0.038 0.278
1 0.84 0.69 9 9 c2 0.659 0.234
1 0.84 0.92 9 6 c2 -0.623 0.291
2 0.610 0.322 50 31 c3 0.760 0.056
2 0.667 0.322 32 31 c3 0.885 0.070
2 0.610 0.528 50 32 c4 0.209 0.052
2 0.667 0.528 32 32 c4 0.345 0.063
2 0.700 0.536 26 31 c5 0.417 0.072
2 0.667 0.536 32 31 c5 0.316 0.064
I hope I am not asking too much of your time, but if you can answer this specific question, it will clarify all the doubts I have with this stage of analysis.
Thank you very much, and I hope to hear from you.
Best wishes,
JU
________________________________
From: Viechtbauer, Wolfgang (SP) <wolfgang.viechtbauer using maastrichtuniversity.nl>
Sent: Wednesday, September 18, 2019 1:36 PM
To: Ju Lee <juhyung2 using stanford.edu>; r-sig-meta-analysis using r-project.org <r-sig-meta-analysis using r-project.org>
Subject: RE: Covariance-variance matrix when studies share multiple treatment x control comparison
Dear Ju,
There are two contrasts in study 1, 7.87 vs -1.36 and 4.35 vs -1.36, so the -1.36 comes from a common reference group. So, there will be two effect sizes for that study (and due to reuse of the reference group data, there is indeed dependence between the two effect sizes). Including the 7.87 vs 4.35 contrast is redundant. All the information about this contrast is already contained in the two contrasts above.
You haven't said what kind of effect size measure you are using for your analysis, but the code you posted comes from an example that uses the standardized mean difference as the measure (http://www.metafor-project.org/doku.php/analyses:gleser2009) -- and it only applies if this is the measure you are also using. You did not post any SDs (which would be needed if you are working with SMDs), maybe just for brevity, but I just wanted to mention this.
Best,
Wolfgang
-----Original Message-----
From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-bounces using r-project.org] On Behalf Of Ju Lee
Sent: Wednesday, 18 September, 2019 19:44
To: r-sig-meta-analysis using r-project.org
Subject: [R-meta] Covariance-variance matrix when studies share multiple treatment x control comparison
Dear Wolfgang and all,
I am running a multivariate mixed effect models using rma.mv and trying to build a variance-covariance matrix to account for inter-dependence rising from shared experimental units.
The issue I have is: what if my analysis includes studies where both controls and treatment groups are repeatedly used to calculate effect sizes (this was because each comparison produces different categorical comparison that are meaningful, but I am also trying to pool all studies to calculate the grand mean effect sizes ).
If I simplify my dataframe, it looks like below. here m1i, m2i are means for treatment and controls and n1i and n2i are sample sizes needed for constructing cov-var matrix.
study treatment m1i m2i n1i n2i
1 1 7.87 -1.36 25 25
1 2 4.35 -1.36 22 25
1 2 4.35 7.87 22 25
2 1 9.32 0.98 38 40
3 1 8.08 1.17 50 50
4 1 7.44 0.45 30 30
4 2 5.34 0.45 30 30
If you look at study 1, all three effect sizes share different subset of experimental group. Based on Wolfgang's code, I am trying to construct Cov-var matrix using following code:
calc.v <- function(x) {
v <- matrix(1/x$n2i[1] + outer(x$yi, x$yi, "*")/(2*x$Ni[1]), nrow=nrow(x), ncol=nrow(x))
diag(v) <- x$vi
v
}
V <- bldiag(lapply(split(dat, dat$study), calc.v))
V
But I am not sure how I can proceed here because all three effect sizes should be interdependent due to sharing some experimental groups, but how can we specify this in the matrix? Especially, between first and third response in the first study, mean of 7.87 is treatment in the first but control in the third response. How can we reasonably account for inter-dependence in such a case?
Thank you very much,
Best,
JU
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