[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 at maastrichtuniversity.nl>
Sent: Wednesday, September 18, 2019 1:36 PM
To: Ju Lee <juhyung2 at stanford.edu>; r-sig-meta-analysis at r-project.org <r-sig-meta-analysis at 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 at r-project.org] On Behalf Of Ju Lee
Sent: Wednesday, 18 September, 2019 19:44
To: r-sig-meta-analysis at 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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