# [R-meta] Non-independent effect sizes for moderator analysis in meta-analysis on odds ratios

Sotola, Lukas K [PSYCH] |k@oto|@ @end|ng |rom |@@t@te@edu
Mon Jun 12 17:00:52 CEST 2023

```Dear all,

I am trying to do a meta-analysis with odds ratios, but am running into one issue. I have a few effect sizes that are not independent. That is, there are a few samples in my data where we extracted two odds ratios for the purposes of performing a moderator analysis. Thus, while we have 6 samples (k = 6), we have 9 effect sizes, as three samples we coded two odds ratios. Normally, when I run a meta-analysis with correlation coefficients, there is some way to indicate a "Study ID" variable of some sort, which will allow the analysis to distinguish effect sizes taken from the same sample for a moderator analysis. That way, multiple effect sizes from the same sample do not get counted multiple times. However, I cannot seem to find an analogous feature using metafor, and even when I run the meta-analysis with a moderator analysis, in the overall analysis (e.g., for heterogeneity and such), the output indicates a "k" that is equal to the number of effect sizes and not equal to the real number of samples (i.e., k = 9). This makes me worry that the results I'm getting are biased.

After using the "escalc" function to create a new dataset with odds ratios as shown on the metafor website, I have attempted the analysis itself in two ways so far. The name of my moderator variable is "HighACEDef" and it has two levels. For my first attempt at the meta-analysis, I use the following R code and get the output that follows it:

Analysis1 <- rma(yi, vi, mods = ~factor(HighACEDef), data=dat1)
Analysis1

Mixed-Effects Model (k = 9; tau^2 estimator: REML)

tau^2 (estimated amount of residual heterogeneity):     0.0252 (SE = 0.0203)
tau (square root of estimated tau^2 value):             0.1587
I^2 (residual heterogeneity / unaccounted variability): 82.50%
H^2 (unaccounted variability / sampling variability):   5.71
R^2 (amount of heterogeneity accounted for):            0.00%

Test for Residual Heterogeneity:
QE(df = 7) = 33.6446, p-val < .0001

Test of Moderators (coefficient 2):
QM(df = 1) = 0.7218, p-val = 0.3955

Model Results:

estimate      se    zval    pval    ci.lb   ci.ub
intrcpt                  0.8144  0.0853  9.5439  <.0001   0.6472  0.9817  ***
factor(HighACEDef)>=4    0.1151  0.1355  0.8496  0.3955  -0.1505  0.3807

---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

The second way I have tried it is with this code and I get the output that follows it. "ES_ID" is a unique identification number for each separate effect size, whereas "ID" is a unique identification number for each sample we coded from. Thus, "ES_ID" has the values of 1-9 while "ID" has the values of 1-6.

Analysis2 <- rma.mv(yi, vi, random = ~ ES_ID | ID, mods = ~factor(HighACEDef), data=dat1)
Analysis2

Multivariate Meta-Analysis Model (k = 9; method: REML)

Variance Components:

outer factor: ID    (nlvls = 6)

inner factor: ES_ID (nlvls = 9)

estim    sqrt  fixed

tau^2      0.0302  0.1739     no

rho        0.6011             no

Test for Residual Heterogeneity:

QE(df = 7) = 33.6446, p-val < .0001

Test of Moderators (coefficient 2):

QM(df = 1) = 0.8522, p-val = 0.3559

Model Results:

estimate      se    zval    pval    ci.lb   ci.ub

intrcpt                  0.8213  0.0914  8.9849  <.0001   0.6421  1.0004  ***

factor(HighACEDef)>=4    0.0967  0.1047  0.9232  0.3559  -0.1086  0.3020

---

Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

I would much appreciate any help with doing this correctly, or just a confirmation that either of the ways I have already done it is correct.

I also had one last question. Is there any way the results can be expressed as odds ratios rather than as log odds ratios?

Thank you,

Lukas Sotola

Lukas K. Sotola, M.S.
PhD Candidate: Iowa State University
Department of Psychology
He/him

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