[R-meta] Meta-analysis when sampling covariance matrices are missing

[Célia Sofia Moreira]

Dear all,

I'm performing a meta-analysis for the first time, and I have two main
questions:

1) I would like to perform a regression between two effect sizes (y2 ~ y1).
However, 'my' trials only report information about means and SD of the
study variables. (I'm comparing two groups.) As far as I understood, if I
had the sampling covariances/correlations of the variables, I could easily
do the regression using metaSEM package. However and unfortunately, it is
impossible to obtain that information. I had some difficulty in finding
recommendations about the way to follow facing this limitation, i.e., if I
should give up the regression or if I should perform an alternative
'weaker' approach. The better reference I found was the Professor Mike
Cheung's book. Googling a bit, I found that some methods allow to obtain
good approximations to the 'true' regression coefficients (obtained with
methods using sampling covariances), such as the 3-level modeling (metafor
or metaSEM) or the robust variance estimates (metafor or robumeta). The
outputs of metafor and metaSEM are below.

1.a) I would like to know your opinion about the reliability of these two
methods as providing good/reliable approximations to the 'true' regression
coefficient. Are there better recommended alternatives? References and
examples (preferably including R codes) would be much appreciated!

1.b) About the R codes, I would like to know if the following are the
recommended:

- metafor1<-rma.mv(y2, v2, mods = ~ y1,  random = ~ 1|Study,   data=dat).

- metaSEM1 <- meta3(y=y2, v=v2, cluster= Study,  x= y1, data=dat). In this
case, Tau2_2 and Tau2_3 (almost) vanish; does this fact mean something
strange?

2) In fact, I would like to repeat the regression for other three effect
sizes as predictors (keeping y2 as dependent variable in all regressions).
In my opinion, the better approach would be to join all four effect sizes
(predictors) in a unique latent variable. However, due to the limitation
referred above, I can not perform MASEM. So, I would like to know your
opinion about gathering all effect sizes in a total parceling predictor
variable (as commonly done in standard regression analysis).

Many thanks!

----------------

R outputs:

> metafor1<-rma.mv(y2, v2, mods = ~ y1,  random = ~ 1|Study,   data=dat);
summary(metafor1)

Multivariate Meta-Analysis Model (k = 18; method: REML)

  logLik  Deviance       AIC       BIC      AICc
 -6.4713   12.9427   18.9427   21.2604   20.9427

Variance Components:

            estim    sqrt  nlvls  fixed  factor
sigma^2    0.0000  0.0000     18     no   Study

Test for Residual Heterogeneity:
QE(df = 16) = 8.1795, p-val = 0.9433

Test of Moderators (coefficient(s) 2):
QM(df = 1) = 4.9846, p-val = 0.0256

Model Results:

         estimate      se     zval    pval    ci.lb   ci.ub
intrcpt   -0.0591  0.1271  -0.4652  0.6418  -0.3083  0.1900
y1         0.1361  0.0610   2.2326  0.0256   0.0166  0.2556  *


> robust(metafor1, cluster=dat$Study)

Number of outcomes:   18
Number of clusters:   18
Outcomes per cluster: 1

Test of Moderators (coefficient(s) 2):
F(df1 = 1, df2 = 16) = 7.1878, p-val = 0.0164

Model Results:

         estimate      se     tval    pval    ci.lb   ci.ub
intrcpt   -0.0591  0.0938  -0.6304  0.5373  -0.2580  0.1397
y1         0.1361  0.0508   2.6810  0.0164   0.0285  0.2437  *


------

> metaSEM1 <- meta3(y=y2, v=v2, cluster= Study,  x= y1, data=dat);
summary(mult1)

Call:
meta3(y = y2, v = v2, cluster = Study, x = y1, data = dat)

95% confidence intervals: z statistic approximation
Coefficients:
             Estimate   Std.Error      lbound      ubound z value Pr(>|z|)
Intercept -5.9140e-02  1.3792e-01 -3.2946e-01  2.1118e-01 -0.4288  0.66807
Slope_1    1.3610e-01  6.1256e-02  1.6044e-02  2.5616e-01  2.2219  0.02629 *
Tau2_2     1.0000e-10  3.3554e+03 -6.5765e+03  6.5765e+03  0.0000  1.00000
Tau2_3     1.0000e-10  3.3554e+03 -6.5765e+03  6.5765e+03  0.0000  1.00000
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Q statistic on the homogeneity of effect sizes: 13.16409
Degrees of freedom of the Q statistic: 17
P value of the Q statistic: 0.7251337

Explained variances (R2):
                       Level 2 Level 3
Tau2 (no predictor)      1e-10       0
Tau2 (with predictors)   1e-10       0
R2                       0e+00       0

Number of studies (or clusters): 18
Number of observed statistics: 18
Number of estimated parameters: 4
Degrees of freedom: 14
-2 log likelihood: 13.49735
OpenMx status1: 0 ("0" or "1": The optimization is considered fine.
Other values may indicate problems.)

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