[R-meta] Meta-analysis when sampling covariance matrices are missing
Célia Sofia Moreira
celiasofiamoreira at gmail.com
Wed Jan 10 01:04:20 CET 2018
Dear all,
I have been reading some of the messages in the list related to my problem,
and I realized that “unknown correlations” is an old topic. Special thanks
to Prof. Wolfgang, James Pustejovsky, and Isabel Schlegel in
https://stat.ethz.ch/pipermail/r-sig-meta-analysis/2017-August/000127.html.
Really helpful!
I also understood that my attempt to perform the multilevel model in my
previous message was wrong. Please, forget the previous questions.
My data are multivariate and so outcomes should be analyzed as such.
However, I only have sampling means and SD, and thus, only variances of the
effects (SMD) are available. So, I will input a covariance matrix
(clubSandwich) and/or RVE (robumeta), always with the indispensable rma.mv
(metafor).
Nevertheless, I would like to investigate a regression between two effects.
However, due to the previous limitation, I have no idea if it is possible,
and, in affirmative case, how to do it. Thus, any recommendations /
suggestions will be much appreciated. In negative case, can the
unstructured correlation matrix obtained with the rma.mv output be used to
assess the strength of the relationship between these effects?
Please, tell me your opinion!
Kind regards
2018-01-07 20:09 GMT+00:00 Célia Sofia Moreira <celiasofiamoreira at gmail.com>
:
> 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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