md.vcov.RdThe function md.vcov computes effect sizes and variance-covariance matrix for multivariate meta-analysis when the effect sizes of interest are all measured by mean difference. See mix.vcov for effect sizes of the same or different types.
md.vcov(r, nt, nc, n_rt = NA, n_rc = NA, sdt, sdc)
| r | A \(N\)-dimensional list of \(p \times p\) correlation matrices for the \(p\) outcomes from the \(N\) studies. |
|---|---|
| nt | A \(N \times p\) matrix storing sample sizes in the treatment group reporting the \(p\) outcomes. |
| nc | A matrix defined in a similar way as |
| n_rt | A \(N\)-dimensional list of \(p \times p\) matrices storing sample sizes in the treatment group reporting pairwise outcomes in the off-diagonal elements. |
| n_rc | A list defined in a similar way as |
| sdt | A \(N \times p\) matrix storing sample standard deviations for each outcome from treatment group. |
| sdc | A matrix defined in a similar way as |
Min Lu
A \(N\)-dimensional list of \(p(p+1)/2 \times p(p+1)/2\) matrices of computed variance-covariance matrices.
A \(N \times p(p+1)/2\) matrix whose rows are computed variance-covariance vectors.
Ahn, S., Lu, M., Lefevor, G.T., Fedewa, A. & Celimli, S. (2016). Application of meta-analysis in sport and exercise science. In N. Ntoumanis, & N. Myers (Eds.), An Introduction to Intermediate and Advanced Statistical Analyses for Sport and Exercise Scientists (pp.233-253). Hoboken, NJ: John Wiley and Sons, Ltd.
Wei, Y., & Higgins, J. (2013). Estimating within study covariances in multivariate meta-analysis with multiple outcomes. Statistics in Medicine, 32(7), 119-1205.
###################################################### # Example: Geeganage2010 data # Preparing covariances for multivariate meta-analysis ###################################################### ## set the correlation coefficients list r r12 <- 0.71 r.Gee <- lapply(1:nrow(Geeganage2010), function(i){matrix(c(1, r12, r12, 1), 2, 2)}) computvcov <- md.vcov(nt = subset(Geeganage2010, select = c(nt_SBP, nt_DBP)), nc = subset(Geeganage2010, select = c(nc_SBP, nc_DBP)), sdt = subset(Geeganage2010, select=c(sdt_SBP, sdt_DBP)), sdc = subset(Geeganage2010, select=c(sdc_SBP, sdc_DBP)), r = r.Gee) # name variance-covariance matrix as S S <- computvcov$matrix.vcov ## fixed-effect model y <- as.data.frame(subset(Geeganage2010, select = c(MD_SBP, MD_DBP))) MMA_FE <- summary(metafixed(y = y, Slist = computvcov$list.vcov)) MMA_FE#> Fixed-effects coefficients #> Estimate Std. Error z Pr(>|z|) 95%ci.lb 95%ci.ub #> MD_SBP -1.9011 0.9689 -1.9620 0.0498 -3.8002 -0.0020 * #> MD_DBP -2.1035 0.5196 -4.0486 0.0001 -3.1219 -1.0852 *** #> --- #> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 #> #> Multivariate Cochran Q-test for heterogeneity: #> Q = 81.0759 (df = 32), p-value = 0.0000 #> I-square statistic = 60.5% #>####################################################################### # Running random-effects model using package "mvmeta" or "metaSEM" ####################################################################### # Restricted maximum likelihood (REML) estimator from the mvmeta package #library(mvmeta) #mvmeta_RE <- summary(mvmeta(cbind(MD_SBP, MD_DBP), S = S, # data = subset(Geeganage2010, select = c(MD_SBP, MD_DBP)), # method = "reml")) #mvmeta_RE # maximum likelihood estimators from the metaSEM package # library(metaSEM) # metaSEM_RE <- summary(meta(y = y, v = S)) # metaSEM_RE ############################################################## # Plotting the result: ############################################################## # obj <- MMA_FE # obj <- mvmeta_RE # obj <- metaSEM_RE # plotCI(y = y, v = computvcov$list.vcov, # name.y = c("MD_SBP", "MD_DBP"), name.study = Geeganage2010$studyID, # y.all = obj$coefficients[,1], # y.all.se = obj$coefficients[,2])