md.vcov: Covariance matrix for mean differences
In metavcov: Variance-Covariance Matrix for Multivariate Meta-Analysis

Description Usage Arguments Value Author(s) References Examples

Compute variance-covariance matrix for multivariate meta-analysis when effect size is mean difference.

1	md.vcov(r,nt,nc,n_rt=0,n_rc=0,sdt,sdc)

`r`	A list of correlation coefficient matrices of the outcomes from the studies. r[[k]][i,j] is the correlation coefficient between outcome i and outcome j from study k.
`nt`	A matrix with sample sizes in the treatment group reporting each of the outcome. nt[i,j] is the sample size from study i reporting the outcome j.
`nc`	Defined in a similar way as nt for control group.
`n_rt`	A list of matrices storing sample sizes in the treatment group reporting pairwised outcomes in the off diagonal elements. n_rt[[k]][i,j] is the sample size reporting both outcome i and outcome j from study k. Diagonal elements of these matrices are not used. The default value is zero, which means the smaller sample size reporting the corresponding two outcomes: i.e. n_rt[[k]][i,j]=min(nt[k,i],nt[k,j]).
`n_rc`	Defined in a similar way as n_rt for control group.
`sdt`	Sample standard deviation from each of the outcome. sdt[i,j] is the sample standard deviation from study i for outcome j.
`sdc`	Defined in a similar way as sdt for control group.

list.md.cov	A list of computed variance-covariance matrices.
md.cov	A matrix whose rows are computed variance-covariance vectors.

Min Lu

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)})

computvocv<-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 covars
covars = computvocv$md.cov

#####################################################
# Running random-effects model using package "mvmeta"
#####################################################
#library(mvmeta)
#mvmeta_RE = summary(mvmeta(cbind(MD_SBP,MD_DBP),S=covars,
#                         data=subset(Geeganage2010,select=c(MD_SBP,MD_DBP)),
#                         method="reml"))
#mvmeta_RE