metavcov (version 2.1.5)

md.vcov: Computing Variance-Covariance Matrices for Mean Differences

Description

The 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.

Usage

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

Value

list.vcov

A \(N\)-dimensional list of \(p(p+1)/2 \times p(p+1)/2\) matrices of computed variance-covariance matrices.

matrix.vcov

A \(N \times p(p+1)/2\) matrix whose rows are computed variance-covariance vectors.

Author

Min Lu

Arguments

r

A \(N\)-dimensional list of \(p \times p\) correlation matrices for the \(p\) outcomes from the \(N\) studies. r[[k]][i,j] is the correlation coefficient between outcome \(i\) and outcome \(j\) from study \(k\).

nt

A \(N \times p\) matrix storing sample sizes in the treatment group reporting the \(p\) outcomes. nt[i,j] is the sample size from study \(i\) reporting outcome \(j\).

nc

A matrix defined in a similar way as nt for the control group.

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_rt[[k]][i,j] is the sample size reporting both outcome \(i\) and outcome \(j\) from study \(k\). Diagonal elements of these matrices are discarded. The default value is NA, which means that the smaller sample size reporting the corresponding two outcomes is imputed: i.e. n_rt[[k]][i,j]=min(nt[k,i],nt[k,j]).

n_rc

A list defined in a similar way as n_rt for the control group.

sdt

A \(N \times p\) matrix storing sample standard deviations for each outcome from treatment group. sdt[i,j] is the sample standard deviation from study \(i\) for outcome \(j\). If outcome \(j\) is not continuous such as MD or SMD, NA has to be imputed in the \(j\)th column.

sdc

A matrix defined in a similar way as sdt for the control group.

References

Lu, M. (2023). Computing within-study covariances, data visualization, and missing data solutions for multivariate meta-analysis with metavcov. Frontiers in Psychology, 14:1185012.

Examples

######################################################
# 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
#######################################################################
# Running random-effects model using package "mixmeta" or "metaSEM"
#######################################################################
# Restricted maximum likelihood (REML) estimator from the mixmeta package
#library(mixmeta)
#mvmeta_RE <- summary(mixmeta(cbind(MD_SBP, MD_DBP)~1, 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])