md.vcov {metavcov}

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)

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 jth column.

sdc

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

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(s)

Min Lu

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])