md.vcov {metavcov}R Documentation

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 NN-dimensional list of p×pp \times p correlation matrices for the pp outcomes from the NN studies. r[[k]][i,j] is the correlation coefficient between outcome ii and outcome jj from study kk.

nt

A N×pN \times p matrix storing sample sizes in the treatment group reporting the pp outcomes. nt[i,j] is the sample size from study ii reporting outcome jj.

nc

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

n_rt

A NN-dimensional list of p×pp \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 ii and outcome jj from study kk. 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×pN \times p matrix storing sample standard deviations for each outcome from treatment group. sdt[i,j] is the sample standard deviation from study ii for outcome jj. If outcome jj is not continuous such as MD or SMD, NA has to be imputed in the jjth column.

sdc

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

Value

list.vcov

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

matrix.vcov

A N×p(p+1)/2N \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])

[Package metavcov version 2.1.5 Index]