smd.vcov {metavcov}

Computing Variance-Covariance Matrices for Standardized Mean Differences

Description

The function lgOR.vcov computes effect sizes and variance-covariance matrix for multivariate meta-analysis when the effect sizes of interest are all measured by standardized mean difference. See mix.vcov for effect sizes of the same or different types.

Usage

smd.vcov(nt, nc, d, r, n_rt = NA, n_rc = NA, name = NULL)

Arguments

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.

d

A N \times p matrix or data frame with standard mean differences (SMD) from the N studies. d[i,j] is the value from study i for outcome j.

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.

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.

name

Names for the outcomes.

Value

ef

A N \times p data frame that transforms the input argument d into Hedges's g (Wei and Higgins, 2013).

list.vcov

A N-dimensional list of p(p+1)/2 \times p(p+1)/2 variance-covariance matrices for Hedges's g (Wei and Higgins, 2013).

matrix.vcov

A N \times p(p+1)/2 whose rows are computed variance-covariance vectors for Hedges's g (Wei and Higgins, 2013).

list.dvcov

A N-dimensional list of p(p+1)/2 \times p(p+1)/2 variance-covariance matrices for SMD (Olkin and Gleser, 2009).

matrix.dvcov

A N \times p(p+1)/2 matrix whose rows are computed variance-covariance vectors for SMD (Olkin and Gleser, 2009).

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
######################################################
data(Geeganage2010)
## 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 <- smd.vcov(nt = subset(Geeganage2010, select = c(nt_SBP, nt_DBP)),
               nc = subset(Geeganage2010, select = c(nc_SBP, nc_DBP)),
               d = subset(Geeganage2010, select = c(SMD_SBP, SMD_DBP)), r = r.Gee,
               name = c("SMD_SBP", "SMD_DBP"))
# name variance-covariance matrix as S
S <- computvcov$matrix.vcov
## fixed-effect model
y <- computvcov$ef
MMA_FE <- summary(metafixed(y = y, Slist = computvcov$list.vcov))
#######################################################################
# 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(SMD_SBP, SMD_DBP)~1,
#                     S = S,
#                     data = y,
#                     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
# pdf("CI.pdf", width = 4, height = 7)
plotCI(y = computvcov$ef, v = computvcov$list.vcov,
        name.y = NULL, name.study = Geeganage2010$studyID,
        y.all = obj$coefficients[,1],
        y.all.se = obj$coefficients[,2])
# dev.off()