smdMTS: Compute Effect Sizes for Multiple Treatment Studies

Description

It computes the standardized mean differences and their asymptotic sampling covariance matrix for k multiple treatment studies. The first group is assumed as the control group.

Usage

smdMTS(m, v, n, homogeneity=c("variance", "none"), bias.adjust=TRUE, 
       all.comparisons=FALSE, list.output=TRUE, lavaan.output=FALSE)

Arguments

A vector of k sample means.

A vector of k sample variances.

A vector of k sample sizes.

homogeneity

If it is variance (the default), homogeneity of variances is assumed. The common standard deviation is used as the standardizer in calculating the effect sizes. If it is none, homogeneity of variances is not assumed. The standard deviation of the first group is used as the standardizer in calculating the effect sizes.

bias.adjust

If it is TRUE (the default), the effect sizes are adjusted for small bias by multiplying \(1-3/(4*(n1+n2)-9)\).

all.comparisons

If it is FALSE (the default), all groups (except the first group) are compared against the first group. If it is TRUE, all pairwise comparisons are calculated. This may be useful in network meta-analysis.

list.output

If it is TRUE (the default), the effect sizes and their sampling covariance matrix are outputed as a list. If it is FALSE, they will be stacked into a vector.

lavaan.output

If it is FALSE (the default), the effect sizes and its sampling covariance matrix are reported. If it is TRUE, it outputs the fitted lavaan-class object.

Details

Gleser and Olkin (2009) introduce formulas to calculate the standardized mean differences and their sampling covariance matrix for multiple treatment studies under the assumption of homogeneity of the covariance matrix. This function uses a structural equation modeling (SEM) approach introduced in Chapter 3 of Cheung (2015) to calculate the same estimates. The SEM approach is more flexible in three ways: (1) it allows homogeneity of variances or not; (2) it allows users to test the assumption of homogeneity of variances by checking the fitted lavaan-class object; and (3) it may calculate all pairwise comparisons.

References

Cheung, M. W.-L. (2015). Meta-analysis: A structural equation modeling approach. Chichester, West Sussex: John Wiley & Sons, Inc.

Cheung, M. W.-L. (2018). Computing multivariate effect sizes and their sampling covariance matrices with structural equation modeling: Theory, examples, and computer simulations. Frontiers in Psychology, 9(1387). https://doi.org/10.3389/fpsyg.2018.01387

Gleser, L. J., & Olkin, I. (2009). Stochastically dependent effect sizes. In H. Cooper, L. V. Hedges, & J. C. Valentine (Eds.), The handbook of research synthesis and meta-analysis. (2nd ed., pp. 357-376). New York: Russell Sage Foundation.

Examples

Run this code

# NOT RUN {
## Sample means for groups 1 to 3
m <- c(5,7,9)

## Sample variances
v <- c(10,11,12)

## Sample sizes
n <- c(50,52,53)

## Assuming homogeneity of variances
smdMTS(m, v, n, homogeneity = "var", bias.adjust=TRUE, all.comparisons=FALSE,
       lavaan.output=FALSE)

## Not assuming homogeneity of variances and comparing all pairwise groups
## Please note that the SD of the first group is used as the standardizer    
smdMTS(m, v, n, homogeneity = "none", bias.adjust=TRUE, all.comparisons=TRUE,
       lavaan.output=FALSE)

## Output the fitted lavaan model
## It provides a likelihood ratio test to test the null hypothesis of
## homogeneity of variances.    
fit <- smdMTS(m, v, n, homogeneity = "var", bias.adjust=FALSE, all.comparisons=FALSE,
              lavaan.output=TRUE)

lavaan::summary(fit)
    
lavaan::parameterestimates(fit)
# }