Fixed effect meta-analysis for correlated test statistics

Fixed effect meta-analysis for correlated test statistics using the Lin-Sullivan method.

Usage

LS(beta, stders, cor = diag(1, length(beta)))

Arguments

beta: regression coefficients from each analysis
stders: standard errors corresponding to betas
cor: correlation matrix between of test statistics. Default considers uncorrelated test statistics

Value

beta:: effect size
se:: effect size standard error
p:: p-value

Details

Perform fixed effect meta-analysis for correlated test statistics using method of Lin and Sullivan (2009). By default, correlation is set to identity matrix to for independent test statistics.

This method requires the correlation matrix to be symmatric positive definite (SPD). If this condition is not satisfied, results will be NA. If the matrix is not SPD, there is likely an issue with how it was generated.

However, evaluating the correlation between observations that are not pairwise complete can give correlation matricies that are not SPD. In this case, consider running Matrix::nearPD( x, corr=TRUE) to produce the nearest SPD matrix to the input.

References

Lin D, Sullivan PF (2009). “Meta-analysis of genome-wide association studies with overlapping subjects.” The American Journal of Human Genetics, 85(6), 862--872. https://doi.org/10.1016/j.ajhg.2009.11.001.

Examples

library(clusterGeneration)
#> Loading required package: MASS
library(mvtnorm)

# sample size
n = 30

# number of response variables
m = 6

# Error covariance
Sigma = genPositiveDefMat(m)$Sigma

# regression parameters
beta = matrix(.6, 1, m)

# covariates
X = matrix(rnorm(n), ncol=1)

# Simulate response variables
Y = X %*% beta + rmvnorm(n, sigma = Sigma)

# Multivariate regression
fit = lm(Y ~ X)

# Correlation between residuals
C = cor(residuals(fit))

# Extract effect sizes and standard errors from model fit
df = lapply(coef(summary(fit)), function(a) 
 data.frame(beta = a["X", 1], se = a["X", 2]))
df = do.call(rbind, df)

# Run fixed effects meta-analysis, 
# assume identity correlation  
LS( df$beta, df$se)
#>        beta        se            p
#> 1 0.8158457 0.1879126 1.414346e-05
 
# Run fixed effects meta-analysis, 
# account for correlation 
LS( df$beta, df$se, C)
#>        beta        se            p
#> 1 0.7488763 0.1975421 0.0001500601