Random effect meta-analysis for correlated test statistics

Random effect meta-analysis for correlated test statistics using RE2C

Usage

RE2C(beta, stders, cor = diag(1, length(beta)), twoStep = FALSE)

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
twoStep: Apply two step version of RE2C that is designed to be applied only after the fixed effect model.

Value

stat1:: statistic testing effect mean
stat2:: statistic testing effect heterogeneity
RE2Cp:: RE2 p-value accounting for correlelation between tests
RE2Cp.twoStep:: two step RE2C test after fixed effect test. Only evaluated if twoStep==TRUE
QE:: test statistic for the test of (residual) heterogeneity
QEp:: p-value for the test of (residual) heterogeneity
Isq:: I^2 statistic

Details

Perform random effect meta-analysis for correlated test statistics using RE2 method of Han and Eskin (2011) , or RE2 for correlated test statistics from Han et al. (2016) . Also uses RE2C method of Lee et al. (2017) to further test for heterogenity in effect size. 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.

For computing Q, QEp, and Isq, the effective number of independent studies is determined by sum(solve(cor)) (Liu and Liang 1997) . When the correlation is diagonal, the studies are independent and this value is simply the number of studies.

References

Han B, Duong D, Sul JH, de Bakker PI, Eskin E, Raychaudhuri S (2016). “A general framework for meta-analyzing dependent studies with overlapping subjects in association mapping.” Human Molecular Genetics, 25(9), 1857--1866. https://doi.org/10.1093/hmg/ddw049.

Han B, Eskin E (2011). “Random-effects model aimed at discovering associations in meta-analysis of genome-wide association studies.” The American Journal of Human Genetics, 88(5), 586--598. https://doi.org/10.1016/j.ajhg.2011.04.014.

Lee CH, Eskin E, Han B (2017). “Increasing the power of meta-analysis of genome-wide association studies to detect heterogeneous effects.” Bioinformatics, 33(14), i379--i388. https://doi.org/10.1093/bioinformatics/btx242.

Liu G, Liang K (1997). “Sample size calculations for studies with correlated observations.” Biometrics, 937--947. https://doi.org/10.2307/2533554.

Examples

library(clusterGeneration)
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 1.166358 0.1464346 1.651602e-15

# Run random effects meta-analysis,
# assume identity correlation  
RE2C( df$beta, df$se)
#>      stat1      stat2        RE2Cp RE2Cp.twoStep       QE       QEp      Isq
#> 1 63.44198 0.02154174 6.196746e-15            NA 5.465673 0.3617246 8.519961

# Run fixed effects meta-analysis, 
# account for correlation 
LS( df$beta, df$se, C)
#>       beta       se            p
#> 1 1.153794 0.175376 4.737006e-11

# Run random effects meta-analysis,
# account for correlation 
RE2C( df$beta, df$se, C)
#>      stat1     stat2       RE2Cp RE2Cp.twoStep       QE      QEp      Isq
#> 1 43.28292 0.2068769 1.53742e-10            NA 5.473035 0.174815 38.51018