Description Usage Arguments Value References Examples
View source: R/StandardMetaAnalysis.R
This function performs maximum likelihood estimation (MLE) of (θ, τ) for the standard random effects meta-analysis model,
y_i = θ + τ u_i + s_i ε_i,
where y_i is the reported treatment effect for the ith study, s_i is the reported standard error for the ith study, θ is the population treatment effect of interest, τ > 0 is a heterogeneity parameter, and u_i and ε_i are independent and distributed as N(0,1).
1 | StandardMetaAnalysis(y, s, init = NULL, tol=1e-10, maxit=1000)
|
y |
An n \times 1 vector of reported treatment effects. |
s |
An n \times 1 vector of reported within-study standard errors. |
init |
Optional initialization values for (θ, τ). If specified, they must be provided in this order. If they are not provided, the program estimates initial values from the data. |
tol |
Convergence criterion for the optimization algorithm for finding the MLE. Default is |
maxit |
Maximum number of iterations for the optimization algorithm for finding the MLE. Default is |
The function returns a list containing the following components:
theta.hat |
MLE of θ. |
tau.hat |
MLE of τ. |
H |
2 \times 2 Hessian matrix for the estimates of (θ, τ). The square root of the diagonal entries of H can be used to estimate the standard errors for (θ, τ). |
conv |
"1" if the optimization algorithm converged, "0" if algorithm did not converge. If |
Bai, R., Lin, L., Boland, M. R., and Chen, Y. (2020). "A robust Bayesian Copas selection model for quantifying and correcting publication bias." arXiv preprint arXiv:2005.02930.
Ning, J., Chen, Y., and Piao, J. (2017). "Maximum likelihood estimation and EM algorithm of Copas-like selection model for publication bias correction." Biostatistics, 18(3):495-504.
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# Example on the antidepressants data set. #
# This is from Section 6.2 of the paper by #
# Bai et al. (2020). #
############################################
# Load the full data
data(antidepressants)
attach(antidepressants)
# Extract the 50 published studies
published.data = antidepressants[which(antidepressants$Published==1),]
# Observed treatment effect
y.obs = published.data$Standardized_effect_size
# Observed standard error
s.obs = published.data$Standardized_SE
#################################
# Fit a standard meta-analysis #
# that ignores publication bias #
#################################
# Set seed
set.seed(123)
SMA.mod = StandardMetaAnalysis(y=y.obs, s=s.obs)
# Point estimate for theta
SMA.theta.hat = SMA.mod$theta.hat
# Use Hessian to estimate standard error for theta
SMA.Hessian = SMA.mod$H
# Standard error estimate for theta
SMA.theta.se = sqrt(SMA.Hessian[1,1])
# 95 percent confidence interval
SMA.interval = c(SMA.theta.hat-1.96*SMA.theta.se, SMA.theta.hat+1.96*SMA.theta.se)
# Display results
SMA.theta.hat
SMA.theta.se
SMA.interval
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