R/meta_ave.R
meta.ave.gen.rc.Rd
Computes the estimate, standard error, and confidence interval for a weighted average effect from multiple studies using the random coefficient (random-effects) meta-analysis model. An estimate of effect-size heterogeneity (tau-squared) is also computed.
meta.ave.gen.rc(alpha, est, se, bystudy = TRUE)
alpha level for 1-alpha confidence
vector of parameter estimates
vector of standard errors
logical to also return each study estimate (TRUE) or not
Returns a matrix. The first row is the average estimate across all studies. If bystudy is true, there is 1 additional row for each study. The matrix has the following columns:
Estimate - estimated effect size
SE - standard error
LL - lower limit of the confidence interval
UL - upper limit of the confidence interval
The random coefficient model assumes that the studies in the meta-analysis are a random sample from some definable superpopulation of studies. This assumption is very difficult to justify. The weighted average estimate will be biased regardless of the number of studies or the sample size in each study. The actual confidence interval coverage probability can much smaller than the specified confidence level if the effect sizes are correlated with the weights (which occurs frequently). The confidence interval for tau-squared assumes that the true effect sizes in the superpopulation of studies have a normal distribution. A large number of studies, each with a large sample size, is required to assess the superpopulation normality assumption and to accurately estimate tau-squared. The confidence interval for the population tau-squared is hypersensitive to very minor and difficult-to-detect violations of the superpopulation normality assumption.
The random coefficient model should be used with caution, and the varying coefficient methods in this package are the recommended alternatives. The varying coefficient methods allows the effect sizes to differ across studies but do not require the studies to be a random sample from a definable superpopoulation of studies. This random coefficient function is included in the vcmeta package primarily for classroom demonstrations to illustrate the problimatic characteristics of the random coefficient meta-analysis model.
Hedges LV, Olkin I (1985). Statistical methods for meta-analysis. Academic Press, New York. ISBN 01-233-63802.
Borenstein M, Hedges LV, Higgins JP, Rothstein HR (2009). Introduction to meta-analysis. Wiley, New York.
est <- c(.022, .751, .421, .287, .052, .146, .562, .904)
se <- c(.124, .464, .102, .592, .864, .241, .252, .318)
meta.ave.gen.rc(.05, est, se, bystudy = TRUE)
#> Estimate SE LL UL
#> Tau-squared 0.03772628 0.0518109 0.00000000 0.1392738
#> Average 0.35394806 0.1155239 0.12752528 0.5803708
#> Study 1 0.02200000 0.1240000 -0.22103553 0.2650355
#> Study 2 0.75100000 0.4640000 -0.15842329 1.6604233
#> Study 3 0.42100000 0.1020000 0.22108367 0.6209163
#> Study 4 0.28700000 0.5920000 -0.87329868 1.4472987
#> Study 5 0.05200000 0.8640000 -1.64140888 1.7454089
#> Study 6 0.14600000 0.2410000 -0.32635132 0.6183513
#> Study 7 0.56200000 0.2520000 0.06808908 1.0559109
#> Study 8 0.90400000 0.3180000 0.28073145 1.5272685
# Should return:
# Estimate SE LL UL
# Tau-squared 0.03772628 0.0518109 0.00000000 0.1392738
# Average 0.35394806 0.1155239 0.12752528 0.5803708
# Study 1 0.02200000 0.1240000 -0.22103553 0.2650355
# Study 2 0.75100000 0.4640000 -0.15842329 1.6604233
# Study 3 0.42100000 0.1020000 0.22108367 0.6209163
# Study 4 0.28700000 0.5920000 -0.87329868 1.4472987
# Study 5 0.05200000 0.8640000 -1.64140888 1.7454089
# Study 6 0.14600000 0.2410000 -0.32635132 0.6183513
# Study 7 0.56200000 0.2520000 0.06808908 1.0559109
# Study 8 0.90400000 0.3180000 0.28073145 1.5272685