Confidence interval for an average effect size using a constant coefficient model

Source: R/meta_ave.R

Computes the estimate, standard error, and confidence interval for a weighted average effect from two or more studies using the constant coefficient (fixed-effect) meta-analysis model.

meta.ave.gen.cc(alpha, est, se, bystudy = TRUE)

Arguments

alpha

alpha level for 1-alpha confidence

est

vector of parameter estimates

se

vector of standard errors

bystudy

logical to also return each study estimate (TRUE) or not

Value

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

Details

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 be much smaller than the specified confidence level when the population effect sizes are not identical across studies.

The constant coefficient model should be used with caution, and the varying coefficient methods in this package are the recommended alternatives. The varying coefficient methods do not require effect-size homogeneity across the selected studies. This constant coefficient meta-analysis function is included in the vcmeta package primarily for classroom demonstrations to illustrate the problematic characteristics of the constant coefficient meta-analysis model.

References

  • 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.

See also

meta.ave.gen

Examples

est <- c(.022, .751, .421, .287, .052, .146, .562, .904)
se <- c(.124, .464, .102, .592, .864, .241, .252, .318)
meta.ave.gen.cc(.05, est, se, bystudy = TRUE)
#>          Estimate         SE          LL        UL
#> Average 0.3127916 0.06854394  0.17844794 0.4471352
#> Study 1 0.0220000 0.12400000 -0.22103553 0.2650355
#> Study 2 0.7510000 0.46400000 -0.15842329 1.6604233
#> Study 3 0.4210000 0.10200000  0.22108367 0.6209163
#> Study 4 0.2870000 0.59200000 -0.87329868 1.4472987
#> Study 5 0.0520000 0.86400000 -1.64140888 1.7454089
#> Study 6 0.1460000 0.24100000 -0.32635132 0.6183513
#> Study 7 0.5620000 0.25200000  0.06808908 1.0559109
#> Study 8 0.9040000 0.31800000  0.28073145 1.5272685

# Should return:
#             Estimate         SE          LL        UL
# Average    0.3127916 0.06854394  0.17844794 0.4471352
# Study 1    0.0220000 0.12400000 -0.22103553 0.2650355
# Study 2    0.7510000 0.46400000 -0.15842329 1.6604233
# Study 3    0.4210000 0.10200000  0.22108367 0.6209163
# Study 4    0.2870000 0.59200000 -0.87329868 1.4472987
# Study 5    0.0520000 0.86400000 -1.64140888 1.7454089
# Study 6    0.1460000 0.24100000 -0.32635132 0.6183513
# Study 7    0.5620000 0.25200000  0.06808908 1.0559109
# Study 8    0.9040000 0.31800000  0.28073145 1.5272685