Effect-Size Calculation for Meta-Analysis in R #rstats

When conducting meta-analysis, you most likely have to calculate or convert effects sizes into an effect size with common measure. There are various tools to do this – one easy to use tool is the Practical Meta-Analysis Effect Size Calculator from David B. Wilson.

This online-tool is now implemented as an R-package: esc: Effect Size Computation for Meta Analysis.

Calculating Effect Sizes

The package covers most of the effect size calculation and conversion options from the online-tool, but in a more compact way, which gives you a better overiew. For instance, getting an effect size from a t-test, means you have to find and choose from four different options in the online tool, while the esc-package just needs one function:

esc_t(t, p, totaln, grp1n, grp2n, 
      es.type = c("d", "g", "or", "logit", "r", "cox.or", "cox.log"), 
      study = NULL, ...)

You can then compute the effect size, depending on your available parameters, like this:

# unequal sample size
esc_t(t = 3.3, grp1n = 100, grp2n = 150)

# equal sample size
esc_t(t = 3.3, totaln = 200)

# unequal sample size, with p-value
esc_t(p = 0.03, grp1n = 100, grp2n = 150)

# equal sample size, with p-value
esc_t(p = 0.03, totaln = 200)

Converting Effect Sizes

The package offers various functions to convert one effect size into another: esc_d2logit() (std. mean diff. to log-odds), esc_d2or() (std. mean diff. to odds ratios), esc_d2r() (std. mean diff. to correlation r), esc_or2d() (odds ratio to std. mean diff.), esc_r2z() (correlation coefficient r into Fisher’s z) and esc_z2r() (Fisher’s z into correlation coefficient r). However, the es.type-argument in each function gives you the required effect size measure directly.

Workflow with the metafor-package

The results of the effect size calculation functions in this package are returned as list with a esc-class attribute. The combine_esc()-function takes one or more of these esc-objects and combines them into a data.frame that can be used as argument for further use, for instance with the rma()-function.

e1 <- esc_2x2(grp1yes = 30, grp1no = 50, grp2yes = 40,
              grp2no = 45, study = "Study 1")
e2 <- esc_2x2(grp1yes = 30, grp1no = 50, grp2yes = 40, grp2no = 45,
              es.type = "or", study = "Study 2")
e3 <- esc_t(p = 0.03, grp1n = 100, grp2n = 150, study = "Study 3")
e4 <- esc_mean_sd(grp1m = 7, grp1sd = 2, grp1n = 50, grp2m = 9, grp2sd = 3,
                  grp2n = 60, es.type = "logit", study = "Study 4")

mydat <- combine_esc(e1, e2, e3, e4)

Now, mydat contains a data frame with the results of several effect size calculations:

> mydat
    study         es    weight sample.size        se        var       ci.lo      ci.hi measure
1 Study 1 -0.3930426  9.944751         165 0.3171050 0.10055556 -1.01455689  0.2284717   logit
2 Study 2  0.6750000  9.944751         165 0.3171050 0.10055556  0.36256305  1.2566780      or
3 Study 3  0.2817789 59.433720         250 0.1297130 0.01682547  0.02754605  0.5360117       d
4 Study 4 -1.3981827  7.721145         110 0.3598812 0.12951447 -2.10353685 -0.6928285   logit

The meta-analysis is then computed like this (note that the different effect-size measures are just for demonstration purposes – usually, you should have only one common effect size that goes into the meta-analysis):

metafor::rma(yi = es, sei = se, method = "REML", data = mydat)

Last words

The package update 0.2.0 includes a small convenient function, write_esc(), to write an Excel-csv-file with the converted effect sizes.