The metafor Package

The data come from studies examining the effectiveness of wrist acupuncture point P6 stimulation for preventing postoperative nausea (Lee & Done, 2004).

library(metafor)
dat <- dat.lee2004
dat <- escalc(measure="OR", ai=ai, n1i=n1i, ci=ci, n2i=n2i, data=dat)

The contents of dat are then:

   id        study year ai n1i ci n2i      yi     vi
1   1      Agarwal 2000 18 100 20 100 -0.1301 0.1303
2   2      Agarwal 2002  5  50 18  50 -1.6219 0.3090
3   3     Alkaissi 1999  9  20  7  20  0.4184 0.4218
4   4     Alkaissi 2002 32 135 31 139  0.0792 0.0825
5   5        Allen 1994  9  23 10  23 -0.1795 0.3595
6   6 Andrzejowski 1996 11  18 12  18 -0.2412 0.4838
7   7       Duggal 1998 69 122 80 122 -0.3805 0.0697
8   8       Dundee 1986  3  25 12  25 -1.9124 0.5390
9   9 Ferrera-Love 1996  1  30  1  30  0.0000 2.0690
10 10       Gieron 1993 11  30 19  30 -1.0931 0.2871
11 11       Harmon 1999  7  44 16  39 -1.3021 0.2759
12 12       Harmon 2000  4  47  6  47 -0.4531 0.4643
13 13           Ho 1996  1  30 13  30 -3.0990 1.1702
14 14         Rusy 2002 24  40 71  80 -1.6600 0.2294
15 15         Wang 2002 16  50 53  88 -1.1687 0.1394
16 16       Zarate 2001 28 110 25 111  0.1610 0.0995

We can fit a random-effects model (using the DerSimonian-Laird estimator) to these data with:

res <- rma(yi, vi, data=dat, method="DL")
print(res, digits=2)

Random-Effects Model (k = 16; tau^2 estimator: DL)
 
tau^2 (estimated amount of total heterogeneity): 0.33 (SE = 0.22)
tau (square root of estimated tau^2 value):      0.58
I^2 (total heterogeneity / total variability):   60.96%
H^2 (total variability / sampling variability):  2.56
 
Test for Heterogeneity:
Q(df = 15) = 38.42, p-val < .01
 
Model Results:
 
estimate       se     zval     pval    ci.lb    ci.ub
   -0.68     0.20    -3.43     <.01    -1.07    -0.29      ***
 
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

These results match what is reported on page 2978.

hc(res, digits=2)

    method tau2 estimate   se ci.lb ci.ub
rma     DL 0.33    -0.68 0.20 -1.07 -0.29
hc      DL 0.33    -0.51 0.22 -1.00 -0.03

Again, these results match what is reported on page 2978.

Henmi, M., & Copas, J. B. (2010). Confidence intervals for random effects meta-analysis and robustness to publication bias. Statistics in Medicine, 29(29), 2969–2983.

Lee, A., & Done, M. L. (2004). Stimulation of the wrist acupuncture point P6 for preventing postoperative nausea and vomiting. Cochrane Database of Systematic Reviews(3), CD003281.