Description Usage Details Source References Examples

This dataset includes 13 studies on the effectiveness of the Bacillus Calmette-Guerin (BCG) vaccine for preventing tuberculosis (see van Houwelingen, Arends, & Stijnen (2002) for details).

1 |

A list of data with the following structure:

- Trial
Number of the trials

- Author
Authors of the original studies

- Year
Year of publication

- VD
Vaccinated group with disease

- VWD
Vaccinated group without the disease

- NVD
Not vaccinated group with disease

- NVWD
Not vaccinated group without the disease

- Latitude
Geographic latitude of the place where the study was done

- Allocation
Method of treatment allocation

- ln_OR
Natural logarithm of the odds ratio: log((VD/VWD)/(NVD/NVWD))

- v_ln_OR
Sampling variance of ln_OR: 1/VD+1/VWD+1/NVD+1/NVWD

- ln_Odd_V
Natural logarithm of the odds of the vaccinated group: log(VD/VWD)

- ln_Odd_NV
Natural logarithm of the odds of the not vaccinated group: log(NVD/NVWD)

- v_ln_Odd_V
Sampling variance of ln_Odd_V: 1/VD+1/VWD

- cov_V_NV
Sampling covariance between ln_Odd_V and ln_Odd_NV: It is always 0

- v_ln_Odd_NV
Sampling variance of ln_Odd_NV: 1/NVD+1/NVWD

Colditz, G. A., Brewer, T. F., Berkey, C. S., Wilson, M. E., Burdick, E., Fineberg, H. V., & Mosteller, F. (1994). Efficacy of BCG vaccine in the prevention of tuberculosis: Meta-analysis of the published literature. *Journal of the American Medical Association*, **271**, 698–702.

Berkey, C. S., Hoaglin, D. C., Mosteller, F., & Colditz, G. A. (1995). A random-effects regression model for meta-analysis. *Statistics in Medicine*, **14**, 395–411.

van Houwelingen, H. C., Arends, L. R., & Stijnen, T. (2002). Advanced methods in meta-analysis: Multivariate approach and meta-regression. *Statistics in Medicine*, **21**, 589–624.

Viechtbauer, W. (2010). Conducting meta-analyses in R with the metafor package. *Journal of Statistical Software*, **36**(3), 1–48. https://www.jstatsoft.org/v36/i03/.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 | ```
data(BCG)
## Univariate meta-analysis on the log of the odds ratio
summary( meta(y=ln_OR, v=v_ln_OR, data=BCG,
x=cbind(scale(Latitude,scale=FALSE),
scale(Year,scale=FALSE))) )
## Multivariate meta-analysis on the log of the odds
## The conditional sampling covariance is 0
bcg <- meta(y=cbind(ln_Odd_V, ln_Odd_NV), data=BCG,
v=cbind(v_ln_Odd_V, cov_V_NV, v_ln_Odd_NV))
summary(bcg)
plot(bcg)
``` |

```
Loading required package: OpenMx
To take full advantage of multiple cores, use:
mxOption(NULL, 'Number of Threads', parallel::detectCores())
"SLSQP" is set as the default optimizer in OpenMx.
mxOption(NULL, "Gradient algorithm") is set at "central".
mxOption(NULL, "Optimality tolerance") is set at "6.3e-14".
mxOption(NULL, "Gradient iterations") is set at "2".
sh: 1: wc: Permission denied
sh: 1: cannot create /dev/null: Permission denied
Call:
meta(y = ln_OR, v = v_ln_OR, x = cbind(scale(Latitude, scale = FALSE),
scale(Year, scale = FALSE)), data = BCG)
95% confidence intervals: z statistic approximation
Coefficients:
Estimate Std.Error lbound ubound z value Pr(>|z|)
Intercept1 -0.7166884 0.0766950 -0.8670079 -0.5663688 -9.3446 < 2.2e-16 ***
Slope1_1 -0.0335019 0.0054079 -0.0441013 -0.0229026 -6.1949 5.831e-10 ***
Slope1_2 -0.0013515 0.0068862 -0.0148483 0.0121453 -0.1963 0.8444
Tau2_1_1 0.0020944 0.0184838 -0.0341331 0.0383219 0.1133 0.9098
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Q statistic on the homogeneity of effect sizes: 163.1649
Degrees of freedom of the Q statistic: 12
P value of the Q statistic: 0
Explained variances (R2):
y1
Tau2 (no predictor) 0.3025
Tau2 (with predictors) 0.0021
R2 0.9931
Number of studies (or clusters): 13
Number of observed statistics: 13
Number of estimated parameters: 4
Degrees of freedom: 9
-2 log likelihood: 13.89208
OpenMx status1: 0 ("0" or "1": The optimization is considered fine.
Other values may indicate problems.)
Call:
meta(y = cbind(ln_Odd_V, ln_Odd_NV), v = cbind(v_ln_Odd_V, cov_V_NV,
v_ln_Odd_NV), data = BCG)
95% confidence intervals: z statistic approximation
Coefficients:
Estimate Std.Error lbound ubound z value Pr(>|z|)
Intercept1 -4.83374 0.34020 -5.50052 -4.16697 -14.2086 < 2e-16 ***
Intercept2 -4.09597 0.43475 -4.94806 -3.24389 -9.4216 < 2e-16 ***
Tau2_1_1 1.43137 0.58304 0.28863 2.57411 2.4550 0.01409 *
Tau2_2_1 1.75733 0.72425 0.33781 3.17684 2.4264 0.01525 *
Tau2_2_2 2.40733 0.96742 0.51122 4.30344 2.4884 0.01283 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Q statistic on the homogeneity of effect sizes: 5270.386
Degrees of freedom of the Q statistic: 24
P value of the Q statistic: 0
Heterogeneity indices (based on the estimated Tau2):
Estimate
Intercept1: I2 (Q statistic) 0.9887
Intercept2: I2 (Q statistic) 0.9955
Number of studies (or clusters): 13
Number of observed statistics: 26
Number of estimated parameters: 5
Degrees of freedom: 21
-2 log likelihood: 66.17587
OpenMx status1: 0 ("0" or "1": The optimization is considered fine.
Other values may indicate problems.)
```

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