Results from 13 studies examining the effectiveness of the Bacillus Calmette-Guerin (BCG) vaccine against tuberculosis.

dat.bcg

Format

The data frame contains the following columns:

trialnumerictrial number
authorcharacterauthor(s)
yearnumericpublication year
tposnumericnumber of TB positive cases in the treated (vaccinated) group
tnegnumericnumber of TB negative cases in the treated (vaccinated) group
cposnumericnumber of TB positive cases in the control (non-vaccinated) group
cnegnumericnumber of TB negative cases in the control (non-vaccinated) group
ablatnumericabsolute latitude of the study location (in degrees)
alloccharactermethod of treatment allocation (random, alternate, or systematic assignment)

Details

The 13 studies provide data in terms of \(2 \times 2\) tables in the form:

TB positiveTB negative
vaccinated grouptpostneg
control groupcposcneg

The goal of the meta-analysis was to examine the overall effectiveness of the BCG vaccine for preventing tuberculosis and to examine moderators that may potentially influence the size of the effect.

The dataset has been used in several publications to illustrate meta-analytic methods (see ‘References’).

Source

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(9), 698--702. https://doi.org/10.1001/jama.1994.03510330076038

References

Berkey, C. S., Hoaglin, D. C., Mosteller, F., & Colditz, G. A. (1995). A random-effects regression model for meta-analysis. Statistics in Medicine, 14(4), 395--411. https://doi.org/10.1002/sim.4780140406

van Houwelingen, H. C., Arends, L. R., & Stijnen, T. (2002). Advanced methods in meta-analysis: Multivariate approach and meta-regression. Statistics in Medicine, 21(4), 589--624. https://doi.org/10.1002/sim.1040

Viechtbauer, W. (2010). Conducting meta-analyses in R with the metafor package. Journal of Statistical Software, 36(3), 1--48. https://doi.org/10.18637/jss.v036.i03

Examples

### copy data into 'dat' and examine data
dat <- dat.bcg
dat
#>    trial               author year tpos  tneg cpos  cneg ablat      alloc
#> 1      1              Aronson 1948    4   119   11   128    44     random
#> 2      2     Ferguson & Simes 1949    6   300   29   274    55     random
#> 3      3      Rosenthal et al 1960    3   228   11   209    42     random
#> 4      4    Hart & Sutherland 1977   62 13536  248 12619    52     random
#> 5      5 Frimodt-Moller et al 1973   33  5036   47  5761    13  alternate
#> 6      6      Stein & Aronson 1953  180  1361  372  1079    44  alternate
#> 7      7     Vandiviere et al 1973    8  2537   10   619    19     random
#> 8      8           TPT Madras 1980  505 87886  499 87892    13     random
#> 9      9     Coetzee & Berjak 1968   29  7470   45  7232    27     random
#> 10    10      Rosenthal et al 1961   17  1699   65  1600    42 systematic
#> 11    11       Comstock et al 1974  186 50448  141 27197    18 systematic
#> 12    12   Comstock & Webster 1969    5  2493    3  2338    33 systematic
#> 13    13       Comstock et al 1976   27 16886   29 17825    33 systematic

# \dontrun{

### load metafor package
library(metafor)

### calculate log risk ratios and corresponding sampling variances
dat <- escalc(measure="RR", ai=tpos, bi=tneg, ci=cpos, di=cneg, data=dat)
dat
#> 
#>    trial               author year tpos  tneg cpos  cneg ablat      alloc      yi     vi 
#> 1      1              Aronson 1948    4   119   11   128    44     random -0.8893 0.3256 
#> 2      2     Ferguson & Simes 1949    6   300   29   274    55     random -1.5854 0.1946 
#> 3      3      Rosenthal et al 1960    3   228   11   209    42     random -1.3481 0.4154 
#> 4      4    Hart & Sutherland 1977   62 13536  248 12619    52     random -1.4416 0.0200 
#> 5      5 Frimodt-Moller et al 1973   33  5036   47  5761    13  alternate -0.2175 0.0512 
#> 6      6      Stein & Aronson 1953  180  1361  372  1079    44  alternate -0.7861 0.0069 
#> 7      7     Vandiviere et al 1973    8  2537   10   619    19     random -1.6209 0.2230 
#> 8      8           TPT Madras 1980  505 87886  499 87892    13     random  0.0120 0.0040 
#> 9      9     Coetzee & Berjak 1968   29  7470   45  7232    27     random -0.4694 0.0564 
#> 10    10      Rosenthal et al 1961   17  1699   65  1600    42 systematic -1.3713 0.0730 
#> 11    11       Comstock et al 1974  186 50448  141 27197    18 systematic -0.3394 0.0124 
#> 12    12   Comstock & Webster 1969    5  2493    3  2338    33 systematic  0.4459 0.5325 
#> 13    13       Comstock et al 1976   27 16886   29 17825    33 systematic -0.0173 0.0714 
#> 

### random-effects model
res <- rma(yi, vi, data=dat)
res
#> 
#> Random-Effects Model (k = 13; tau^2 estimator: REML)
#> 
#> tau^2 (estimated amount of total heterogeneity): 0.3132 (SE = 0.1664)
#> tau (square root of estimated tau^2 value):      0.5597
#> I^2 (total heterogeneity / total variability):   92.22%
#> H^2 (total variability / sampling variability):  12.86
#> 
#> Test for Heterogeneity:
#> Q(df = 12) = 152.2330, p-val < .0001
#> 
#> Model Results:
#> 
#> estimate      se     zval    pval    ci.lb    ci.ub     ​ 
#>  -0.7145  0.1798  -3.9744  <.0001  -1.0669  -0.3622  *** 
#> 
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 

### average risk ratio with 95% CI
predict(res, transf=exp)
#> 
#>    pred  ci.lb  ci.ub  pi.lb  pi.ub 
#>  0.4894 0.3441 0.6962 0.1546 1.5490 
#> 

### mixed-effects model with absolute latitude and publication year as moderators
res <- rma(yi, vi, mods = ~ ablat + year, data=dat)
res
#> 
#> Mixed-Effects Model (k = 13; tau^2 estimator: REML)
#> 
#> tau^2 (estimated amount of residual heterogeneity):     0.1108 (SE = 0.0845)
#> tau (square root of estimated tau^2 value):             0.3328
#> I^2 (residual heterogeneity / unaccounted variability): 71.98%
#> H^2 (unaccounted variability / sampling variability):   3.57
#> R^2 (amount of heterogeneity accounted for):            64.63%
#> 
#> Test for Residual Heterogeneity:
#> QE(df = 10) = 28.3251, p-val = 0.0016
#> 
#> Test of Moderators (coefficients 2:3):
#> QM(df = 2) = 12.2043, p-val = 0.0022
#> 
#> Model Results:
#> 
#>          estimate       se     zval    pval     ci.lb    ci.ub    ​ 
#> intrcpt   -3.5455  29.0959  -0.1219  0.9030  -60.5724  53.4814     
#> ablat     -0.0280   0.0102  -2.7371  0.0062   -0.0481  -0.0080  ** 
#> year       0.0019   0.0147   0.1299  0.8966   -0.0269   0.0307     
#> 
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 

### predicted average risk ratios for 10-60 degrees absolute latitude
### holding the publication year constant at 1970
predict(res, newmods=cbind(seq(from=10, to=60, by=10), 1970), transf=exp)
#> 
#>     pred  ci.lb  ci.ub  pi.lb  pi.ub 
#> 1 0.9345 0.5833 1.4973 0.4179 2.0899 
#> 2 0.7062 0.5149 0.9686 0.3421 1.4579 
#> 3 0.5337 0.4196 0.6789 0.2663 1.0697 
#> 4 0.4033 0.2956 0.5502 0.1958 0.8306 
#> 5 0.3048 0.1916 0.4848 0.1369 0.6787 
#> 6 0.2303 0.1209 0.4386 0.0921 0.5761 
#> 

### note: the interpretation of the results is difficult because absolute
### latitude and publication year are strongly correlated (the more recent
### studies were conducted closer to the equator)
plot(dat$year, dat$ablat, pch=19, xlab="Publication Year", ylab="Absolute Lattitude")

cor(dat$year, dat$ablat)
#> [1] -0.6630572

# }