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Meta-analysis · binary outcome

Forest plot example: BCG vaccine trials (risk ratio, random effects)

Forest plot of the 13 classic BCG vaccine trials with events and totals per arm, a random-effects pooled risk ratio and heterogeneity statistics.

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VaccinatedNot vaccinatedStudyEventsTotalEventsTotalWeightRR [95% CI]Aronson 19484123111395.0%0.41 [0.13, 1.26]Ferguson & Simes 19496306293036.3%0.20 [0.09, 0.49]Rosenthal 19603231112204.4%0.26 [0.07, 0.92]Hart & Sutherland 19776213,59824812,8679.7%0.24 [0.18, 0.31]Frimodt-Moller 1973335,069475,8088.9%0.80 [0.52, 1.25]Stein & Aronson 19531801,5413721,45110.1%0.46 [0.39, 0.54]Vandiviere 197382,545106296.0%0.20 [0.08, 0.50]TPT Madras 198050588,39149988,39110.2%1.01 [0.89, 1.14]Coetzee & Berjak 1968297,499457,2778.7%0.63 [0.39, 1.00]Rosenthal 1961171,716651,6658.4%0.25 [0.15, 0.43]Comstock 197418650,63414127,3389.9%0.71 [0.57, 0.89]Comstock & Webster 196952,49832,3413.8%1.56 [0.37, 6.53]Comstock 19762716,9132917,8548.4%0.98 [0.58, 1.66]Total (95% CI)1,065191,0641,510166,283100.0%0.49 [0.34, 0.70]0.050.21520Favours vaccineFavours controlHeterogeneity: Tau² = 0.31; Chi² = 152.23, df = 12 (P < 0.001); I² = 92%Test for overall effect: Z = 4.00 (P < 0.001)
Risk ratios for tuberculosis in vaccinated vs unvaccinated groups, pooled with a random-effects model.

About this example

The BCG vaccine trials (Colditz et al., JAMA 1994) are a standard teaching dataset for meta-analysis. Each trial reports tuberculosis cases and group sizes in vaccinated and unvaccinated participants, from which a risk ratio and its variance are computed.

The random-effects pooled risk ratio is about 0.49, but heterogeneity is very high (I² above 90%), so the average effect hides large differences between trials. CleanFigure reproduces the metafor results for this dataset exactly.

The data

StudyEvents TTotal TEvents CTotal C
Aronson 1948412311139
Ferguson & Simes 1949630629303
Rosenthal 1960323111220
Hart & Sutherland 1977621359824812867
Frimodt-Moller 1973335069475808
Stein & Aronson 195318015413721451
Vandiviere 19738254510629
TPT Madras 19805058839149988391
Coetzee & Berjak 1968297499457277
Rosenthal 1961171716651665
Comstock 19741865063414127338
Comstock & Webster 19695249832341
Comstock 197627169132917854

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