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I am trying to meta-analyze c-statistic using the meta::metaprop function in R. However, I noticed that I can only enter the number of events and the total sample size with the function. When I do this the 95% confidence intervals for each c-statistic are not the same as what are reported in the in papers.

For example, in a paper by S3 and colleagues, a C-index of 0.78 (95% CI 0.75–0.81; N=5123) is reported. When the data are transferred to metaprop (event = 0.78 * 5123; N = 5123), the 95% CI is 0.77 to 0.79.

The code is below:

library(tidyverse)
library(meta)
library(metafor)

data=as.data.frame(rbind(c("s1",0.81,6652,8212),
                         c("s1.1",0.78,6691,8578),
                         c("s2",0.78,3996,5123),
                         c("s3",0.75,4035,5380)))
data <- as_tibble(data)
data$studytype=c("Internal Validation","External Validation","External Validation","External Validation")
data$year=c(2020,2020,2020,2021)
data$validationcohort=c("S1","S1.1", "S2","S3")

data <- plyr::rename(data,c("V1"="Author","V2"="Cstat","V3"="Event","V4"="Number"))

view(data)

data
#> # A tibble: 4 x 7
#>   Author            Cstat Event Number studytype           year validationcohort
#>   <chr>             <chr> <chr> <chr>  <chr>              <dbl> <chr>           
#> 1 s1.1 et al.       0.81  6652  8212   Internal Validati~  2020 s1.1  
#> 2 s1.1 et al.       0.78  6691  8578   External Validati~  2020 s1.1 
#> 3 s2 et al.         0.78  3996  5123   External Validati~  2020 s2
#> 4 s3 et al.         0.75  4035  5380   External Validati~  2021 s3

m1<- metaprop(as.numeric(Event),as.numeric(Number),data=data,studlab=Author,comb.random = TRUE,sm="PAS")
m1
#>                   proportion           95%-CI %W(fixed) %W(random)
#> s1 et al.             0.8100 [0.8014; 0.8185]      30.1       25.2
#> s1.1 et al.           0.7800 [0.7711; 0.7887]      31.4       25.3
#> s2 et al.             0.7800 [0.7684; 0.7913]      18.8       24.7
#> s3 et al.             0.7500 [0.7382; 0.7615]      19.7       24.8
#> 
#> Number of studies combined: k = 4
#> 
#>                      proportion           95%-CI
#> Fixed effect model       0.7835 [0.7786; 0.7884]
#> Random effects model     0.7805 [0.7560; 0.8041]
#> 
#> Quantifying heterogeneity:
#>  tau^2 = 0.0008 [0.0002; 0.0123]; tau = 0.0290 [0.0156; 0.1107]
#>  I^2 = 95.7% [91.9%; 97.8%]; H = 4.85 [3.52; 6.68]
#> 
#> Test of heterogeneity:
#>      Q d.f.  p-value
#>  70.51    3 < 0.0001
#> 
#> Details on meta-analytical method:
#> - Inverse variance method
#> - DerSimonian-Laird estimator for tau^2
#> - Jackson method for confidence interval of tau^2 and tau
#> - Arcsine transformation
#> - Clopper-Pearson confidence interval for individual studies

Help would be seriously appreciated!

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