[R-meta] Calculating pooled effect size

[Adelina Artenie]

Hi,

This is probably a silly question but can�t see where my error is, so it would be great to have your thoughts. I am doing a RE meta-analysis of rates and the pooled rate that I am getting does not equal the value I get from summing the individual effects multiplied by their prob. weights. I am ignoring the SE for this exercise, just looking at the pooled effect.

In this example, the pooled effect produced by R is 10.5499. If I do sum(individual rates * w.random) /sum(w.random), I get 12.45 (768.85 / 61.75). The pooled overall effect in R is consistently smaller relative to what I get when I calculate this by hand.

Thank you in advance.
Adelina

***
library(meta)
library(metafor)

my_dat <- data.frame(
  ID = 1:19,
  Rate = c(14.1, 19.4, 19.0, 12.5, 5.8, 7.2, 14.0, 11.6, 22.5, 11.1, 9.5, 1.1, 9.8, 7.9, 11.2, 28.7, 7.1, 15.5, 11.2),
  LB = c(9.6, 14.8, 11.6, 9.7, 4.3, 4.2, 6.0, 5.6, 11.6, 8.2, 8.0, 0.8, 7.9, 7.1, 8.9, 20.6, 4.3, 13.1, 9.0),
  UB = c(20.7, 25.5, 31.1, 16.1, 7.7, 12.1, 32.5, 24.4, 43.8, 14.9, 11.3, 1.6, 12.2, 8.7, 14.2, 40.2, 11.7, 18.3, 13.9)
)

ln_rate <- log(my_dat$Rate)
ln_LB <-log(my_dat$LB)
ln_UB <-log(my_dat$UB)

my_metagen <- metagen(TE = ln_rate,
                         lower = ln_LB,
                         upper = ln_UB,
                         studlab = ID,
                         data = my_dat,
                         sm = "IRLN",
                         method.tau = "DL",
                         comb.fixed = FALSE,
                         comb.random = TRUE, backtransf = TRUE,
                         title = "title",
                         text.random = "Overall")

summary(my_metagen)
weights(my_metagen)

study_ids <- my_metagen$studlab
weights_random <- my_metagen$w.random
weight_table <- data.frame(Temporary_ID = study_ids, w.random = weights_random)
print(weight_table)





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