[R-meta] Duplicating the results of the metabin() function

[Samuel Leonard]

Hi Meta Analysts,

I'm having trouble duplicating by hand the results produced by the
metabin() function.  In particular the Q statistic.

Here's a toy example:

## get metabin() for a simple example

library(meta)
test.dat <- data.frame(exposed.events = c(3, 4, 5), exposed.n = c(10, 11,
12),
                       unexposed.events = c(14, 7, 2), unexposed.n = c(20,
11, 7))
result <- metabin(event.e = exposed.events, n.e = exposed.n, event.c =
unexposed.events, n.c = unexposed.n, data = test.dat, method.tau = "PM", sm
= 'OR')

## calculate Q by hand

OR <- result$TE
weights.fixed <- result$w.fixed

Q <- sum(weights.fixed * (OR - result$TE.fixed)**2)

## they don't seem to match

> Q
[1] 3.963568
> result$Q
[1] 3.049176

This is confusing to me because according to the literature I've read the
I^2 statistic is calculated directly from Cochran's Q.  And performing a
simple calculation on Q to obtain I^2 matches the result of the package:

## calculate I^2 by hand from the result's Q

> (result$Q - 2)/result$Q
[1] 0.3440851
> result$I2
[1] 0.3440851


I'd appreciate any insight into why my Q calculation is different than the
packages.  Or any literature about what other statistic Q can refer to in
this case other than Cochran's Q.

Thank you!
Sam Leonard

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