Dear all,
I received some valuable replies and I am now able to present a
solution to my problem. A special thank goes to Georgia Salanti. She
kindly explained to me that "in Bayesian framework however ,
where talking about SE does not make sense, the `weight´ (the idea
that small studies contribute less than big studies) is conveyed in a
distributional way".
I also re-discoverd an article by Sharon-Lise T. Normand [1], which
clearly demonstrates what to do (p 344-345).
Below is my adaption (for OpenBUGS) of her BUGS-code[2]:
# Bayesian random effects model
# d=risk difference, var.d=variance
model{
for(i in 1:K){
sinv[i] <- 1/(var.d[i]);
d[i] ~ dnorm(theta[i],sinv[i]);
theta[i] ~ dnorm(mu,sigma)
}
mu ~ dnorm(0.0,0.000001);
sigma ~ dgamma(0.001,0.001);
tau <- 1/sigma;
}
# data
list(d = c(0.028, 0, 0.02, 0.018, 0.035, 0.044),var.d = c(0.002,
0.004, 0.001, 0.001, 0.001, 0.001),K=6)
# inits
list(mu=0,sigma=1,theta=c(0,0,0,0,0,0))
Kind regards,
Bernd Weiss
[1] Normand, Sharon-Lise T., 1999: Tutorial in Biostatistics. Meta-
Analysis: Formulating, Evaluating, Combining, and Reporting,
Statistics in Medicine 18: 321--359.
[2] Maybe, someone is interested in comparing the Bayesian findings
to a conventional random effects model. Here's some R code...
library(meta)
n.t <- c(39,44,107,103,110,154)
n.c <- c(43,44,110,100,106,146)
e.t <- c(2,4,6,7,7,11)
e.c <- c(1,4,4,5,3,4)
p.t <- e.t/(n.t)
p.c <- e.c/n.c
# risk difference
rd <- p.t-p.c
sd.rd <- sqrt((p.t*(1-p.t)/n.t)+(p.c*(1-p.c)/n.c))
var.rd <- sd.rd^2
metabin(e.t,n.t,e.c,n.c,sm="RD",method="Inverse")
# odds ratio
or <- (p.t/(1-p.t))/(p.c/(1-p.c))
log.or <- log(or)
sd.log.or <- sqrt(1/e.t+1/(n.t-e.t)+1/e.c+1/(1-n.c))
var.log.or <- sd.log.or^2
metabin(e.t,n.t,e.c,n.c,sm="OR",method="Inverse")
-------------------------------------------------------------------
This list is for discussion of modelling issues and the BUGS software.
For help with crashes and error messages, first mail [log in to unmask]
To mail the BUGS list, mail to [log in to unmask]
Before mailing, please check the archive at www.jiscmail.ac.uk/lists/bugs.html
Please do not mail attachments to the list.
To leave the BUGS list, send LEAVE BUGS to [log in to unmask]
If this fails, mail [log in to unmask], NOT the whole list
|