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Re: st: gllamm for meta-analysis w/ multiple outcomes within studies

From   Roger Harbord <>
Subject   Re: st: gllamm for meta-analysis w/ multiple outcomes within studies
Date   Wed, 28 Mar 2007 08:45:20 +0100

I can't claim to be a gllamm expert so I can't answer your queries on
-gllamm- syntax. The approach you're suggesting is generally referred to
as 'multivariate meta-analysis'. I suggest you have a look at some of
the literature on this topic, e.g. Lidia Arends' thesis
<>, or Richard Riley's work such as

Some questions that you may need to think about include:
How do you know the effect sizes are not correlated between studies? Do
you have the full data for all the studies or are you using published
summary data? If the latter, how are you going to get information on the
within-study correlation, and how are you going to deal with outcome
reporting bias, i.e. the tendency to report only outcomes that are
'statistically significant'?

Joseph Coveney posted some code to do bivariate meta-analysis using
-glamm- to Statalist two or three years ago, so you could search the
archive for that.

Georg Matt wrote:
Dear Stata gllamm experts,

I would very much appreciate comments and insights on using gllamm
(or xtmixed) for a meta-analysis with multiple outcomes within each
study.  This appears to be a situation that cannot be handled with
the existing meta-analysis routines in Stata (e.g., metareg), because
these routines assume that there is only one effect size per study.

Say, there are 100 independent studies, each with between 1 and 10
effect sizes.  Each effect size has a (conditional) variance
associated with it, the inverse of which typically serves as a weight
in, for instance, WLS analyses. The effect sizes are correlated
within studies but not between studies.    There are covariates to
account for within and between study differences in effect size.

I would like to use gllamm (or xtmixed) to approach this as a two-
level analysis problem with multiple correlated effect sizes (level
1) nested within studies (level 2).

(A) Assume that all level 1 slopes are fixed and only the intercept
is random.
How can this be done in gllamm or xtmixed?  Would something like the
following work?

1. v is the conditional variance of each effect size d; lns is the
log standard deviation.
gen lns = ln(v)/2

2. define the eq to transfer the log standard deviations to gllamm
eq het: lns

3. gllamm syntax: x1 - x3 a re covariates with fixed slopes
gllamm d x1 x2 x3, i(id) s(het) constraint( ????)   adapt nip(10)

What is/are the proper constraint(s) here?

(B) Assuming that there is also a random slope at level one (variable
z), would the following work?

1. as before
2. as before
2.1 define eqs for intercept and slope
eq st_c: cons
eq st_z: z

3.1 gllamm syntax
gllamm d x1 x2 x3 z, i(id) nrf(2) eqs(st_c st_z) s(het) constraint
( ????) adapt nip(10)

What is/are the proper constraint(s) here?

I hope these questions make sense.  If not, please let me know, and I
would be happy to clarify.

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