Re: st: providing raw weights for multivariate meta-analysis

[Nick Darson <nick.darson@googlemail.com>]

Scott and Paul, thanks a lot for your comments.

Mvmeta is a very interesting program - however, my issue is that I
want to account for several dependencies (not only several outcome
measures or effect sizes that stem from the same observation).
Typically, to model the multivariate outcomes, the first level
consists of the outcome measures and
the second level of the cases. For my project, I need to add one or
two more levels due to further dependencies (to be precise, my
observations are partly based on the same control condition  and I
also have several observations from the same studies). This would make
up a three-four level model.

HLM is very convenient for such a multilevel meta-analysis approach-
but it allows to model three levels only (HLM7, which was released
recently, has a four level module, but it is not possible to provide
precision weights to the first level of the four level module yet).

Therefore, I was wondering whether I could use the same technique in
Stata (to have a four level meta-regression model). Two points are
relevant:
1.) Providing raw weights (non-normalized) to the first level.
This appears to be feasible when using GLLAMM and for xtmixed in Stata
12 (to my understanding, pweights should work - it provides the
inverse of a variable such that smaller values count more: e.g. 0.1
becomes a weight of 10, 0.5 a weight of 2. This would correspond to
the objective in a meta-analysis when I provide the sampling variance
as weights: studies with a smaller variance/ SE count more).
2.) Constraining the lowest level variance to 1.
This seems to be the critical problem. Xtmixed allows to specify the
residuals of the lowest level to a certain degree (independent,
exchangeable, etc)- but it does not allow specifying exact values,
such as a variance of 1 ("independent" still assumes one equal
variance parameter, please correct me if I am wrong on this).
Gllamm seems to be more flexible as it can use the option
"constraint". However, this appears to be very complex and
inconvenient for the model I would need (maybe for someone else not,
but I must admit I reach the limits of my modeling skills here  - I
just started using Stata 4 months ago).
For example, this seems to be the Gllamm code for a bivariate model:
http://www.stata.com/statalist/archive/2009-08/msg01415.html .

Would have been great to implement more flexibility in the variance
structure of level 1 of xtmixed (maybe in a future version?).




On Tue, Jul 12, 2011 at 2:40 AM, Seed, Paul <paul.seed@kcl.ac.uk> wrote:
> Nick Darson might benefit from looking at the user-defined commands that Stata
> has for meta-analysis - in particular -metan-, -metareg- and -mvmeta-.
> The last is designed to address his exact problem directly.
> findit meta will give a more comprehensive list.
>
> Going back to his original question, there are 3 standard systems of weights
> in Stata, none of which appear to be what he wants:
> [fweight=f] is appropriate for frequency data - clearly not what he has.
> [aweight=n] assume that the values given are means (or averages), from samples of size n;
> all drawn from populations with the same SD. This is not what he has
> [pweight=w] are for weighted samples, and include a Huber-White robust SE correction;
> so that only the relative sizes of the weights are important.
>
> gllamm and xtmixed are both highly flexible commands (gllamm more so, but also
> substantially slower to run).
>
> BW
>
>
> Paul T Seed, Senior Lecturer in Medical Statistics,
> Division of Women's Health, King's College London and King's Health Partners
> 020 7188 3642.
>
>
>
>
> On Sun, Jul 10, 2011 at 2:54 PM, Nick Darson <nick.darson@googlemail.com> wrote:
>> Thanks a lot for the info and the links.
>>
>> I have not looked much into gllamm yet, but the description of Stata
>> 12 xtmixed looks very promising for the weighting issue (I guess not
>> being able to provide specific weights for each level was the problem
>> to which Hox 2010 referred).
>>
>> With regard to the "non-normalized" weighting issue, I found in the
>> mean-time the following link, which I wanted to share:
>>
>> http://www.cpc.unc.edu/projects/nutrans/research/usda/help/home
>>
>> The site states that "pweight does not automatically normalize the
>> sample weight like aweight does.  Stata's survey commands do not allow
>> aweight.
>>
>> Note:  A normalized sample weight sums to the number of observations
>> in the data set and its mean is 1. "
>>
>> Hence, it looks to me as if I can simply use "pweights", providing the
>> effect size variances to the first level as weights (and pweights
>> provides the inverse weight of this variable, non-normalized). Then,
>> restraining the first level variance to 1 and the multivariate model
>> should work (I hope).
>>
>> I might try estimating such a model in Stata 12 and compare the
>> results with those of HLM using the V-known function (eventually, I
>> want to use Stata as I would like to add another level - HLM only
>> allows three levels when using the V-known function).
>
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