Re: st: Meta analysis in single group,

[David Hoaglin <dchoaglin@gmail.com>]

Tiago,

That is the usual situation: the estimated variances are used as if
they were the true variances.

The sizes of the studies may not be the major issue.  I would be
interested in seeing empirical evidence that having approximately
equal sample sizes in the studies leads to small bias in the summary
estimate.

The behavior of the inverse-variance-weighted mean will generally
depend on the effect measure.  It's a good idea to pay attention to a
warning (applicable to fixed-effect analyses) given by Yates and
Cochran in 1938 and repeated by Cochran in 1954 that, if the estimates
(here of the effect) and the estimates of their variances are
correlated, the summary estimate may be biased.  Bias can definitely
be a problem when the effect measure is the risk difference, and the
risk ratio and the odds ratio are likely to have similar difficulties.
 To be safe, one should avoid using inverse-variance weights with
those effect measures.

David

On Thu, Jan 5, 2012 at 11:36 AM, Tiago V. Pereira
<tiago.pereira@mbe.bio.br> wrote:
> David,
>
> If I am not wrong, within-study variances are usually assumed to be known,
> but are estimated from the data. So, once the combined studies are of
> approximately equal size, bias in the summary estimate is likely to be
> small, if any.
>
> The only problem I see for the `pre-pos' case is regarding the correlation
> estimate between time points (i.e. the correlation between pre and pos) if
> one does not have the raw data. Assumption of zero correlation will
> provide a conservative Wald test (Z test) if the true correlation is >0,
> but an anti-conservative Z test otherwise. Again, if the studies to be
> combined are  approximately of equal size, bias in point estimates will be
> small.
>
> Tiago

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