Meta-regression analysis - metareg command problem

[Guest]

Dear Statalisters,

I have a question regarding the "metareg" command (see e.g. Stata Journal article by Harbord/Higgins (2008): http://www.stata-journal.com/article...rticle=sbe23_1).

Consider the following (simplified) scenario:

The primary regression (of the underlying primary studies) is y = am + bn + e, where

• a and b are coefficients with standard error a_stderr and b_stderr
• m and n are explanatory variables (continuous)
• e is random error.

I am interested in the common effect size of m on y by performing a meta-regression.

The data suggest that random effects meta-regression is to be used, i.e. besides calculating the usual sampling error across all primary studies an additional primary study specific random error is also calculated. The "metareg" command seems to fulfill this condition.

If the meta-analysis dataset consists of one observation per study (e.g. having 30 studies and 30 observations) then "metareg m <explanatory variables>, wsse(a_stderror)" works.

However, if the meta-analysis dataset consists of let's say 2 observation per study (e.g. having 30 studies but 60 observations) then "metareg m <explanatory variables>, wsse(a_stderror)" seems to consider each observation as a single study, i.e. calculating 60 instead of 30 additional primary study specific random error terms. In this case the results of the metareg command are probably false.

Do you have an idea/suggestion how to solve this problem? Is there a possibility to tell the "metareg" command to treat observations in the meta-analysis dataset as one study if they belong to the same primary study?

Thanks in advance for your help.

[Guest]

Does anyone have an idea?

[Carlo Lazzaro]

Guest:
in -rnethelp "http://www.stata-journal.com/software/sj8-4/sbe23_1/metareg.hlp"- is reported that

metareg performs random-effects meta-regression using aggregate-level data.

I could be wrong, but -metareg- description seems to imply one observation for each study.

Kind regards,
Carlo

[Sven Trelle]

Hi Guest,
your assumption is correct, metareg assumes independence between observations. The question is why are there multiple observations per study? Do these relate to subgroups (if yes, I do not see any problem because that seems to be reason why you want to perform the meta-regression)?
Alternatively, if it is all binary data you might be able to tackle the problem with the usual multi-level mixed effects regression commands.
Sven

[David Fisher]

Hi -- a bit late to this discussion I know, but to follow on from Sven's comment re subgroups:
As others have pointed out, -metareg- assumes one observation per study. If indeed Guest's multiple-observations-per-study relate to study subgroups, then one solution would be to perform a two-stage analysis, where the first stage is to obtain a single observation per study. Using Guest's terminology, -metareg- assumes that m is the effect size in study i, with standard error m_stderr (it is 'm' that would have the known standard error -- 'a' is a coefficient to be estimated from the data), and that n is the (mean) value of the explanatory variable within study i. Therefore, if m and n are observed within multiple subgroups j of the same study i, then m(ij) and m_stderr(ij) may be combined to form m(i) and m_stderr(i) using -metan-, and the n(ij) may be combined to form study-level means n(i) simply by weighting on sample size. (This obviously assumes fixed effects within studies, which is surely reasonable.) You can then meta-regress these single-observations-per-study using -metareg- as originally desired.
Thanks,
David.

ETA:
Alternatively, again depending on the context of the analysis (which isn't made clear in the OP), and if the subgroups are defined in the same way in each study, you could estimate the effect difference (or "interaction") within each study, and use -metan- to pool these effect differences/interactions across studies (either with fixed or random effects). This avoids use of -metareg- altogether, but may be answering a different question.