# Re: st: re. study weight in meta analysis

 From Roger Harbord To statalist@hsphsun2.harvard.edu, roger.webb@man.ac.uk Subject Re: st: re. study weight in meta analysis Date Sun, 14 Mar 2004 11:13:00 -0000

I agree it looks a bit strange but i'm pretty sure it's OK...

The apparent oddity arises because the point estimates of the risk ratio vary a lot between your studies and you're using the "Mantel-Haenszel" method (the default for -metan-) which does a weighted average of risk ratios, not log risk ratios. Ratio measures behave more intuitively on a log scale.

Consider a meta-analysis of two studies, one with RR=0.5 and one with RR=2. If both RRs were averaged with the same weight, the result would be (2 + 0.5) / 2 = 1.25. However we might expect the pooled RR to be 1, not 1.25. To get an average of 1 the study with RR=2 must be given less weight than the study with RR=0.5.

So in general to compensate for not using a log scale, studies with large risk-ratios receive less weight than you might expect from their size and number of events. In this situation the weights cannot be interpreted as the amount of information contributed by each study.

The weight is calculated as :

(no. of events in control gp) x (total in intervention gp)
----------------------------------------------------------
total in both groups combined

The weights are more intuitive when averaging log risk ratios, which other pooling methods do. However in cohort studies with small numbers of events you're right to be using Mantel-Haenszel methods as they have better properties in such situations. Your example has revealed that there's a danger of over-interpreting the weights when using Mantel-Haenszel methods.

Roger.
----------------------------------------------------
Roger Harbord mailto:roger.harbord@bristol.ac.uk
Department of Social Medicine, University of Bristol

--On 12 March 2004 11:40 +0000 roger webb <roger.webb@man.ac.uk> wrote:

```Dear Statalist

I?m conducting a meta-analysis for population-based studies of a
rare mortality outcome (stillbirths) using the ?metan? procedure.

My question concerns the derivation and interpretation of the study
weights in the final column of this Stata output:

. metan ideath inodeath cdeath cnodeath, rr
label(namevar=studyno)

Study |       RR  [95% Conf. Interval]  % Weight
--------------+-----------------------------------------
1             |      3.5   1.04399   11.7339   6.34589
2             |        4     .4517   35.4217   2.37971
3             |  1.62944   1.02163   2.59886   51.6439
4             |  2.50294   1.25479   4.99266   15.2031
5             |  3.95477   1.15619   13.5274   4.80286
6             |  .810097   .282934   2.31947   19.6245
--------------------------------------------------------
MH pooled RR  |  1.88825   1.36146   2.61886
--------------------------------------------------------
Heterogeneity chi-squared =   6.35 (d.f. = 5) p=0.273
Test of RR=1 : z= 3.81 p = 0.000

The raw data for studies 4 and 6 are as follows:

Study 4:
(RR=2.50; study weight: 15.2%)
Exposed cohort: deaths (n=8); survivors (n=927)
Unexposed cohort: deaths (n=5,319); survivors (n=1,550,656)

Study 6:
(RR=0.81; study weight: 19.6%)
Exposed cohort: deaths (n=4); survivors (n=614)
Unexposed cohort: deaths (n=25); survivors (n=3,104)

The sample sizes and numbers of events are smaller in Study 6
than in Study 4 and yet Study 6 has the larger study weighting.
Could anyone kindly provide an explanation for this? Thanks.

Regards
Roger Webb
University of Manchester, UK
```
```
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