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st: Mantel-Haenszel weights and metan

From   Mike Bradburn <>
Subject   st: Mantel-Haenszel weights and metan
Date   Tue, 16 Mar 2004 17:03:40 +0000

As a co-author of the -metan- program, I'd just like to confirm Roger Harbord's explanation about Mantel-Haenszel (MH) weights. They are unintuitive, they don't quite reflect the study's "weight" (in the normal way of thinking about weights), but despite this I would use the MH method anyway.

To illustrate the quirk further, think about this ficticious example with two studies
study 1:
group 1 10/100 events
group 2 20/100 events => RR=0.5
study 2:
group 1 20/100 events
group 2 10/100 events => RR=2
Below is what -metan- would do to these data :

Study | RR [95% Conf. Interval] % Weight
1 | 0.500 0.247 1.014 66.67
2 | 2.000 0.987 4.054 33.33
M-H pooled RR | 1.000 0.624 1.602 100.00
Heterogeneity chi-squared = 7.39 (d.f. = 1) p = 0.007
I-squared (variation in RR attributable to heterogeneity) = 86.5%

Test of RR=1 : z= 0.00 p = 1.000

The MH method gives the second study less weight than the first, for the reasons that Roger stated: to get the correct relative risk of 1, the first RR needs twice as much weight as the second to contribute equally. The MH weights should therefore be treated with caution, which is deeply unfortunate since a major reason for presenting a forest graph is to emphasize how much each study contributes.

Inverse-variance weightings are far more intuitive. Both of the above studies would get identical weights, and "weight" here does mean the same as "contribution". But the estimated variances are based on large sample theory, and consequently the weights (and therefore the pooled estimate) are inaccurate for rare events (based on as yet unpublished simulation work which we really should get finished). Looking at Roger's data, I suspect he is better off avoiding the inverse-variance method and sticking instead to the MH weights, despite the above issue over interpretation.

As a final note, if the study effect sizes are relatively homogeneous then the discrepancy between "contribution" and "MH weight" should be fairly small. If on the other hand the studies vary, the bigger question is perhaps "should I be pooling these studies using a fixed effect model at all?". But these arguments seem irrelevant here, as imprecision of individual studies seems to be the reason behind the variety in the estimated RRs.

And on an unrelated note, we are working on an updated version of -metan-, still for the moment in version 7 graphics but with a few new features. I'll post a note with more details to the list when it's ready later this week.


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