[R] Meta-analysis on a repeated measures design with multiple trials per subject using metafor

Marc Heerdink m.w.heerdink at uva.nl
Wed Jul 3 14:15:18 CEST 2013

Hi all,

I am currently attempting to compile a summary of a series of five 
psychological experiments, and I am trying to do this using the metafor 
package. However, I am quite unsure which of the scenarios described in 
the metafor help pages applies to these data, because it is a repeated 
measures design, with multiple trials in each condition.

Assume that for every participant, I have a basic contingency table such 
as this one:

		1   	2
1		10 	20
2		20	10

(if this ASCII version does not work, I have 30 trials in each 
treatment, and participants give either response 1 or 2; the exact 
numbers don't matter)

The problem that I am trying to solve is how to convert these numbers to 
an effect size estimate that I can use with metafor.

As far as I understand it, I can only use it to get an effect size for 
outcomes that are dichotomous; i.e., either 1 or 0 for any subject. 
However, I have proportion data for every participant.

I have considered and tried these strategies:

1. Base the effect size on within-participant proportion differences. 
That is, in the table above, the treatment effect would be 
(20/30)-(10/30) = 1/3; and I would take the M and SD of these values to 
estimate a study-level effect ("MN" measure in metafor).

2. Use the overall treatment * response contingency table, ignoring the 
fact that these counts come from different participants ("PHI" or "OR" 
measures in metafor). In a study with 10 participants, I would get cell 
counts around 150.

However, from the research I've done into this topic, I know that 1) is 
not applicable to (as far as I understand) an odds ratio, and I suspect 
2) overestimates the effect.

A third method would be to use the regression coefficients, that I can 
easily obtain since I have all the raw data that I need. However, it is 
unclear to me whether and if yes, how I can use these in the metafor 

 From my understanding of another message about this topic I found on 
this list (1), I understand that having access to the raw data is an 
advantage, but I am not sure whether the scenario mentioned applies to 
my situation.


I would very much appreciate any suggestions or hints on this topic.


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