# [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:

treatment
1   	2
response
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
package.

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.

1:
http://r.789695.n4.nabble.com/meta-analysis-with-repeated-measure-designs-td2252644.html

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

Regards,
Marc

```