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

Marc Heerdink m.w.heerdink at uva.nl
Sun Jul 7 23:51:27 CEST 2013

```Dear Michael and other readers,

On 07/06/2013 02:56 PM, Michael Dewey wrote:
[..]
>> Because everything was randomized, I can only calculate the total
>> number of times a certain response was used under each type of trial.
>> There is no pairing of trials under two treatments, so I am forced to
>> use the marginal totals from your table.
>
> But presumably you could calculate some statistic suitable for
> summarising the relevant features here? Difference in proportions, odds
> ratio, ...

Using the totals, it is indeed easy to calculate the difference in
proportions or odds ratio based on these totals. However, I am not sure
how I should calculate a study-level statistic suitable for
meta-analysis on the basis of these participant-level proportion
differences.

So, for instance, I have the following table;

pp	proportion_difference
1	0.1
2	0.05
3	0.08
4	0.02
..
N	..

Can I just calculate the mean and standard deviation of these proportion
differences -- mean(proportion_difference) and sd(proportion_difference)
-- and use these for meta-analysis? If yes, what escalc measure should I
use?

[..]
>> One alternative that I have tried over the last few days, is to use
>> the b parameter of interest and it's corresponding standard error from
>> the lme4 regression output that I use to analyse the individual
>> experiments. Then, I use rma(yi, sei) to do a meta-analysis on these
>> parameters. I am not sure this is correct though, since it takes into
>> account between-subjects variance (through a random effect for
>> subject), and it is sensitive to the covariates/moderators I include
>> in the models that I get the b parameters from.
>
> So you end up with 5 values of b? The fact that they adjust for
> different moderators does not seem an issue to me, indeed it could be
> argued to be an advantage of the meta-analytic approach here.

OK, thank you for your comment on this one. I think the results of a
meta-analysis using these 5 b values are indeed more or less sensible,
which is encouraging. I think I will go this way if it turns out I
cannot find a simpler approach, as a simpler approach would be easier to
sell to potential reviewers.

[..
> I think we are all assuming you have different participants in each
> experiment but I thought I would raise that as a question.

You are right in assuming this, I have different participants in all 5
experiments.

Thanks all for the help so far, your suggestions are highly appreciated!

Regards,
Marc

```