I am doing a meta-analysis where I have the baseline and 2 months post-intervention measurement of a continuous variable (say a) for two groups (control and intervention). I also have measurements for another continuous variable (say b) at post-intervention. The idea is if (a) increases after the intervention, (b) should also be higher in the intervention group. Note that all measurements are in average (since this is a meta-analysis and each average belongs to one study). Is there any idea how could I test the association that an increment in (a) after the intervention will also increase (b)? Thank you so much in advance.
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If you have the necessary information to do a meta-analysis on your b variable then you could presumably do a meta-regression to see if the increase in a is a moderator variable. You will need estimates of variability in order to be able to do any of these analyses and that may be an issue depending on what the primary studies have published.
If what you are proposing can be expressed as $y = b_i - b_c$ where $i$ is intervention and $c$ control then you have some choices. You could as you suggest in the comments fit
$$ y = \beta ((a_{i1} - a_{i0}) - ((a_{c1} - a_{c0})) $$
where the subscripts 0 and 1 refer to the two time points and I am ignoring error terms for simplicity.
Or
$$ y = \beta (a_{i1} - a_{c1}) + \gamma (a_{i0} - a_{c0}) $$
which would be more flexible as the first one subtracts the baseline values whereas the second allows for them to have their own coefficient.
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$\begingroup$ Thank you so much for your response. So this is what I was thinking to set up the meta-regression: b (response)= constant + beta_1*(difference in "a" between baseline and 2 months) + beta_2*group (group is a dummy variable, 0= control, 1=intervention) + beta_3* (difference in "a" * group) + error. As long as the interaction term is significant, I could tell the intervention has significant contribution (in whatever direction given the sign of the coefficient). Please let me know if I got it right. Thank you so much once again! $\endgroup$ Commented Nov 28, 2016 at 20:55
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$\begingroup$ Can you edit that into your question so it is easier for subsequent readers? $\endgroup$– mdeweyCommented Nov 28, 2016 at 21:29
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$\begingroup$ I think what you suggest should work but you are proposing, I think, to to do this per arm rather than per study in which case you need to take into account that the pairs of arms belong each to one study. $\endgroup$– mdeweyCommented Nov 28, 2016 at 21:31
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$\begingroup$ I think this might work, define y= b_int - b_cont, x= ((a_post.int) - (a_baseline))_int - ((a_post.int) - (a_baseline))_cont. So y is basically difference and x is difference in differences. Then run a meta regression like y=a+beta*x +e. What is your thought about it? $\endgroup$ Commented Nov 29, 2016 at 16:20
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$\begingroup$ Thank you so much for your suggestion. Surely, with mathematical notation, it looks way simpler to understand. I really appreciate your input, now I have a direction to work with. $\endgroup$ Commented Nov 30, 2016 at 15:54