I am having troubles making sense of a REML-based meta-regression with an interaction between a factor and numeric variable, fitted with rma.
In my study, I have included RCTs from 19 meta-analyses to investigate the association between %women in the RCTs and the effect sizes (i.e. logOR).
The slope for %women, without interaction, is not significant (see below, M_REML0, p=0.6858), and I am now investigating the interaction between %women (CF1_Women..IMP) and the ID for the meta-analysis (i.e. if the slope for %women varies in the different meta-analyses).
1) The interaction seem significant when testing for moderators, but the between-trial variation, tau^2, does not decrease as expected. Why is that?
(When I try method="ML" instead of REML, then tau^2 does decrease as expected; see anova(M0,M1) below)
M_REML0 (without interaction), tau^2 = 0.2076
M_REML1 (with an interaction), tau^2 = 0.2127, Test of Moderators (interaction terms) p-val = 0.0044
(see full outputs below)
2) I am in doubt how to get the estimate for the slopes ? e.g. for meta-analysis with ID 8.
estimate se zval pval ci.lb ci.ub
intrcpt -0.3567 1.0739 -0.3322 0.7398 -2.4616 1.7481
CF1_Women..IMP 0.0114 0.0139 0.8244 0.4097 -0.0157 0.0386
(...)
CF1_Women..IMP:id8 -0.0718 0.0214 -3.3572 0.0008 -0.1137 -0.0299 ***
(see full output below)
I would think it would be calculated as CF1_Women..IMP + CF1_Women..IMP:id8, i.e. 0.0114 +(-0.0718) = -0.0604 (with corresponding 95%CI of -0.1294 to 0.0087). Is that correct?
Or is the slope for ID 8 simply the estimate reported for CF1_Women..IMP:id8, i.e. (-0.0718, 95%CI -0.1137 to -0.0299)?
I am asking because when I do a meta-regression with only RCTs for ID 8, I get -0.0940 (95%CI -0.1864 to -0.0016; output not shown), which is more similar to the CF1_Women..IMP:id8 estimate.
Also, when I calculate the slopes for all the meta-analysis IDs, none of them are significantly different from 0, despite the interaction term is significant. I guess that is possible, but it makes me doubt the way I calculated the slopes.
Thanks a lot in advance! Your help is very appreciated!
Best,
Sabrina
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