I am working on a meta-analysis, and a colleague has suggested following the approach outlined by Piepho et al 2012 in their paper here: https://www.jstor.org/stable/41806045. I would like some advice on how to implement this approach in R.
In a nutshell, Piepho et al suggest not to model the difference between treatments as you would in a standard meta-analysis (they call this the 'baseline contrasts' approach). Instead, they suggest to model the mean of each treatment, using treatment and trial as predictors, and to compare treatments means after modelling (a 'two-way' or 'conditional' model).
As an example, say we have four treatments, A, B C, and D, with A as the control. We have 50 papers reporting treatment means for different trials. All papers have a mean estimate for A, and at least one of B, C, and/or D. Each treatment mean has a standard error associated with it. The treatment mean is a continuous numeric variable, and it makes sense to use the log value of the treatment mean.
What I would do is:
- Run a mixed model in lme4:
mod <- log(treatment.mean) ~ treatment + (1|paper) - Extract the ratio of modelled overall treatment mean estimates using contrasts in emmeans:
ems <- emmeans(mod, trt.vs.ctrl1 ~ treatment, ref="A")$contrasts(this also tests for pairwise differences between the control and other treatments).
Questions:
- Is the above approach generally correct to follow Piepho et al 2012?
- How do I include the standard errors for the treatment means from each paper in this model? As weights? (If so then in what form?)
- I think Piepho et al (2012) also actually suggest including 'paper' as a fixed effect, not a random effect. Is that correct? If I do that, emmeans can't estimate the overall means.
- Is is possible to implement Piepho et al's approach in metafor? (I can't find info on this but may be using the wrong search terms).