I talked myself into giving a talk in a group seminar about meta-analyses in September, but that was shifted to November, so that everyone could attend. So, here it is.
I have a couple of thoughts about how meta-analyses in ecology are different to medicine, where they are mainly used. I think this should colour how we approach them. There were also a couple of points brought up during the discussion that are worth raising.
Most medical meta-analyses have quite a tight focus: a treatment for some ailment (e.g. a drug) is being investigated in several studies. In contrast, ecological meta-analyses tend to ask questions about effects across species and regions, e.g. questions like the effects of plant litter on vegetation. This, I think, changes the emphasis, and suggests that the classical meta-analysis approach needs to be adapted. In particular, I don’t see much use for fixed effect analyses. These assume that there is a single “true” value for whatever statistic is being examined: a treatment has one effect, across all study populations. But if we’re looking at effects across species, I’m sceptical that this would hold. Thus, it is better to use a random effects model (which assumes that each studies has a different effect, and then summarises the distribution). Using a random effects model changes the interpretation, though. We can’t say that what is estimated is the overall effect (e.g. “doubling plant litter reduces germination by 30%”). Instead, we can say something like “plant litter generally has a negative effect on vegetation, although the magnitude of the litter effect varies”. Indeed, it might be that the effect can go in both directions: one can imagine a situation where the variation between studies is large, so that although the average effect is zero, there is almost always an effect, but it can go in all sorts of directions.
A related thought is that meta-regression should probably be more important in ecology and evolution. These go beyond summarising the (average) effect to modelling what it depends on (e.g. whether there is a difference between glasshouse and field studies). I’ve been partly responsible for one of the more excessive meta-regressions, where we ended up modelling the standard errors too and it’s an approach that is asking to be exploited. Of course (as we discussed during my talk), we need enough studies to be able to do this.
Another big issue we got onto during the discussion session was the problems of making sure the information given in papers was enough to be able to do the meta-analysis. This means estimates need to be given (whether significant or not), as well as their standard errors: not having the standard errors leads to terrors like Bayesian analyses. It’s difficult to see how to enforce this: it would need journals to crack down. But our discussion shifted onto a slightly different topic of reproducible research: providing the data and tools to repeat analyses. There are initiatives to encourage researchers to provide their data (e.g. through Dryad), some journals now insist on this being done and the DfG (the main German funding agency) will soon insist on this too. But it would be useful to also have the precise statistical fiddlings available, e.g. the R code. This would obviously mean that missing statistics could be calculated (and the data also mined in all sorts of other ways).
Hm, as I’m mentioning R, one thing I forgot to include in my talk was that there are several R packages for doing meta-analyses: MADAM, meta, metafor and rmeta, as well as a package, copas, for adjusting for publication bias. There are also a couple of packages for meta-regression: metaLik and metatest, plus several more specialised packages. Of these I’ve only looked at meta and rmeta, so I can’t compare them all. Anyone care to chime in?