# Interpreting a mixed-effects meta-analysis using the metafor package in R

This relates to an earlier question. Mixed effects meta-analysis using metafor package in R

It is very easy to perform a mixed-effects meta-analysis e.g. using metafor rma(yi,sei,data = df,method ="REML",mods = ~ mod1+mod2+mod3. However, certain aspects of its implementation and interpretation are not clear (to me at least). I would be extremely grateful if someone could shed light on the following.

In summary, I am not sure whether a mixed-effects meta-analysis is useful as a standalone analysis (i.e. as an alternative to random- or fixed-effects) to calculate a pooled effect size. Equally, is the pooled effect size adjusted for the specified confounders (i.e. mods1, 2 and 3 above). Alternatively, is a mixed-effects meta-analysis useful only to investigate heterogeneity following a traditional (e.g. random-effects) meta-analysis (this is how it seems to be used most)?

Here is a hypothetical example: imagine meta-analysing studies investigating the effect of soda on blood pressure (BP). The effect sizes are unadjusted mean differences (MDs) in BP, but the participants were not matched for age, and so in each study there are differences in the ages of drinkers and non-drinkers of soda, which may account for some of the differences in BP. Thus, one could argue that there is almost no point performing a random- or fixed-effect meta-analysis of the unadjusted MDs because it would be impossible to untangle the effect of soda on BP when the ages vary (i.e. given that age is such an important determinant of blood pressure.

Therefore, is a mixed-effects meta-analysis with mean differences in age (i.e. between drinkers and non-drinker) as a "moderator" an acceptable method to calculate an age adjusted pooled MD in BP between soda drinkers and non-drinkers? Is this a superior alternative to a traditional random- or fixed-effects meta-analysis of the unadjusted MDs?

Is the output of that mixed-effects meta-analysis interpreted in the same way as random- or fixed-effects meta-analyses but with adjustment for the moderator incorporated in the pooled effect size? For example, based on the output, can you say: "With adjustment for age, the mean difference in BP between drinkers and non-drinkers is 2 (95% CI 1-3)"?

• Don't have the time for a longer answer, but the answer is pretty much yes, probably, yes (the intercept of the model is the estimated/predicted average MD when the MD of age is 0). But be careful with your syntax: rma(yi, sei, ...) will interpret the sei variable as if these are variances. You should use: rma(yi, sei=sei, ...) assuming that the standard error variable is actually named sei. – Wolfgang Jul 5 '16 at 16:15