How to test several predictors' effect when you use means and standard deviations (or SE) from published papers? For explanatory purposes, I will give a fake example to understand my question (and goal). Let's suppose I get from different published papers data about the concentration of a substance (subst.concent) depending on age (age) and if they are smokers or non-smokers (smoking). Following this example, I find that for smokers, the concentration of that substance increase as age increase, while for non-smokers there is no effect. Here a graph of what I find with my actual data (but modified to the "smokers" example):

I would like to test the effect of both age and smoking in subst.concent. I would expect to find a significant interaction between age and smoking. I tried a linear regression using the mean of each "population", however, I don't think this is the most appropriate since it doesn't consider the SD and for instance, the model gives an R² of 1, when I guess all the variance is not explained by my two variables.
How could I test the age and smoking effect in my subst.concent and the magnitude of their effect using both the mean and the SD?
Thanks in advance!!!
 A: Yes, you can address this from a meta-analytic perspective. Let $y_{ij}$ be the observed concentration and $\mbox{SD}_{ij}$ and $n_{ij}$ the corresponding SD and sample size for the $i$th study and $j$th group within the study (so for a particular age and smoking status). Some studies may just report the results for a single group, which is fine. Then $v_{ij} = \mbox{SD}_{ij}^2 / n_{ij}$ is the estimated sampling variance of $y_{ij}$ if we assume that the concentration values are like means. Also, let $\mbox{age}_{ij}$ and $\mbox{smoke}_{ij}$ denote the age and smoking status (coded 0/1) for the groups.
Once you have estimates with corresponding sampling variances (and possibly some predictor variables), you can think of this as a meta-analysis. However, your data have a multilevel structure (since you have studies reporting concentration values for multiple groups), so you should use a multilevel meta-analytic model. Such a model is described by Konstantopoulos (2011). An example illustrating the analysis of such data is given here:
http://www.metafor-project.org/doku.php/analyses:konstantopoulos2011
In your case, think "study = district" and "group = school". Then you also want to add age and smoking status as predictors to the model (and maybe their interaction). You can also model non-linear associations for the age variable (e.g., using polynomials or splines).
References
Konstantopoulos, S. (2011). Fixed effects and variance components estimation in three-level meta-analysis. Research Synthesis Methods, 2(1), 61-76.
