I'm interested in evaluting the evidence in the literature I've collected for spatial/anatomical variation in an MRI measure. The data consists of mean values, standard deviations and sample sizes, with widely varying numbers of data points for different regions.
They're not RCTs, but as per these answers:
https://stats.stackexchange.com/questions/156754/method-of-meta-analysis-of-studies-to-determine-mean-blood-level
https://stats.stackexchange.com/questions/109223/how-to-perform-a-meta-analysis-of-studies-without-a-control-group?noredirect=1&lq=1
and this package:
https://rdrr.io/cran/meta/man/metamean.html
I've understood I can use the mean as an outcome measure, and can use the other data to calculate the sampling variances. My issue is I'm not sure of the best way to approach the widely different numbers/quality of studies for different regions. For example, I have estimates for overall grey matter or white matter from up to 30 studies, but for other regions I might have as few as one.
Broadly, I'm interested in two questions, that seem to me to imply different approaches:
1) To what extent does the existing literature support the idea that there IS regional variability? This would evaluate the evidence against the null hypothesis that there is no regional variability. I'd also like to evaluate the contribution of potential demographic and MRI-related confounders/ covariates, and if they prove to be significant, normalise the data with respect to them or otherwise account for them. This seems to imply a kind of regression across studies, but I'm not sure how best to account for the different contributions of different studies across regions.
2) What is the 'best' estimate (the most supported) of the value of my MRI measure in the literature. The object is partly to indicate the level of evidence for the 'best' estimate, in the hopes of encouraging better study of it in larger populations. I also want to compare the 'best extimate' to the values computed from a toy model informed by histology of what the value 'should' be. This seems to point to separate meta-analyses of each region, becuase the the level of evidence for each region is likely to be different.
I'm hoping for pointers as to the best method and approach to take. I'd thought to use R for the analysis, but if anyone has advice about other (preferably free) software that is suited to the task that would be useful too.
Many thanks