# Methods of Meta Analysis

I have question on the methods of performing meta analysis. I have data that consists of multiple Randomized Control Trials (RCT) with different dose levels and observational studies with different dose level as well. The responses are brain pressure measured as continuous random variable. So my understanding is that I have to perform meta analysis on the studies that share same level of treatment (same dose) and I can include both RCT and observational studies in that treatment level analysis. Is there any thing I can do as a whole study? What kind of answer should I provide to my client?

• Did you forget a few words in the question? In the original version it is a bit hard to read (I am wondering whether network meta-analysis could be something you want to look into, but am not sure from the current question). – Björn Dec 29 '16 at 8:09
• You seem to want to use meta-regression but until you fill in the missing words it is a bit hard to say. – mdewey Dec 29 '16 at 9:46
• Missing words after "RCT with different ?" and "The responses are ?". We want you to fill is the missing word(s) in each sentences. – Michael R. Chernick Dec 29 '16 at 12:58
• @Björn. I don't know what happened but some words went missing and I rewrote the question. How can I unhold this question? – Moses Kim Jan 1 '17 at 9:25
• @mdewey. I have rewritten the question, please let me know if you have any suggestions. Thank you – Moses Kim Jan 1 '17 at 9:26

I think you have three options here.

You could select one dose and then use all the studies which use that dose, trials and observational. If you do that you would probably want to include a moderator variable for study type with two levels (trials versus observational). This analysis might be appropriate if there is wide clinical agreement on the standard dose. If the two study types differ substantially you might want to fall back on a stratified analysis and presentation.

However if the studies are all comparing several doses then it seems unlikely that there is a clinical consensus about the best dose and so you need to do either a multi-level meta-analysis with meta-regression or a network meta-analysis. In the multi-level analysis you would have a random effect for study and fixed effects for dose and study type. The network meta-analysis would proceed similarly. If you use R then there are some useful references and examples on Wolfgang Viechtbauer's pages about his metafor package here. there are also packages for network meta-analysis, see the CRAN Task View on meta-analysis (disclaimer, I maintain it). If you use Stata I think you will find that Ian White's mvmeta command can be tweaked to do these analyses but I do not use Stata myself.

So it seems that you have two separate problems and each needs separate solutions

1. The first is how to combine observational and RCT data
2. the second is how to use information on multiple dosages to infer effectiveness of one particular dosage

Lets see the first: There are multiple ways to combine observational and RCT data most of which can be found at this paper: http://onlinelibrary.wiley.com/doi/10.1002/sim.7223/abstract

the authors provide also code to do each approach and their relative merits. Keep in mind that if you choose to use Priors you would need a Bayesian approach.

with regards to the second problem: Combining multiple dosages is not straight forward. If you have a big network and the interventions can be categorized in classes, e.g. based on the molecular pathway of function, then you can apply a three-level Hierarchical model, with a Random Effect within each class. In your case a class may be a particular drug of different dosages and the assumption would the exchangeability across different dosages of the same drug. see this paper for example http://www.sciencedirect.com/science/article/pii/S1098301514047317.

Another approach would be to do some model-based work where you assign either a dose-responnse non-linear Emax model, but a simpler linear may work too. For example see this paper http://onlinelibrary.wiley.com/doi/10.1002/psp4.12091/full

Finally , you could even try to some random walk, where the effect of each dosage is more likely to be similar to the effects of adjacent dosages