How to run Bayesian A/B testing when your users have a cardinal feature that impacts the treatment set Suppose you want to run a Bayesian A/B testing to establish whether a certain action influenced conversion rate of your users. What would be the best ways to incorporate the notion that each user has a cardinal feature (e.g. age, average money spent) that impacts the conversion rate when the action is applied (e.g. users in the treatment set that spent more money are more likely to not convert)?
Another example would be the following: you want to check the effect of a drug on curing a condition (cured/not cured) so you give sample a placebo and another the real drug. You also suspect that the age has an impact in curing the condition once the drug is given (e.g. the older you are, the more the the drug has effect in curing the condition).
Is A/B testing the right way to approach this problem or can you suggest any other solutions?
Do you have any suggestion on sources with walk through concrete examples one can utilize to learn more on how to conduct this kind of non-plain scenario with Bayesian techniques?
 A: [To address your question change: I've interpreted your question as using A/B testing in the more modern context of real-time testing that attempts to not only explore but also to exploit what it's learning. Bandits do this. But if you mean that you're going to collect data without acting on it, and then at the end do a batch analysis, Glen_b's answer is better.]
It sounds like you're talking about using a Beta-Binomial multi-arm bandit approach to A/B testing where you have a context ("cardinal feature"). The simplest way to do that -- assuming there aren't a lot of cardinal features -- would be to have a bandit per cardinal feature class.
You might also look into Contextual Bandits, which are more sophisticated (and complicated).
[To address your comment: I think the standard basic solution is to have M N-arm bandits for N choices, where M is the number of different classes (cardinal feature categories) you have. That's the simplest solution, though it would be impractical if you have many cardinal feature classes. (That is, M is high, which complicates things computationally and also means some bandits may have very few examples.)]
If you have more than two choices (A/B/C/...) you can use a Dirichlet-Multinomial multi-arm bandit.
A: Your description could be clearer but it sounds like you're looking to adjust for the fact that the distribution of some relevant covariates (like age) may differ across the two groups (A/B), where you want to compare proportions. If I understand the situation correctly you'd typically use something like logistic regression to deal with that.
Many posts on site discuss logistic regression*, a few discuss the Bayesian version. You might start with a site search, for example. 
*(as does Wikipedia and numerous other places on the internet, as well as a great many books)
