How to compare treatments in multitreatment setting of observational treatment study I am researching uplift models to measure effect of treatment. Particularly when there are multiple treatments and I want to compare/order treatments based on their causal effect on average/individual. In literature (e.g. here study) authors often compare each treatment to control group and estimate effect, then order based on this effect. In case of observational data one must correct heterogeneous treatment groups with e.g. propensity score matching - where  individuals from control group are matched to treated individuals based on similarity to ensure homogeneous subjects in each group. 
Now to my question. As is the case with observational data, the subjects in each group may be heterogeneous. For example, younger people are assigned more frequently to treatment A, while older people to treatment B, control group is randomly assigned. 
Now if I do matching between treatment A and control, I will sample mostly young people from control. Same with old people with treatment B and control. Now let say I am interested in effect on marketing ad A and ad B and no ad - control. Generally (assumption for this example) younger people are more likely to respond to online ad, while older are less likely. If no ad is shown the effect of age is negligible. If either add is shown, younger people will respond more. Thus effect of ad A will be much higher than effect of ad B, since most of young people are assigned to ad A. This is not causal effect of the treatment as it is biased by the age of the groups. It only compares treatment to control. It cannot be used to compare treatment A to treatment B. 
Am I overlooking something? What is the correct way to compare treatment A to treatment B?
Thank you
 A: So what I hear you saying is that, while you're really interested in the effect of the treatment $T$ on the outcome $O,$ there is another variable age, $A,$ that you think is likely confounding the results. You're absolutely right. Here is a causal diagram, as per Judea Pearl's ideas:

There is a backdoor path from $T$ to $O:$ $T\leftarrow A\to O.$ Therefore, you must condition on $A$ to obtain the correct causal effect of $T$ on $O.$ You can use the backdoor adjustment formula:
$$P(O=o|\operatorname{do}(T=t))=\sum_aP(O=o|T=t,A=a)\,P(A=a).$$
Here the first expression is saying, "What is the probability that I would get outcome $o$ if I set $T=t?$ That's what that '$\operatorname{do}$' operator expresses.
In words, you need to adjust, or condition, on the age to get the correct causal effect of the treatment.
For more details, I would strongly encourage you to take a look at The Book of Why, by Pearl and Mackenzie, Causal Inference in Statistics: A Primer, by Pearl, Glymour, and Jewell, and lastly, Causality: Models, Reasoning, and Inference, by Pearl. 
