Can age ever be confounded if it is the independent variable in an observational study? This is a follow-up to my previous question: "Basic understanding of control variables in observational studies"
I have understood the answer, but am still trying to figure out what I think of the Wikipedia example that I'd cited.
Basically, the example is the effect of age on happiness, and discusses whether you should ever control for health. The example says no, because:

To identify the control variables needed here, one could ask what
other variables determine not only someone's life satisfaction but
also their age. Many other variables determine life satisfaction. But
no other variable determines how old someone is (as long as they
remain alive). (All people keep getting older, at the same rate, no
matter what their other characteristics.) So, no control variables are
needed here.

What I understand by this explanation is that age can never (or close to never) be confounded if it is the independent variable in the study.
I have three questions about this explanation:

*

*Is it not mixing up the individual with the population? E.g., let's say wealth completely determines happiness and has a strong effect on longevity. You have a population of 100 people, 60 are age sixty and 40 age seventy. Happiness is measured as 1 = happy and 0 = not. At sixty, half the people are wealthy. At seventy, 3/4s are. Average happiness at sixty = 0.5 (30x1/60) and at seventy = 0.75. Happiness correlates positively with age, but controlling for wealth eliminates this. In this case, shouldn't one control for wealth?


*Is their a clear theoretical reason to, or not to, control for health in the Wiki example? To my understanding, if Age = X, Happiness = Y, and Health = Z, you have a number of valid relationships: X → Y, X → Z → Y, Z → X, and U → Z. This seems to give contradictory reasons to, or not to, control.


*Does it depend on what question you want to ask? In my original question, FP0 said:

Maybe they consider that since age changes by itself without external
influence, then they want to consider that the additional effects of
the variables I imagined above should be "included" in the global
effect of age, since age has a causal impact on them. In my opinion it
depends on whether you want to aggregate the different effects of age
since age is causal on those factors, or if you want to identify them
individually, and estimate the remaining effects of age separately.

If the answers to 1 and 3 are 'yes,' I have issues with the Wiki example.
 A: Observational studies adjust for age all the time! I would not be surprised if age was the most common adjustment variable in observational studies.
If age is the exposure (as in both examples of @SextusEmpiricus), the variable of interest, then you must include it in the model (how else are you going to estimate its effect?) and it - by definition - cannot be a confounding variable and be "adjusted for". Adjusting for just means that you include the variable in some model or condition on it in some other way (e.g. stratified analysis).
You would adjust for age if it isn't the variable of interest and lies on a backdoor path between your exposure and outcome in the DAG. An extremely simple example is shown below:

Here, we're interested in the causal effect of physical activity (PA) on cardiovascular disease (CVD). If age is both causally related to physical activity and cardiovascular disease, there is a backdoor path from PA <- Age -> CVD. By adjusting for age (conditioning on it), you block the path. So in this example, you must adjust for age to get the unbiased causal effect of PA on CVD.
A: First image below: With variables 'health' and 'wealth' you describe a situation with mediators. Age has a causal effect on health and wealth, and these in their turn have an effect on happiness.
Second image below: Controlling would relate to a (confounding) variable that has a causal effect on both the exposure variable (age in the example) and the outcome variable (happiness). Since there are few parameters that cause age, there is not much to control for.

I agree that the example is not so strong and in the example this is also nuanced by the sentence:

(as long as they remain alive)

There might be a confounding survivorship bias if one would argue that age causes happiness because we observe older people are more happy. The bias is that one assumes that there is no causal relationship from happiness to age which might be false.
