I working with observational data and defining assumptions for DAG seems to be more complex than often in examples provided in textbooks. For me, it would be much easier to just skip DAG part and condition for everything, and probably there will be no problem in publishing. However, I like the idea of being explicit with my causal assumptions under methods.
I'll give a simplified example with only two predictors, and thus it would be easier to follow.
- a crude analysis shows very clear multifold regional disparities in income between people from different towns
- variables or nodes like sex and age differ between towns (p < 0.05), indicating a need for adjusted analysis
- I have done different uni- and multi-level models with all kind of combinations of predictors and the result of regional disparities always holds.
Blue arrows seem to be okay for me; however, relationships between towns and sex/age are quite hard to define. I'll bring few, maybe stupid, examples
- town may be the cause of different sex distribution by offering more jobs for one sex (e.g. men and mining towns)
- sex may be a reason to change residence (e.g. local policies discriminate women and they move to another town)
- town may be polluted and shorten our expected living years (age)
- age may be a reason to change residence (e.g. moving to another town to go to university)
As you see, causal assumptions can be unidirectional (red, green) or bidirectional (orange), or is it even more reasonable to show them as undirectional (no arrows) (black)?
- As age and sex differed between towns, there will be a question about adjusted analysis. The goal is to use adjusted analysis to confirm the results of crude data analysis (to make them more bulletproof) - regional disparities between towns.
What would be the best way to achieve my goal?
For me, it seems that publishing the most conservative result would be reasonable since the result won't change with any adjusting.
What would be the most conservative adjusting?
- adjusting for everything, age and sex, and even if they may partially act as mediators (unknown direction or bidirectional arrows)?
- should I show a causal graph with undirected arrows (how should I name it then)?
- should I show a causal graph with bidirectional arrows (still named DAG?)
- am I right that undirected and bidirected arrows both make sex and age confounders due to opening a back-door path?
How would you solve and present this situation in your article?