Tools to evaluate causality from different scientific domains

(i). The path analytic ‘tracing rule’ and ‘causal calculus’

*** The ‘tracing rule’ is a visual inspection rule that allows one to ‘turn correlation into causation’ by decomposing a correlation into its causal and non-causal components. It has been updated recently to handle visually Judea Pearl’s ‘causal calculus’[i]: deriving observational/associational consequences from hypothesized/known causal structures.

*** Path analysis was the first formal method promising to separate out the causal and non-causal components from the ‘surface’ association/correlation BMI↔A1c: The answer is simply: (1). Direct causal effect BMI-> A1c; (2). Direct causal effect A1c-> BMI; (3). Causal effects on both from a common cause 3rd-> A1c & 3rd-> BMI; (4). Other combinations of these where other variables are involved, like causes of these 3 variables.

If BMI -> SysBP -> A1c (with no direct BMI -> A1c causal effect), we would expect to see in observational data the correlation between BMI & A1c to be about the product of the correlation between BMI & SysBP and the correlation between SysBP & A1c; if however the causal real-world looks instead like BMI -> A1c -> SysBP, different observational consequences ensue.[ii]

* Elias Barenboim developed a revolutionary tool that coded the entire ’causal calculus’ math and can derive step by step the implications of any causal model: CausalFusion.net (requires free registration).

[CONTENT to be added: tracing rule for specific statistical models/analyses]

(ii). Other fields: POs and econom~ics/etrics

[CONTENT to be added]

*** The last part, # 4, will briefly go over some remaining challenges and opportunities for both advancing this field, and for better explaining it, like the ‘equivalence of potential outcomes (‘Rubin’, more properly Cochran’s…) and causal calculus (Pearl) approaches to causality’.

Footnotes:

[i] “BoW, p. & “It happened not because I am smarter but because I took Sewall Wright’s idea seriously and milked it to its logical conclusions as much as I could.” SEMNET

[ii] Note that the ‘no direct effect, the entire effect is indirect, through a mediator’ situation is not far-fetched: the famous one is the ‘blessing of the cars à auto accidents’ intervention [CITE???], which worked only through the ‘drivers using more often seat belts’ mediator: the direct effect is not logically possible.

Also of note: rarely we have only three variables on hand to investigate, the causal models are often larger than this, and the consequences are more intricate, but an online app does this reasoning for us: see an example from Family Practice  at http://dagitty.net/m4TETpl (model derived from some data analyses though).