In the diagram below, the arrow from the HDL gene (IV) to the Lifestyle is not a likely scenario.  It is unlikely because for people to alter their Lifestyle, one has to know whether high-HDL or low-HDL gene was assigned at birth.  Since GWAS was not available until 2008, in addition to such information has not been readily available for individuals, it is unlikely that the arrow from the HDL gene to the Lifestyle exists, which is why the HDL is a good IV.  

(Note) The following diagram was taken from the Book of Why.  The rectangle highlight, the text, "instrumental variable," the arrow from the HDL genet to the Lifestyle (all in blue), and the "X" (in red) were added for a better explanation. 


Fig. 7.12 Causal Diagram for MR Example

Mendelian Randomization (MR) is an instrumental variable method that aims to figure out an exposure (X) that causes a specific outcome (Y) by introducing a genetic factor as an instrumental variable (IV).  Some of the advantages of MR are:
- Observational studies are generally conducted to understand "association" as supposed to determine causality.  
- Using genotypes as an IV would minimize potential effects from confounding because the genotypes are given at birth and much more likely to be permanent, which allows the IV to be random.  
-  RCT is not always feasible or practical because of potential ethical and cost implications.  MR can provide information on causality in many situations where randomized controlled trials are not possible.  

University of Michigan - Ann Arbor

In a causal diagram, an instrumental variable is a variable that satisfies the following properties:

- The instrumental variable has a causal effect on the treatment variable.  
- The instrumental variable is not associated with unmeasured confounder(s).
- The instrumental variable affects the outcome only via the treatment variable; i.e., there is no direct effect of the instrumental variable on the outcome variable.
- Assumptions: linearity or monotonicity

Instrumental Variable

Pearl, J., & Mackenzie, D. (2018). $\mathit{The \ Book \ of \ Why: \ The \ New \ Science \ of \ Cause \ and \ Effect.}$ Basic Books.

The Book of Why

FIGURE 7.9. General setup for instrumental variables.


General setup for instrumental variables (Fig. 7.9)

FIGURE 7.8. Diagram for cholera after the introduction of an instrumental variable. 


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