FIGURE 7.9. General setup for instrumental variables.


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

General setup for instrumental variables (Fig. 7.9)

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


The Cholera Diagram (Fig 7.8)

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.  

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