18.1 Basics of causal inference

• Running example: Omega 3 supplements effect on blood pressure(\(y\)).

hypo_data <- tribble(
    ~Unit, ~Female, ~Age, ~y0, ~y1,
    "Audrey", 1, 40, 140, 135,
    "Anna",   1, 40, 140, 135,
    "Bob" ,   0, 50, 150, 140,
    "Bill",   0, 50, 150, 140,
    "Caitlin", 1, 60, 160, 155,
    "Cara",    1, 60, 160, 155,
    "Dave",    0, 70, 170, 160,
    "Doug",    0, 70, 170, 160,
    
)

• Causal effect: comparison between different potential outcomes (\(y^0\) if you didn’t get treatment, \(y^1\) if you did) of what what might have occurred under different scenarios.

• Fundamental problem: You cant observe these two outcomes! You only get one. (unlike in our hypothetical example)

• Close substitutes:

  • Pre-post (use pre-study variable). Issue: Things change.
  • Crossover trials - randomize the order of receipt of treatments. (Book does not go into details).