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L4-04 · Backdoor adjustment

Standardize outcome risks across a valid adjustment set to calculate an intervention effect.

Level 4 icon Level 4 · Undergraduate
Objective. Standardize outcome risks across a valid adjustment set to calculate an intervention effect.
Before this lesson. L4-02, L4-03, L3-07
Hands-on lab. Confounding and intervention

Learn

The backdoor criterion gives a sufficient graphical condition for adjustment. A valid set contains no descendants of treatment and blocks every path that enters treatment through an incoming arrow. It removes noncausal paths while leaving the directed treatment-to-outcome paths needed for the total effect.

Calculate each outcome risk within a treatment and adjustment stratum. Then average those risks using the population distribution of the adjustment variables. Use the same population weights for every treatment value. Treatment-specific weights can preserve the selection difference that caused the original bias.

The formula also needs suitable data support. Positivity requires observations at each treatment value in the strata used for the target population. Consistency connects the recorded treatment with the intervention definition. Correct measurement and a sufficient causal model remain essential even when the arithmetic is exact.

Practice

Solution

The adjusted risk under one is (0.25+0.65)/2 = 0.45. Under zero it is (0.15+0.35)/2 = 0.25. The adjusted risk difference is 0.20.

Check your understanding

Which weights appear in the ordinary backdoor formula?

Show the answer

B. The population distribution P(Z)

Both intervention risks are standardized to the same target distribution P(Z). Treatment-specific weights can retain differences caused by confounding.

Sources

This lesson draws on Pearl, 2009Hernan & Robins, 2020.

Next: L4-05 · Frontdoor identification

References
  1. Pearl, J. (2009). Causal inference in statistics: An overview. Statistics Surveys, 3(none), 96–146. 10.1214/09-ss057
  2. Hernan, M., & Robins, J. (2020). Causal Inference: What If. https://miguelhernan.org/whatifbook
  3. Bareinboim, E. (2025). Causal Artificial Intelligence: A Roadmap for Building Causally Intelligent Systems. https://causalai-book.net/