AIPW and double robustness

Combine outcome predictions with a propensity-weighted correction, then make either model—or both models—too simple.

What does double robustness guarantee?

With valid causal assumptions and sufficient overlap, AIPW can approach the true effect as samples grow if either the outcome model or the treatment propensity model consistently learns the correct relationship. This is double robustness.

Try it in the experiment

  1. Start with both models capturing the curved relationships.
  2. Make one model too simple, then restore it and change the other.
  3. Make both too simple and redraw several samples.

Double robustness does not fix an invalid adjustment set, unmeasured confounding, or absent overlap. It need not give the closest estimate in this sample.

Precise guarantee and limits

Under causal identification assumptions and regularity conditions, AIPW is consistent if either model is correctly specified and consistently estimated. Positivity requires that people at each relevant combination of adjustment variables can receive either treatment. See Bang & Robins (2005).

If both models are misspecified, there is no general guarantee, although particular errors can cancel. Double robustness also does not guarantee lower mean squared error than other estimators. See Kang & Schafer (2007).