Double Robustness in Estimation of Causal Treatment Effects

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2. Counterfactual Model Exception: Randomized study • Treatment is assigned with no regard to how a subject might respond to either treatment or control • Formally , treatment received is independent of potential outcome: • This means that (Y0, Y1) � Z E(Y |Z = 1) = E{ Y1Z+Y0(1−Z) |Z = 1} = E(Y1|Z = 1) = E(Y1) and similarly E(Y |Z = 0) = E(Y0) • Y (1) − Y (0) is an unbiased estimator for ∆ Double Robustness, EPID 369, Spring 2007 12
2. Counterfactual Model In contrast: Observational study • Exposure to treatment is not controlled, so exposure may be related to the way a subject might potentially respond: (Y0, Y1) �� Z • And, indeed, E(Y |Z = 1) �= E(Y1) and E(Y |Z = 0) �= E(Y0), and Y (1) − Y (0) is not an unbiased estimator for ∆ Double Robustness, EPID 369, Spring 2007 13
Page 1 and 2: Double Robustness in Estimation of
Page 3 and 4: 1. Introduction Simplest situation:
Page 5 and 6: Define: 2. Counterfactual Model Z =
Page 7 and 8: 2. Counterfactual Model Problem: Do
Page 9 and 10: 2. Counterfactual Model Conditional
Page 11: 2. Counterfactual Model What is bei
Page 15 and 16: 3. Adjustment by Regression Modelin
Page 21 and 22: 4. Adjustment by Inverse Weighting
Page 23 and 24: 4. Adjustment by Inverse Weighting
Page 25 and 26: 5. Doubly Robust Estimator Modified
Page 27 and 28: 5. Doubly Robust Estimator �µ1,D
Page 29 and 30: 5. Doubly Robust Estimator Scenario
Page 31 and 32: 5. Doubly Robust Estimator Result:
Page 33 and 34: E 5. Doubly Robust Estimator �
Page 35 and 36: Summary: If OR 5. Doubly Robust Est
Page 37 and 38: 6. Some Interesting Issues Issue 1:

Double Robustness in Estimation of Causal Treatment Effects

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