Double Robustness in Estimation of Causal Treatment Effects
Double Robustness in Estimation of Causal Treatment Effects
Double Robustness in Estimation of Causal Treatment Effects
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2. Counterfactual Model<br />
What is be<strong>in</strong>g estimated? If we estimate ∆ by Y (1) − Y (0)<br />
• Y (1) estimates E(Y |Z = 1) = population mean outcome among<br />
those observed to receive treatment<br />
• E(Y |Z = 1) = E{Y1Z + Y0(1 − Z)|Z = 1} = E(Y1|Z = 1). . .<br />
• . . . which is not equal to E(Y1) = mean outcome if entire<br />
population received treatment<br />
• Similarly, Y (0) estimates E(Y |Z = 0) = E(Y0|Z = 0) �= E(Y0)<br />
• Thus , what is be<strong>in</strong>g estimated <strong>in</strong> general is<br />
E(Y |Z = 1) − E(Y |Z = 0) �= ∆ = E(Y1) − E(Y0)<br />
<strong>Double</strong> <strong>Robustness</strong>, EPID 369, Spr<strong>in</strong>g 2007 11