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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3. Adjustment by Regression Model<strong>in</strong>g<br />
Regression <strong>of</strong> Y on Z and X: We can identify the regression<br />
E(Y |Z, X),<br />
as this depends on the observed data<br />
• E.g., for cont<strong>in</strong>uous outcome, E(Y |Z, X) = α0 + αZZ + X T αX<br />
• In general, E(Y |Z = 1, X) is the regression among treated ,<br />
E(Y |Z = 0, X) among control<br />
Usefulness: Averag<strong>in</strong>g over all possible values <strong>of</strong> X (both treatments)<br />
E{ E(Y |Z = 1, X) } = E{ E(Y1|Z = 1, X) } = E{ E(Y1|X) } = E(Y1)<br />
and similarly E{ E(Y |Z = 0, X) } = E(Y0)<br />
<strong>Double</strong> <strong>Robustness</strong>, EPID 369, Spr<strong>in</strong>g 2007 15
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