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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4. Adjustment by Inverse Weight<strong>in</strong>g<br />
Propensity score: Probability <strong>of</strong> treatment given covariates<br />
e(X) = P (Z = 1|X) = E{I(Z = 1)|X} = E(Z|X)<br />
• X � Z|e(X)<br />
• Under no unmeasured confounders, (Y0, Y1) � Z|e(X)<br />
• Customary to estimate by postulat<strong>in</strong>g and fitt<strong>in</strong>g a logistic<br />
regression model, e.g.<br />
P (Z = 1|X) = e(X, β) = exp(β0 + X T β1)<br />
1 + exp(β0 + X T β1)<br />
e(X, β) =⇒ e(X, � β)<br />
<strong>Double</strong> <strong>Robustness</strong>, EPID 369, Spr<strong>in</strong>g 2007 20
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