Augmented IPW estimator of the ATE

Handbook eq. (23.4) p.512: $$\frac{1}{n}\sum_i \left\{ \frac{W_i(Y_i-m_{1i})}{p_{1i}} + m_{1i} - \frac{(1-W_i)(Y_i-m_{0i})}{p_{0i}} - m_{0i} \right\}$$ Consistent if either the outcome model or the propensity model is correct. With m1 = m0 = 0 it collapses to the Horvitz-Thompson IPW difference, which is a useful check on a call.

Usage

Eaiprl(y, D, X = NULL, ml_outcome = NULL, ml_propensity = NULL)

Arguments

y

Outcomes.

D

Treatment indicator, 0/1.

X

Accepted for signature compatibility.

ml_outcome

List or pair (m1, m0) of fitted outcome predictions.

ml_propensity

Fitted \(P(D=1|X)\), strictly in (0, 1).

Value

Named list with estimate, se, ci_lower, ci_upper, influence, ipw, plugin, n, method.

References

Robins, Rotnitzky & Zhao (1994) JASA 89:846-866.

Examples

Eaiprl(c(1, 0, 1, 0), c(1, 0, 1, 0),
       ml_outcome = list(rep(0, 4), rep(0, 4)),
       ml_propensity = rep(0.5, 4))
#> $estimate
#> [1] 1
#> 
#> $se
#> [1] 0.5
#> 
#> $ci_lower
#> [1] 0.02001801
#> 
#> $ci_upper
#> [1] 1.979982
#> 
#> $influence
#> [1] 2 0 2 0
#> 
#> $ipw
#> [1] 1
#> 
#> $plugin
#> [1] 0
#> 
#> $n
#> [1] 4
#> 
#> $method
#> [1] "augmented IPW ATE (Robins, Rotnitzky & Zhao 1994)"
#>